1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS DE LA NATURALEZA/CAMPO ELÉCTRICO Atracción entre dos cargas iguales Dos cargas iguales, que se encuentran a una distancia de #d metros, se repelen con una fuerza de #f N. Calcula el valor de las cargas en mC

]]> 1.0000000 0.3333333 0 0 #q <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>1000</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><mi>f</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>d</mi><mo>/</mo><mo>(</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#q</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.01))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> distribución de cargas (Terminar) En la distribución de cargas de la figura sabemos que A= #qa μC, B= #qb μC, C = #qc μC,. Si las distancia x = #dx m e y = #dy m. Calcula el módulo de la intensidad de campo, en N/C, que se ejercerá sobre el vértice que falta.

]]> 1.0000000 0.3333333 0 0 #et]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dy</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>dx</mi><mo>/</mo><mi>dy</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>dy</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><mo>(</mo><msup><mi>dy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>dx</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qc</mi><mo>/</mo><msup><mi>dx</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>etx</mi><mo>=</mo><mi>ea</mi><mo>+</mo><mo>(</mo><mi>eb</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ety</mi><mo>=</mo><mi>ec</mi><mo>+</mo><mo>(</mo><mi>eb</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>et</mi><mo>=</mo><msqrt><mrow><msup><mi>etx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ety</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos cargas Tenemos un sistema formado por dos cargas: una de #q1 mC situada en el punto ( #x1 , 0) y otra de #q2 mC situada en el punto ( #x2 , 0). Calcula el módulo de la  intensidad de campo, en N/C,  en el  punto ( #xp , #yp)  (Las distancias están en metros)

]]> 1.0000000 0.3333333 0 0 #et]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mo>(</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><msup><mi>yp</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mo>(</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x2</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><msup><mi>yp</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>yp</mi><mo>/</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>yp</mi><mo>/</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>)</mo><mo>+</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ex</mi><mo>=</mo><mi>e1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>+</mo><mi>e2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ey</mi><mo>=</mo><mi>e1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>+</mo><mi>e2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>et</mi><mo>=</mo><msqrt><mrow><msup><mi>ex</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ey</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Intensidad de campo. Dos cargas pos neg Tenemos dos cargas puntuales A y B cuyos valores son #qa mC y #qb mC situadas en los puntos (#xa,0) y (#xb,0) respectivamente. Calcula la intensidad de campo(E), en N/C, en el origen de corrodenadas, indicando si será positiva o negativa.

]]> 1.0000000 0.3333333 0 0 #e]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>xa</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><msup><mi>xb</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>eb</mi><mo>+</mo><mi>ea</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Intensidad de campo. Dos cargas puntuales sobre un eje Tenemos dos cargas puntuales A y B cuyos valores son #qa mC y #qb mC situadas en los puntos (#xa,0) y (#xb,0) respectivamente. Calcula la intensidad de campo(E), en N/C, en el origen de corrodenadas, indicando si será positiva o negativa.

]]> 1.0000000 0.3333333 0 0 #e]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>xa</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><msup><mi>xb</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>eb</mi><mo>+</mo><mi>ea</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Modelo de Bohr En el modelo de Rutherford del átomo de hidrógeno, el electrón gira describiendo órbitas circulares alrededor de un protón. Si la órbita de un electrón tiene un radio de #r pm, calcúlese la fuerza de atracción (N)protón-electrón y la velocidad (m/s) del electrón para que la órbita sea estable.

Datos: masa del electrón = 9.1·10-31 Kg; carga del electrón = 1.6·10-19 C

]]> 1.0000000 0.3333333 0 0 Fuerza = #fVelcocidad = #v]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re</mi><mo>=</mo><mi>r</mi><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qe</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><mi>qe</mi><mo>*</mo><mi>qe</mi><mo>/</mo><msup><mi>re</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><mi>f</mi><mo>*</mo><mi>re</mi><mo>/</mo><mi>me</mi></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>z</mi><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>f</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>c</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS DE LA NATURALEZA/GRAVITACIÓN Calcular la masa de un planeta Un determinado planeta tiene un radio de #r km. Calcula cuál será su masa, si un objeto de #mo Kg  pesa #p N en su superficie

]]> 1.0000000 0.3333333 0 0 #mp <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>150</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mp</mi><mo>=</mo><mi>p</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>mo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#mp</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.02))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos planetas Si el radio de la órbita de la Tierra alrededor del Sol es de 150 millones de kilómetros. Calcula el radio de la órbita (km) de un planeta que tarde #t años en girar alrededor del Sol

]]> 1.0000000 0.3333333 0 0 #r2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mn>150</mn><mo>.</mo><mn>0</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mroot><msup><mi>t</mi><mn>2</mn></msup><mn>3</mn></mroot></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Gravedad en un planeta Calcula la aceleración de la gravedad, en m/s2, en un planeta cuyo radio es #r Km y cuya masa es #m Kg.

]]> 1.0000000 0.3333333 0 0 #g]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>950</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>g1</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>m</mi><mo>/</mo><mo>(</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">g</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Satélite El radio de la Tierra es de 6370 Km y su masa es de 5.97·1024 Kg. Calcula la velocidad que deberá tener un satélite (m/s) para que su órbita ecuatorial sea estable a #h Km sobre el suelo

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>8000</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>14</mn></mrow></msup><mo>*</mo><mn>5</mn><mo>.</mo><mn>97</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>/</mo><mo>(</mo><mi>h</mi><mo>+</mo><mn>6370</mn><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un cuerpo a una cierta altura El radio de la Tierra es de 6370 Km y su masa es de 5.97·1024 Kg. Calcula el peso, en N, de una persona de #m kg si lo situamos a una altura de #h Km sobre la superficie terrestre

]]> 1.0000000 0.3333333 0 0 #p <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>800</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>17</mn></mrow></msup><mo>*</mo><mn>5</mn><mo>.</mo><mn>97</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>*</mo><mi>m</mi><mo>/</mo><mo>(</mo><mi>h</mi><mo>+</mo><mn>6370</mn><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#p</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL Calcular coeficiente de rozamiento Un bloque de #m gramos se desliza por una mesa horizontal con una velocidad de #v cm/s. Si se detiene en #d cm. ¿Cuál será el coeficiente de rozamiento?

]]> 1.0000000 0.3333333 0 0 #mu]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>250</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>a</mi><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>u</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcular el módulo de la aceleración La única fuerza que se ejerce sobre un cuerpo tiene dos componentes Fx= #fx N y Fy = #fy N. Calcule el módulo de su aceleración em m/s2 si su masa es #m Kg

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fy</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><mi>fx</mi><mo>*</mo><mi>fx</mi><mo>+</mo><mi>fy</mi><mo>*</mo><mi>fy</mi></mrow></msqrt><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg hacia arriba de forma que baje con una aceleración de #a m/s2 (copia) Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg hacia arriba de forma que baje con una aceleración de #a m/s2 

]]> 1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>-</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg hacia arriba de forma que suba con una aceleración de #a m/s2 Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg verticalmente hacia arriba de forma que suba con una aceleración de #a m/s2 

]]> 1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>m</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.01))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de fuerzas De un cuerpo de #m Kg tiran tres fuerzas A, B y C de #v1, #v2 y #v3  N respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

  1. El valor en N de la fuerza resultante.
  2. El ángulo positivo que forma  la fuerza resultante con la fuerza A
]]> 1.0000000 0.3333333 0 0 Fuerza = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>z</mi><mi>a</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>&#x000E1;</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Una locomotora tira de un tren Una locomotora de #ml Kg tira de un vagón de #mt1 Kg con una aceleración de #a m/s2 como máximo por una vía horizontal. ¿Cuál será la aceleración máxima si tira de un vagón de #mt2 Kg?

]]> 1.0000000 0.3333333 0 0 #af <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ml</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mt1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mt2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>18</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>af</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>ml</mi><mo>+</mo><mi>mt1</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ml</mi><mo>+</mo><mi>mt2</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#af</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/CUERPOS EN SUPERFICIES Cuerpo en superficie vertical Un cuerpo de #m g está apoyado sobre una superficie vertical. Si el coeficiente de rozamiento es #mu ¿Qué fuerza horizontal, en N, tendremos que ejercer, como mínimo, contra el objeto para que no resbale y caiga? 

]]> 1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>mu</mi><mo>*</mo><mn>1000</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.01))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fuerza en cuerpo apoyado (copia) Si ejercemos una fuerza de #fu N sobre el cuerpo A de masa #mas Kg con un ángulo #an º. Calcula:

  1. El valor de la aceleración, en m/s2 con la que se moverá horizontalmente en ausencia de rozamientos.
  2. El valor de la fuerza normal en N
]]> 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 1.0000000 0.3333333 0 0 aceleración = #acN = #fn]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mas</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>fu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>/</mo><mi>mas</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mo>(</mo><mi>fu</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>mas</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>a</mi><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">N</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>f</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y fuerza Por un plano inclinado #an º tiramos hacia arriba, con una fuerza paralela al mismo, de una caja de masa #m Kg. Si el coeficiente de rozamiento de la caja con el plano es de #k, calcula la fuerza mínima, en N, que tendremos que ejercer para que ésta siga:

  1. Subiendo con velocidad constante
  2. Bajando con velocidad constante  
]]> 1.0000000 0.3333333 0 0 1.- Subida = #fs2.- Bajada = #fb]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>peso</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>px</mi><mo>=</mo><mi>peso</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fr</mi><mo>=</mo><mi>peso</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fs</mi><mo>=</mo><mi>px</mi><mo>+</mo><mi>fr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fb</mi><mo>=</mo><mi>px</mi><mo>-</mo><mi>fr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo>&#xA0;</mo><mi>S</mi><mi>u</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>f</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo>&#xA0;</mo><mi>B</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>d</mi><mi>a</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>f</mi><mi mathvariant="normal">b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie horizontal empujamos una caja Sobre una superficie horizontal empujamos una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s2, si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>190</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>fe</mi><mo>/</mo><mi>m</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>mu</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.02</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie inclinada empujamos una caja baja(copia) (copia) Sobre una superficie inclinada #an º  queremos frenar la caida de una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s2, si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pt</mi><mo>-</mo><mi>fe</mi><mo>-</mo><mi>pr</mi><mo>)</mo><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie inclinada empujamos una caja (copia) Sobre una superficie inclinada #an º hacemos subir una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s2, si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>250</mn><mo>,</mo><mn>280</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>fe</mi><mo>-</mo><mi>pt</mi><mo>-</mo><mi>pr</mi><mo>)</mo><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/LEY DE HOOKE Calcula la longitud Calcula la longitud de un muelle, en cm, cuya constante elástica de de #k N/m y cuya longitud en reposo es de #lo cm, si tiramos de él con una fuerza de #f N 

]]> 1.0000000 0.3333333 0 0 #l <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1000</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>/</mo><mi>k</mi><mo>)</mo><mo>+</mo><mi>lo</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#l</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Constante elástica de un muelle Un determinado muelle mide #l1 cm si tiramos de él con una fuerza de #f1 N y #l2 cm si tiramos con una fuerza de #f2 N. Calcula su constante elástica, en N/m, y su longitud en reposo en cm

]]> 1.0000000 0.3333333 0 0 K =#kL0 =#lo]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>22</mn><mo>,</mo><mn>45</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>lo</mi><mo>+</mo><mi>l1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>lo</mi><mo>+</mo><mi>l2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l2</mi><mo>-</mo><mi>lo</mi><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>f1</mi><mo>-</mo><mi>f2</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>l2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mn>100</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>k</mi><mo>*</mo><mi>l1</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>-</mo><mi>f1</mi><mo>)</mo><mo>/</mo><mi>k</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>k</mi><mspace linebreak="newline"/><msub><mi>L</mi><mrow><mn>0</mn><mo>&#xA0;</mo></mrow></msub><mo>=</mo><mo>#</mo><mi>l</mi><mi>o</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Objeto colgando de un muelle Un muelle mide en reposo #lo cm y, si colgamos de él un objeto de #m g, mide #l1 cm. Calcula su constante elástica en N/m

]]> 1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>65</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>98</mn><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Objeto colgando de un muelle (copia) Un muelle mide en reposo #lo cm y, si colgamos de él un objeto de #m g, mide #l1 cm. Calcula su constante elástica en N/m

]]> 1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>65</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>98</mn><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un objeto con dos muelles Un objeto está en una superficie horizontal sujeto a dos paredes enfrentadas por dos muelles cuyos datos se indican el la tabla. Si las paredes distan #lp cm. Calcula la longitud del muelle A en cm

 

 
 AB
L0 (cm) #lo1 #lo2
K(N/m) #k1 #k2

 

 

 

]]> 1.0000000 0.3333333 0 0 #la <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>200</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>300</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>lo1</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>lo2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>lp</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>la</mi><mo>=</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>k2</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>k1</mi><mo>*</mo><mi>l1</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>k2</mi><mo>*</mo><mi>l2</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>k1</mi><mo>+</mo><mi>k2</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#la</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/SISTEMAS DE CUERPOS Plano con tres cuerpos En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º, calcula:

  1. La aceleración del sistema hacia la derecha, en m/s.
  2. La tensión de las cuerdas A-B y B-C en N.

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1.0000000 0.3333333 0 0 1.- Aceleración = #a2.- Tensión A-B =#t1        Tensión B-C = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>mc</mi><mo>-</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>+</mo><mi>mc</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>mc</mi><mo>*</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>-</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo>&#x000A0;</mo><mi>A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo>&#x000A0;</mo><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mi>A</mi><mo>-</mo><mi>B</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mi>B</mi><mo>-</mo><mi>C</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano con tres cuerpos rozamiento En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º y el coeficiente de rozamiento entre los cuerpos y la superficie es de #k, calcula:

  1. La aceleración del sistema hacia la derecha, en m/s2.
  2. La tensión de las cuerdas A-B y B-C en N.

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1.0000000 0.3333333 0 0 1.- Aceleración = #a2.- Tensión A-B =#t1        Tensión B-C = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pxa</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pc</mi><mo>=</mo><mi>mc</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pc</mi><mo>-</mo><mi>frb</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>pxa</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>+</mo><mi>mc</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>a</mi><mo>)</mo><mo>+</mo><mi>pxa</mi><mo>+</mo><mi>fra</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>pc</mi><mo>-</mo><mo>(</mo><mi>mc</mi><mo>*</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo>&#x000A0;</mo><mi mathvariant="normal">A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo>&#x000A0;</mo><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mi mathvariant="normal">A</mi><mo>-</mo><mi>B</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mo>&#x000A0;</mo><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mi>n</mi><mo>&#x000A0;</mo><mi>B</mi><mo>-</mo><mi mathvariant="normal">C</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano con tres cuerpos rozamiento mínimo En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º  calcula el coeficiente de rozamiento mínimo entre los cuerpos y la superficie para que el sistema no se mueva.

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1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mo>(</mo><mi>mc</mi><mo>-</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mb</mi><mo>+</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y recto En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la fuerza necesaria para que suba con velocidad constante

 

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1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>fra</mi><mo>+</mo><mi>pta</mi><mo>+</mo><mi>frb</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y recto (copia) En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la aceleración del sistema,(m/s2) y la tensión de la cuerda (N)

 

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1.0000000 0.3333333 0 0 aceleración =#aTensión =#t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pta</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>frb</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>a</mi><mo>)</mo><mo>+</mo><mi>frb</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#xF3;</mi><mi>n</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>&#xF3;</mi><mi>n</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Plano inclinado y vertical En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la aceleración del sistema,(m/s2) y la tensión de la cuerda (N)

 

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1.0000000 0.3333333 0 0 aceleración =#aTensión =#t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pb</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>pta</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>pb</mi><mo>-</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#243;</mi><mi>n</mi><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>&#243;</mi><mi>n</mi><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/MOMENTO LINEAL Bolas que chocan con ángulo Dos bolas A y B de masas #ma Kg y #mb Kg respectivamente chocan según indica la figura y se quedan unidas. Si α= #aa º y β = #ab º. Si la Bola A se mueve inicialmetne a #va m/s. Calcula, en m/s:

  1. La velocidad de B 
  2. La velocidad del conjunto después del choque 

 

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1.0000000 0.3333333 0 0 Velocidad de B = #vbVelocidad del conjunto = #vt]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>&nbsp;</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aar</mi><mo>=</mo><mi>aa</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>abr</mi><mo>=</mo><mi>ab</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mi>va</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>aar</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>abr</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vt</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>va</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>aar</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>vb</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>abr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo>&#x000A0;</mo><mi>d</mi><mi mathvariant="normal">e</mi><mo>&#x000A0;</mo><mi>B</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>v</mi><mi>b</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo>&#x000A0;</mo><mi>d</mi><mi mathvariant="normal">e</mi><mi>l</mi><mo>&#x000A0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">j</mi><mi>u</mi><mi>n</mi><mi>t</mi><mi>o</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>v</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Bomba que cae y explota Una bomba de masa #mi Kg cae durante #t1 segundos libremente. En ese momento explota dividiéndose en dos trozos. #t2 segundos después el trozo mayor ( #po % de la masa) se mueve con una velocidad #v1 m/s y un ángulo de #a1 º bajo la horizontal. Calcula la rapidez, en m/s, del otro trozo en ese instante

]]> 1.0000000 0.3333333 0 0 #v2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>po</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mi</mi><mo>*</mo><mi>po</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>mi</mi><mo>-</mo><mi>m1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>85</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1r</mi><mo>=</mo><mo>-</mo><mi>a1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>mi</mi><mo>*</mo><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mo>-</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a1r</mi><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>pt</mi><mo>+</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a1r</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Bomba que explota Una bomba de #mini Kg explota y se divide en dos trozos de #m1 y #m2 Kg. El primero se mueve hacia la derecha con una velocidad de #v1 m/s. Calcula la velocidad del otro trozo, si la bomba inicialmente:

  1. Estaba en reposo.
  2. Se movía hacia la derecha con una velocidad #vb m/s
]]> 1.0000000 0.3333333 0 0 Si está en reposo = #vf1Si se movía inicialmente = #vf2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mini</mi><mo>=</mo><mi>m1</mi><mo>+</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf1</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>vb</mi><mo>*</mo><mi>mini</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi mathvariant="normal">i</mi><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>&#x000E1;</mi><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi>n</mi><mo>&#x000A0;</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi>o</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>v</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><mi>S</mi><mi mathvariant="normal">i</mi><mo>&#x000A0;</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo>&#x000A0;</mo><mi mathvariant="normal">m</mi><mi>o</mi><mi>v</mi><mi>&#x000ED;</mi><mi>a</mi><mo>&#x000A0;</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi>lm</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>v</mi><mi>f</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Coche y camón al encuentro Por una carretera horizontal un camión, de masa #mca Kg va con una velocidad de #vca m/s. Un coche, de masa #mco Kg se dirige a su encuentro a una velocidad de #vco m/s. tras chocar se quedan unidos. Calcula la rapidez del conjunto.

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>600</mn><mo>,</mo><mn>900</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>6000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>mca</mi><mo>*</mo><mi>vca</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>mco</mi><mo>*</mo><mi>vco</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mca</mi><mo>+</mo><mi>mco</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Coche y camón uno detrás de otro Por una carretera horizontal un camión, de masa #mca Kg va con una velocidad de #vca m/s. Un coche, de masa #mco Kg tiene la misma dirección y sentido a una velocidad de #vco m/s. tras chocar se quedan unidos. Calcula la rapidez del conjunto.

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>600</mn><mo>,</mo><mn>900</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>6000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>mca</mi><mo>*</mo><mi>vca</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>mco</mi><mo>*</mo><mi>vco</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mca</mi><mo>+</mo><mi>mco</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos bolas Dos bolas A y B de igual masa se dirigen una al encuentro de la otra a la misma velocidad #v1 m/s formando un ángulo de 90º. Tras chocar, una de ellas se desvía #a º y sale con una velocidad #v2 m/s. Calcula la velocidad de la segunda

]]> 1.0000000 0.3333333 0 0 #vf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ar</mi><mo>=</mo><mi>a</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>v1</mi><mo>-</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ar</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>v1</mi><mo>-</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ar</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#vf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', &quot;</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>