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, °, ', "</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, °, ', "</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> </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>