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> </mo><mo>=</mo><mo>#</mo><mi>k</mi><mspace linebreak="newline"/><msub><mi>L</mi><mrow><mn>0</mn><mo> </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
| A | B |
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>