Advanced Frictionless Dynamics 1 A woman of mass #M kg is lowered to the ground from an upper story window with a rope in which the tension is kept constant at #B N.  Calculate the acceleration of the woman during the descent in meters per second squared.

Acceleration of Woman: {#1} m/s^2

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>800</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>B</mi><mo>-</mo><mo>(</mo><mi>M</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>)</mo><mo>)</mo><mo>/</mo><mi>M</mi></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Advanced Frictionless Dynamics 2 Two masses of #A kg and #B kg are connected by a light cord that passes over a light, frictionless pulley attached to a fixed support.  Calculate the downward acceleration of the #B kg mass in meters per second squared and the tension in the cord in Newtons.


Acceleration of System: {#1} m/s^2

Tension in Cord:  {#2} N

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2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</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>B</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>*</mo><mo>(</mo><mi>B</mi><mo>-</mo><mi>A</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mi>C</mi><mo>+</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Advanced Frictionless Dynamics 3 A mass of #A g is suspended from a light cord, and a #B g mass is suspended under it by another cord.  Calculate the tension in each cord when the two masses are lowered with an acceleration of #C m/s^2 downward.

Mass of A:  #A Grams

Mass of B:  #B Grams

Acceleration:  #C m/s^2 downward



Tension in Top Cord:: {#1} N

Tension in Bottom Cord:  {#2} N

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2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>500</mn><mo>,</mo><mn>1000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1200</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>random</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>U</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>B</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>)</mo><mo>-</mo><mo>(</mo><mi>B</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>-</mo><mi>U</mi><mo>-</mo><mo>(</mo><mi>A</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mi>C</mi></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Advanced Frictionless Dynamics 4 Two masses, each of #A grams, are connected by a light cord over a frictionless pulley.  One mass is free to slide over a frictionless horizontal surface, and the other falls vertically, as shown in the diagram below.  Calculate the acceleration of each mass and the tension in the cord.

Mass of Each:  #A Grams


Acceleration of System: {#1} m/s^2

Tension in Cord:  {#2} N

]]> 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2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1500</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>905</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mi>C</mi></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Advanced Frictionless Dynamics 5 An aluminum ball of mass #A grams sinks in an oil bath with an acceleration of #B m/s^2.  What is the magnitude of the combined buoyancy and frictional force resisting its fall in Newtons?

Magnitude of buoyancy and frictional forces:: {#1} N



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1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1500</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>random</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>C</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>-</mo><mi>B</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>