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<h2 class="hd hd-2 unit-title">Topics and Reading List</h2>
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<p> This skill challenge allows you to practice using Newton's Laws. These are skills that will be very important in problem solving, so it's good to practice them first so they can become second nature by the time you need them in longer problems.</p>
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<h2 class="hd hd-2 unit-title">SC2v1: Newton's 3rd Law Pairs</h2>
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<h3 class="hd hd-2">SC2v1: Newton's 3rd Law Pairs</h3>
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<h2 class="hd hd-2 unit-title">SC2Q1: Newton's 3rd Law (Practice)</h2>
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<p> The three non-credit problems below will help you to review the concept of Newton's 3rd Law pairs of forces.</p>
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SC2Q1-1: Newton&#39;s 3rd Law - Book on a table (Practice)
</h3>
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<p>
A book is at rest on a horizontal table. The forces acting on it are the contact normal force of magnitude [mathjaxinline]N[/mathjaxinline] pointing up and the gravitational force of magnitude [mathjaxinline]W[/mathjaxinline] pointing down. </p>
<p>
Determine if the statements are true or false. </p>
<p><b class="bfseries">1.</b> The normal and the weight are equal in magnitude and opposite in direction because the book is at rest. <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div class="inputtype option-input inline">
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<p><b class="bfseries">2.</b> The normal and the weight are equal in magnitude because of Newton's 3rd law. <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div class="inputtype option-input inline">
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<p><b class="bfseries">3.</b> The normal and the weight form a Newton's 3rd law pair. <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div class="inputtype option-input inline">
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SC2Q1-2: Newton&#39;s 3rd Law - Pushing two blocks against a wall (Practice)
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Blocks 1 and 2 are being pushed against a vertical wall by a horizontal force of magnitude [mathjaxinline]F[/mathjaxinline]. Because of friction between blocks 1 and 2, as well as between block 2 and the wall, both blocks stay stationary without falling down. </p>
<p>
Determine if the following pairs of forces are Newton's 3rd Law Pairs. </p>
<p><b class="bfseries">1.</b> Weight of block 1 and the frictional force exerted by block 2 on block 1. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_2_1">
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</label>
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<input type="radio" name="input_module_mod2_lp_2_2_1" id="input_module_mod2_lp_2_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_2_2_1-choice_2-label" for="input_module_mod2_lp_2_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_2_2_1"> <text> No</text>
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</div></div> <b class="bfseries">2.</b> Weight of both blocks and the frictional force between the wall and block 2. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_3_1">
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<input type="radio" name="input_module_mod2_lp_2_3_1" id="input_module_mod2_lp_2_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_lp_2_3_1-choice_1-label" for="input_module_mod2_lp_2_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_2_3_1"> <text> Yes</text>
</label>
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</div></div> <b class="bfseries">3.</b> Friction exerted by block 1 on block 2 and friction exerted by block 2 on block 1. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_4_1">
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</div></div> <b class="bfseries">4.</b> The applied force F and the normal force from the wall on block 2.<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_5_1">
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</div></div> <b class="bfseries">5.</b> The applied force F and the normal force exerted by block 2 on block 1. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_6_1">
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</div></div> <b class="bfseries">6.</b> Normal force exerted by block 1 on block 2, and the normal force exerted by block 2 on block 1. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_2_7_1">
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SC2Q1-3: Newton&#39;s 3rd Law - Pushing a Safe (Practice)
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<p>
Consider the situation shown in the picture: a person is trying to move a very heavy safe by pushing it along the ground. The force exerted by the person on the safe is perfectly horizontal. Neither the person nor the safe is moving. </p>
<p>
Determine if the following pairs of forces are Newton's 3rd Law Pairs. </p>
<p><b class="bfseries">1.</b> The force exerted by the person on the safe and the friction exerted by the ground on the safe. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_3_2_1">
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</div></div> <b class="bfseries">2.</b> The friction force exerted by the ground on the person and the force exerted by the safe on the person. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_3_3_1">
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</div></div> <b class="bfseries">3.</b> The force exerted by the person on the safe and the force exerted by the safe on the person. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_3_4_1">
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</div></div> <b class="bfseries">4.</b> The friction force exerted by the ground on the safe and the friction exerted by the ground on the person. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_3_5_1">
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<h2 class="hd hd-2 unit-title">SC2Q2: Newton's 3rd Law</h2>
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SC2Q2: Newtons 3rd Law
</h3>
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<p>
Blocks 1 and 2 are at rest on a horizontal and frictionless surface as shown. [mathjaxinline]\vec{\textbf{F}}_1[/mathjaxinline] is pushing block 1 to the right, and [mathjaxinline]\vec{\textbf{F}}_2[/mathjaxinline] is pushing block 2 to the left. Because of the presence of friction between the two blocks, both blocks are stationary with respect to the surface. </p>
<p><b class="bfseries">(Part a)</b> If [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]F_2[/mathjaxinline] are the magnitudes of vectors [mathjaxinline]\vec{\textbf{F}}_1[/mathjaxinline] and [mathjaxinline]\vec{\textbf{F}}_2[/mathjaxinline], then: </p>
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<text> [mathjaxinline]F_1&gt;F_2[/mathjaxinline]</text>
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<p><b class="bfseries">(Part b)</b> Which of the pair of forces listed below is a Newton 3rd law pair? </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_sk_1_3_1">
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<text> [mathjaxinline]\vec{\textbf{F}}_1[/mathjaxinline] and the frictional force on block 1 by block 2</text>
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<text> [mathjaxinline]\vec{\textbf{F}}_1[/mathjaxinline] and [mathjaxinline]\vec{\textbf{F}}_2[/mathjaxinline]</text>
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<text> The Normal force exerted by block 1 on block 2 and the Normal force exerted by block 2 on block 1</text>
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<text> The gravitational force on both blocks, and the normal force by the surface on block 2</text>
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<h3 class="hd hd-2">SC2v2: Internal and External Forces</h3>
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<h2 class="hd hd-2 unit-title">SC2Q3: Internal and External Forces (Practice)</h2>
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<p> The four non-credit problems below will help you to review the definition of Internal and External Forces.</p>
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SC2Q3-1: System and External Forces 1 part1 (Practice)
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<p class="problemIntro">Two blocks of mass \(m_1\) and \(m_2\) are placed next to each other on a horizontal table. The blocks are being pushed by a force of magnitude \(F\) to the right. <em><b>Choosing block 1 as our system</b></em>, Newton's 2nd law can be written as:</p>
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<center>\(\sum{\mathbf{\vec{F}}} = m_1 \mathbf{\vec{a}}\)</center>
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<p class="problemQ">Determine which horizontal forces should be included in \(\sum{\mathbf{\vec{F}}}\) by dragging the green checkmark onto the force. </p>
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SC2Q3-2: System and External Forces 1 part 2 (Practice)
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<p class="problemIntro">Two blocks of mass \(m_1\) and \(m_2\) are placed next to each other on a frictionless table. The blocks are being pushed by a force of magnitude \(F\) to the right. <em><b>Choosing block 2 as our system</b></em>, Newton's 2nd law can be written as:</p>
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<p class="problemQ">Determine which horizontal forces should be included in \(\sum{\mathbf{\vec{F}}}\) by dragging the green checkmark onto the force. </p>
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SC2Q3-3: System and External Forces 2 part 1 (Practice)
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<p class="problemIntro">Two blocks of mass \(m_1\) and \(m_2\) are connected by a heavy rod of mass \(m_{rod}\), and placed on a frictionless table. Block 2 is being pulled by a force of magnitude \(F\) to the right. <em><b>Choosing block 1 and the rod as our system</b></em>, Newton's 2nd law can be written as:</p>
<p class="problemIntro">
<center>\(\sum{\mathbf{\vec{F}}} = (m_1 + m_{rod}) \mathbf{\vec{a}}\)</center>
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<p class="problemQ">Determine which horizontal forces should be included in \(\sum{\mathbf{\vec{F}}}\) by dragging the green checkmark onto the force. </p>
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SC2Q3-4: System and External Forces 2 part 2 (Practice)
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<p class="problemIntro">Two blocks of mass \(m_1\) and \(m_2\) are connected by a heavy rod of mass \(m_{rod}\), and placed on a frictionless table. Block 2 is being pulled by a force of magnitude \(F\) to the right. <em><b>Choosing block 1 and block 2 as our system</b></em>, Newton's 2nd law can be written as:</p>
<p class="problemIntro">
<center>\(\sum{\mathbf{\vec{F}}} = (m_1 + m_2) \mathbf{\vec{a}}\)</center>
</p>
<p class="problemQ">Determine which horizontal forces should be included in \(\sum{\mathbf{\vec{F}}}\) by dragging the green checkmark onto the force. </p>
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<h2 class="hd hd-2 unit-title">SC2Q4: System and External Forces</h2>
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<p><font face="arial,helvetica" size="5"> System and External Forces</font></p><p>Three objects of masses \(m_1\), \(m_2\) and \(m_3\) are on a flat surface as shown in the figure below. Object 1 has a long extension on one side, and it is connected to object 3 via a hinge at the end of the extension. Object 1 is in contact with object 2 but they are not fixed together.</p><p> Object 1 is being pushed by an external force of magnitude \(F\), and as a result, all three objects are accelerating to the right with an acceleration of magnitude \(a\). There is significant friction, of magnitude \(f\), between object 3 and the surface in the direction shown.<img src="/assets/courseware/v1/f13261f1031cf68209de991e439c010b/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_System_and_Interactions_Problem.svg"/></p>
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SC2Q4-1: Systems and External Forces Part 1
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<p class="problemQ"> Considering <b>only objects 1 and 2</b> as our system, the forces and acceleration satisfy the relation: <center>\(\sum{\vec{F}} = (m_1 + m_2) \vec{a}\)</center></p>
<p class="problemQ">in which \(\sum{\vec{F}}\) is the sum of all the forces <em>acting on the system.</em></p>
<p class="problemQ">Determine which forces shown in the figure are part of \(\sum{\vec{F}}\) by dragging a green checkmark over those forces.</p>
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SC2Q4-2: Systems and External Forces Part 2
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<p class="problemQ"> Considering <b> only objects 2 and 3 </b> as our system, the forces and acceleration satisfy the relation: <center>\(\sum{\vec{F}} = (m_2 + m_3) \vec{a}\)</center></p>
<p class="problemQ">in which \(\sum{\vec{F}}\) is the sum of all forces <em>acting on the system.</em></p>
<p class="problemQ">Determine which forces shown in the figure are part of \(\sum{\vec{F}}\) by dragging a green checkmark over those forces.</p>
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<h2 class="hd hd-2 unit-title">SC2v3: Applying Newton's 2nd Law</h2>
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<h2 class="hd hd-2 unit-title">SC2Q5: Choosing a System and Applying Newton's 2nd Law (Practice)</h2>
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<p> The three non-credit exercises below will help you to practice how to select a system
to solve a given problem. </p>
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<h3 class="hd hd-3 problem-header" id="module_mod2_lp_8-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_lp_8-problem-progress" tabindex="-1">
SC2Q5-1: Choosing a System - Pushing two blocks (Practice)
</h3>
<div class="problem-progress" id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_lp_8-problem-progress"></div>
<div class="problem">
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<center>
<img src="/assets/courseware/v1/d648e286e3d55ebfa1024147e5d23b2f/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_mod2_lp_fig008.svg" width="440"/>
</center>
<p>
Blocks 1 and 2 are placed on a frictionless surface and subjected to two forces of magnitudes [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]F_2[/mathjaxinline] as shown. As a result the blocks move together with an acceleration of magnitude [mathjaxinline]a[/mathjaxinline] towards the right. </p>
<p><b class="bfseries">(Part a)</b> If the magnitudes [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] are given, what system should we choose if we want to calculate the magnitude [mathjaxinline]F_2[/mathjaxinline] by applying Newton's second law only once? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_8_2_1">
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<input type="radio" name="input_module_mod2_lp_8_2_1" id="input_module_mod2_lp_8_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_lp_8_2_1-choice_1-label" for="input_module_mod2_lp_8_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_2_1">
<text> Block 1</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_2_1" id="input_module_mod2_lp_8_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_8_2_1-choice_2-label" for="input_module_mod2_lp_8_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_2_1">
<text> Block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_2_1" id="input_module_mod2_lp_8_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_lp_8_2_1-choice_3-label" for="input_module_mod2_lp_8_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_2_1">
<text> Block 1 and Block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_2_1" id="input_module_mod2_lp_8_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="module_mod2_lp_8_2_1-choice_4-label" for="input_module_mod2_lp_8_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_2_1">
<text> cannot calculate [mathjaxinline]F_2[/mathjaxinline] by applying Newton's second law only once</text>
</label>
</div>
<span id="answer_module_mod2_lp_8_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_module_mod2_lp_8_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p><b class="bfseries">(Part b)</b> If the magnitudes [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] are given but the magnitude [mathjaxinline]F_2[/mathjaxinline] is unknown, what system should we choose if we want to calculate, [mathjaxinline]F_{21}[/mathjaxinline], the magnitude of the force that block 2 exerts on block 1 by applying Newton's second law only once? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_8_3_1">
<fieldset aria-describedby="status_module_mod2_lp_8_3_1">
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_3_1" id="input_module_mod2_lp_8_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_lp_8_3_1-choice_1-label" for="input_module_mod2_lp_8_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_3_1">
<text> Block 1</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_3_1" id="input_module_mod2_lp_8_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_8_3_1-choice_2-label" for="input_module_mod2_lp_8_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_3_1">
<text> Block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_3_1" id="input_module_mod2_lp_8_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_lp_8_3_1-choice_3-label" for="input_module_mod2_lp_8_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_3_1">
<text> Block 1 and Block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_3_1" id="input_module_mod2_lp_8_3_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="module_mod2_lp_8_3_1-choice_4-label" for="input_module_mod2_lp_8_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_3_1">
<text> cannot calculate [mathjaxinline]F_{21}[/mathjaxinline] by applying Newton's second law only once</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_8_3_1" id="input_module_mod2_lp_8_3_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="module_mod2_lp_8_3_1-choice_5-label" for="input_module_mod2_lp_8_3_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_8_3_1">
<text> [mathjaxinline]F_{12} = F_{21}[/mathjaxinline], do not need to choose a system</text>
</label>
</div>
<span id="answer_module_mod2_lp_8_3_1"/>
</fieldset>
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<span class="status unanswered" id="status_module_mod2_lp_8_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<h3 class="hd hd-3 problem-header" id="module_mod2_lp_9-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_lp_9-problem-progress" tabindex="-1">
SC2Q5-2: Choosing a system - Pushing three blocks (Practice)
</h3>
<div class="problem-progress" id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_lp_9-problem-progress"></div>
<div class="problem">
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<center>
<img src="/assets/courseware/v1/91a5b39c93e0b0ee8a77eb03dd7e5088/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_mod2_lp_fig009.svg" width="440"/>
</center>
<p>
Three blocks of masses [mathjaxinline]m_1[/mathjaxinline], [mathjaxinline]m_2[/mathjaxinline] and [mathjaxinline]m_3[/mathjaxinline] are placed on a frictionless surface and subjected to two forces of magnitudes [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]F_2[/mathjaxinline] as shown. As a result the blocks move together with an acceleration of magnitude [mathjaxinline]a[/mathjaxinline] towards the right. </p>
<p><b class="bfseries">(Part a)</b> If [mathjaxinline]m_1[/mathjaxinline], [mathjaxinline]m_2[/mathjaxinline], [mathjaxinline]m_3[/mathjaxinline], [mathjaxinline]F_2[/mathjaxinline], and [mathjaxinline]a[/mathjaxinline] are given and [mathjaxinline]F_1[/mathjaxinline] is unknown, what choice of system will allow us to calculate [mathjaxinline]F_{12}[/mathjaxinline], the magnitude of the force exerted by block 1 on block 2, by applying Newton's second law only once? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_9_2_1">
<fieldset aria-describedby="status_module_mod2_lp_9_2_1">
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_lp_9_2_1-choice_1-label" for="input_module_mod2_lp_9_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 1</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_9_2_1-choice_2-label" for="input_module_mod2_lp_9_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_lp_9_2_1-choice_3-label" for="input_module_mod2_lp_9_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 1 and block 2</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="module_mod2_lp_9_2_1-choice_4-label" for="input_module_mod2_lp_9_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 1 and block 3</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="module_mod2_lp_9_2_1-choice_5-label" for="input_module_mod2_lp_9_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 2 and block 3</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_6" class="field-input input-radio" value="choice_6"/><label id="module_mod2_lp_9_2_1-choice_6-label" for="input_module_mod2_lp_9_2_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Block 1, block 2 and block 3</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_9_2_1" id="input_module_mod2_lp_9_2_1_choice_7" class="field-input input-radio" value="choice_7"/><label id="module_mod2_lp_9_2_1-choice_7-label" for="input_module_mod2_lp_9_2_1_choice_7" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_2_1">
<text> Cannot calculate [mathjaxinline]F_{12}[/mathjaxinline] by applying Newton's second law only once</text>
</label>
</div>
<span id="answer_module_mod2_lp_9_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_module_mod2_lp_9_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_module_mod2_lp_9_solution_1"/>
</div></p>
<p><b class="bfseries">(Part b)</b> If the mass of block 2 increases, while [mathjaxinline]m_1[/mathjaxinline], [mathjaxinline]m_3[/mathjaxinline], [mathjaxinline]F_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] stays the same, which of the following statements are true? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_9_3_1">
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<div class="field">
<input type="checkbox" name="input_module_mod2_lp_9_3_1[]" id="input_module_mod2_lp_9_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="module_mod2_lp_9_3_1-choice_0-label" for="input_module_mod2_lp_9_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_3_1">
<text>[mathjaxinline]F_1[/mathjaxinline] increases and [mathjaxinline]F_{12}[/mathjaxinline] decreases</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_module_mod2_lp_9_3_1[]" id="input_module_mod2_lp_9_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="module_mod2_lp_9_3_1-choice_1-label" for="input_module_mod2_lp_9_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_3_1">
<text>[mathjaxinline]F_1[/mathjaxinline] increases and [mathjaxinline]F_{12}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_module_mod2_lp_9_3_1[]" id="input_module_mod2_lp_9_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="module_mod2_lp_9_3_1-choice_2-label" for="input_module_mod2_lp_9_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_3_1">
<text>[mathjaxinline]F_{23}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_module_mod2_lp_9_3_1[]" id="input_module_mod2_lp_9_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="module_mod2_lp_9_3_1-choice_3-label" for="input_module_mod2_lp_9_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_3_1">
<text>[mathjaxinline]F_{23}[/mathjaxinline] remains the same</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_module_mod2_lp_9_3_1[]" id="input_module_mod2_lp_9_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="module_mod2_lp_9_3_1-choice_4-label" for="input_module_mod2_lp_9_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_9_3_1">
<text>[mathjaxinline]F_{23}[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_lp_9_3_1"/>
</fieldset>
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<span class="status unanswered" id="status_module_mod2_lp_9_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<h3 class="hd hd-3 problem-header" id="module_mod2_lp_10-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_lp_10-problem-progress" tabindex="-1">
SC2Q5-3: Choosing a system - Pushing two blocks one on top of the other (Practice)
</h3>
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Two blocks of masses [mathjaxinline]m_1[/mathjaxinline] and [mathjaxinline]m_2[/mathjaxinline] are stacked together and placed on a frictionless surface. There is friction between the two blocks. A force of magnitude [mathjaxinline]F[/mathjaxinline] is applied on block 2 as shown. As a result, the blocks move together with an acceleration of magnitude [mathjaxinline]a[/mathjaxinline] directed to the right. </p>
<p><b class="bfseries">(Part a)</b> If [mathjaxinline]m_1[/mathjaxinline] increases and [mathjaxinline]m_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, and the blocks continue moving together then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_10_2_1">
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<div class="field">
<input type="radio" name="input_module_mod2_lp_10_2_1" id="input_module_mod2_lp_10_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_lp_10_2_1-choice_1-label" for="input_module_mod2_lp_10_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_10_2_1">
<text> The pushing force [mathjaxinline]F[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_10_2_1" id="input_module_mod2_lp_10_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_10_2_1-choice_2-label" for="input_module_mod2_lp_10_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_10_2_1">
<text> The pushing force [mathjaxinline]F[/mathjaxinline] remains constant</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_10_2_1" id="input_module_mod2_lp_10_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_lp_10_2_1-choice_3-label" for="input_module_mod2_lp_10_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_10_2_1">
<text> The pushing force [mathjaxinline]F[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_lp_10_2_1"/>
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<span class="status unanswered" id="status_module_mod2_lp_10_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<span id="solution_module_mod2_lp_10_solution_1"/>
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<p><b class="bfseries">(Part b)</b> Consider [mathjaxinline]F_{12}[/mathjaxinline] to be the magnitude of the frictional force exerted by block 1 on block 2. If [mathjaxinline]m_1[/mathjaxinline] increases and [mathjaxinline]m_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, and the blocks continue moving together, then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_lp_10_3_1">
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<text> [mathjaxinline]F_{12}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_10_3_1" id="input_module_mod2_lp_10_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_lp_10_3_1-choice_2-label" for="input_module_mod2_lp_10_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_10_3_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] remains the same</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_lp_10_3_1" id="input_module_mod2_lp_10_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_lp_10_3_1-choice_3-label" for="input_module_mod2_lp_10_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_lp_10_3_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_lp_10_3_1"/>
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<span class="status unanswered" id="status_module_mod2_lp_10_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<h2 class="hd hd-2 unit-title">SC2Q6: Applying Newton's 2nd Law</h2>
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<h3 class="hd hd-3 problem-header" id="module_mod2_sk_3-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_sk_3-problem-progress" tabindex="-1">
SC2Q6: Applying Newton&#39;s Second Law
</h3>
<div class="problem-progress" id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@module_mod2_sk_3-problem-progress"></div>
<div class="problem">
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<center>
<img src="/assets/courseware/v1/58d1d37506067fbcdc5d9f3524855753/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_mod2_sk_fig002.svg" width="440"/>
</center>
<p>
In the figure, a horizontal force of magnitude [mathjaxinline]F_1[/mathjaxinline] is pushing block 1 to the right, and a horizontal force of magnitude [mathjaxinline]F_2[/mathjaxinline] is pushing block 2 to the left. As a result both blocks move together along the horizontal and frictionless surface with an acceleration of magnitude [mathjaxinline]a[/mathjaxinline]. </p>
<p>
Consider [mathjaxinline]F_{12}[/mathjaxinline] to be the magnitude of the contact force exerted by block 1 on block 2. </p>
<p><b class="bfseries">Part a.</b> If [mathjaxinline]F_1[/mathjaxinline] increases and [mathjaxinline]m_1[/mathjaxinline], [mathjaxinline]m_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_sk_3_2_1">
<fieldset aria-describedby="status_module_mod2_sk_3_2_1">
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_2_1" id="input_module_mod2_sk_3_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_sk_3_2_1-choice_1-label" for="input_module_mod2_sk_3_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_2_1">
<text> [mathjaxinline]F_{2}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_2_1" id="input_module_mod2_sk_3_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_sk_3_2_1-choice_2-label" for="input_module_mod2_sk_3_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_2_1">
<text> [mathjaxinline]F_{2}[/mathjaxinline] remains the same</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_2_1" id="input_module_mod2_sk_3_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_sk_3_2_1-choice_3-label" for="input_module_mod2_sk_3_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_2_1">
<text> [mathjaxinline]F_{2}[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_sk_3_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_module_mod2_sk_3_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p><b class="bfseries">Part b.</b> If [mathjaxinline]m_2[/mathjaxinline] increases and [mathjaxinline]m_1[/mathjaxinline], [mathjaxinline]F_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_sk_3_3_1">
<fieldset aria-describedby="status_module_mod2_sk_3_3_1">
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_3_1" id="input_module_mod2_sk_3_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_sk_3_3_1-choice_1-label" for="input_module_mod2_sk_3_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_3_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_3_1" id="input_module_mod2_sk_3_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_sk_3_3_1-choice_2-label" for="input_module_mod2_sk_3_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_3_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] remains the same</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_3_1" id="input_module_mod2_sk_3_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_sk_3_3_1-choice_3-label" for="input_module_mod2_sk_3_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_3_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_sk_3_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_module_mod2_sk_3_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p><b class="bfseries">Part c.</b> If [mathjaxinline]m_1[/mathjaxinline] increases and [mathjaxinline]m_2[/mathjaxinline], [mathjaxinline]F_1[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_sk_3_4_1">
<fieldset aria-describedby="status_module_mod2_sk_3_4_1">
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_4_1" id="input_module_mod2_sk_3_4_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_sk_3_4_1-choice_1-label" for="input_module_mod2_sk_3_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_4_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_4_1" id="input_module_mod2_sk_3_4_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_sk_3_4_1-choice_2-label" for="input_module_mod2_sk_3_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_4_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] remains the same</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_4_1" id="input_module_mod2_sk_3_4_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="module_mod2_sk_3_4_1-choice_3-label" for="input_module_mod2_sk_3_4_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_4_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] decreases</text>
</label>
</div>
<span id="answer_module_mod2_sk_3_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_module_mod2_sk_3_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p><b class="bfseries">Part d.</b> If [mathjaxinline]m_1[/mathjaxinline] increases and [mathjaxinline]m_2[/mathjaxinline], [mathjaxinline]F_2[/mathjaxinline] and [mathjaxinline]a[/mathjaxinline] remain the same, then: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_module_mod2_sk_3_5_1">
<fieldset aria-describedby="status_module_mod2_sk_3_5_1">
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_5_1" id="input_module_mod2_sk_3_5_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="module_mod2_sk_3_5_1-choice_1-label" for="input_module_mod2_sk_3_5_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_5_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] increases</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_module_mod2_sk_3_5_1" id="input_module_mod2_sk_3_5_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="module_mod2_sk_3_5_1-choice_2-label" for="input_module_mod2_sk_3_5_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_module_mod2_sk_3_5_1">
<text> [mathjaxinline]F_{12}[/mathjaxinline] remains the same</text>
</label>
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