<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-block-type="vertical" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@vertical+block@vert-ls03_06_2" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <h2 class="hd hd-2 unit-title">W3PSQ1: Whirling a Ball (Practice)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ls_ls03_ls03_13" class="problems-wrapper" role="group" aria-labelledby="ls_ls03_ls03_13-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ls_ls03_ls03_13-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ1-1: Whirling a ball - Part I (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_13-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/0a9d48a10510a5d63b3e18aa6f80b36b/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls03_13.svg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; A child, not shown in the figure, is playing with a ball of mass [mathjaxinline]m[/mathjaxinline] that is attached to a massless string of length [mathjaxinline]L[/mathjaxinline]. The child whirls the ball in such a way that the ball describes a vertical circle with its center fixed (the gravitational force is contained in the plane of the circle). At the instant shown in the figure, the ball is passing through point A. The angle between the string and the horizontal is [mathjaxinline]\theta[/mathjaxinline], the speed of the ball is [mathjaxinline]v_ A[/mathjaxinline], and the tension in the string is [mathjaxinline]T[/mathjaxinline]. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; Drag and drop the corresponding terms of Newton&#39;s second law at the instant when the particle is passing through point A. Be consistent with the coordinate system shown in the figure. &lt;/p&gt; &lt;span&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_13_2_1&#34; class=&#34;capa_inputtype&#34;&gt; &lt;div class=&#34;drag_and_drop_problem_div&#34; id=&#34;drag_and_drop_div_ls_ls03_ls03_13_2_1&#34; data-plain-id=&#34;ls_ls03_ls03_13_2_1&#34;&gt; &lt;/div&gt; &lt;div class=&#34;drag_and_drop_problem_json&#34; id=&#34;drag_and_drop_json_ls_ls03_ls03_13_2_1&#34; style=&#34;display:none;&#34;&gt;{&#34;one_per_target&#34;: &#34;true&#34;, &#34;base_image&#34;: &#34;/assets/courseware/v1/eb2d629feb9d03c19fabaa2337aa84b3/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls03_13_dnd_ls03_13_dnd_dnd.png&#34;, &#34;draggables&#34;: [{&#34;target_fields&#34;: [], &#34;id&#34;: &#34;A&#34;, &#34;label&#34;: &#34;&#34;, &#34;icon&#34;: 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aria-describedby=&#34;input_ls_ls03_ls03_13_2_1&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_13_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/p&gt; &lt;p id=&#34;answer_ls_ls03_ls03_13_2_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_ls_ls03_ls03_13_solution_1&#34;/&gt; &lt;/div&gt;&lt;/span&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_ls_ls03_ls03_13_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ1-1: Whirling a ball - Part I (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ls_ls03_ls03_13&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ls_ls03_ls03_13&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_13-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_13-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_13-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ls_ls03_ls03_14" class="problems-wrapper" role="group" aria-labelledby="ls_ls03_ls03_14-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ls_ls03_ls03_14-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ1-2: Whirling a ball - Part II (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_14-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; What is [mathjaxinline]a_ r[/mathjaxinline], the radial component of the acceleration vector at the instant when the ball passes through point A. Express your answer in terms of [mathjaxinline]L[/mathjaxinline] and v_A for [mathjaxinline]v_ A[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]a_ r =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_14_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ls_ls03_ls03_14_2_1&#34; id=&#34;input_ls_ls03_ls03_14_2_1&#34; aria-describedby=&#34;status_ls_ls03_ls03_14_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ls_ls03_ls03_14_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_14_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ls_ls03_ls03_14_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ls_ls03_ls03_14_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ls_ls03_ls03_14_2_1_dynamath&#34; name=&#34;input_ls_ls03_ls03_14_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; Calculate [mathjaxinline]a_{\theta }[/mathjaxinline], the tangential component of the acceleration vector at the instant when the ball passes through point A. Express your answer in terms of [mathjaxinline]g[/mathjaxinline] and theta for [mathjaxinline]\theta[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]a_{\theta } =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_14_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ls_ls03_ls03_14_3_1&#34; id=&#34;input_ls_ls03_ls03_14_3_1&#34; aria-describedby=&#34;status_ls_ls03_ls03_14_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ls_ls03_ls03_14_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_14_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ls_ls03_ls03_14_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ls_ls03_ls03_14_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ls_ls03_ls03_14_3_1_dynamath&#34; name=&#34;input_ls_ls03_ls03_14_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part d)&lt;/b&gt; Calculate [mathjaxinline]T[/mathjaxinline], the tension in the string at the instant when the ball passes through point A. Express your answer in terms of [mathjaxinline]g[/mathjaxinline], [mathjaxinline]m[/mathjaxinline], [mathjaxinline]L[/mathjaxinline], v_A for [mathjaxinline]v_ A[/mathjaxinline] and theta for [mathjaxinline]\theta[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]T =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_14_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ls_ls03_ls03_14_4_1&#34; id=&#34;input_ls_ls03_ls03_14_4_1&#34; aria-describedby=&#34;status_ls_ls03_ls03_14_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ls_ls03_ls03_14_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_14_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ls_ls03_ls03_14_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ls_ls03_ls03_14_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ls_ls03_ls03_14_4_1_dynamath&#34; name=&#34;input_ls_ls03_ls03_14_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_ls_ls03_ls03_14_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ1-2: Whirling a ball - Part II (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ls_ls03_ls03_14&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ls_ls03_ls03_14&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_14-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_14-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_14-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-block-type="vertical" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@vertical+block@vert-ls03_06_4" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <h2 class="hd hd-2 unit-title">W3PSQ2: Box on a Loop-the-Loop (Practice)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ls_ls03_ls03_15" class="problems-wrapper" role="group" aria-labelledby="ls_ls03_ls03_15-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ls_ls03_ls03_15-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ2: Box on a Loop-the-Loop (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_15-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/858f7c477a3a821cd2ef1b35e51bba9c/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls03_15.svg&#34; width=&#34;400&#34;/&gt; &lt;/center&gt; &lt;p&gt; A box is sliding along a frictionless track. The loop-the-loop portion of the track is contained in the vertical plane and has a radius [mathjaxinline]R[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; It is found that when the box is at the top of the loop the force exerted by the track on the box is half the box&#39;s weight. What is [mathjaxinline]v_{top}[/mathjaxinline], the speed of the box at the top of the loop? &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]v_{top} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_15_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ls_ls03_ls03_15_2_1&#34; id=&#34;input_ls_ls03_ls03_15_2_1&#34; aria-describedby=&#34;status_ls_ls03_ls03_15_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ls_ls03_ls03_15_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_15_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ls_ls03_ls03_15_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ls_ls03_ls03_15_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ls_ls03_ls03_15_2_1_dynamath&#34; name=&#34;input_ls_ls03_ls03_15_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_ls_ls03_ls03_15_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ2: Box on a Loop-the-Loop (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ls_ls03_ls03_15&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ls_ls03_ls03_15&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-block-type="vertical" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@vertical+block@vert-W03PS01-1" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <h2 class="hd hd-2 unit-title">W03PS01: Worked Example - Orbital Circular Motion (Practice)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pset_pset4_8a" class="problems-wrapper" role="group" aria-labelledby="pset_pset4_8a-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pset_pset4_8a-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ3-1: Universal Law of Gravitation and Orbital Uniform Circular Motion Part a (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8a-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;p&gt; A person on a spherical asteroid of mass [mathjaxinline]m_1[/mathjaxinline] and radius [mathjaxinline]R[/mathjaxinline], sees a small satellite of mass [mathjaxinline]m_2[/mathjaxinline] orbiting the asteroid in a circular orbit of period [mathjaxinline]T[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Express you answer in terms of some or all of the following: m_1 for [mathjaxinline]m_1[/mathjaxinline], m_2 for [mathjaxinline]m_2[/mathjaxinline], pi for [mathjaxinline]\pi[/mathjaxinline], [mathjaxinline]T[/mathjaxinline], and the universal gravitational constant [mathjaxinline]G[/mathjaxinline]. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; What is the radius [mathjaxinline]r_{\text {sat}}[/mathjaxinline] of the satellite&#39;s orbit? &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]r_{\text {sat}} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset_pset4_8a_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset_pset4_8a_2_1&#34; id=&#34;input_pset_pset4_8a_2_1&#34; aria-describedby=&#34;status_pset_pset4_8a_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;30&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset_pset4_8a_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset_pset4_8a_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_pset_pset4_8a_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset_pset4_8a_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset_pset4_8a_2_1_dynamath&#34; name=&#34;input_pset_pset4_8a_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pset_pset4_8a_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ3-1: Universal Law of Gravitation and Orbital Uniform Circular Motion Part a (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_pset_pset4_8a&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_pset_pset4_8a&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8a-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8a-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8a-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-block-type="video" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W3PSv1-1: Worked Example - Orbital Circular Motion - Radius</h3> <div id="video_W03PS01-1" class="video closed" data-metadata='{&#34;savedVideoPosition&#34;: 0.0, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;completionPercentage&#34;: 0.95, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1/handler/transcript/available_translations&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1/handler/xmodule_handler/save_user_state&#34;, &#34;prioritizeHls&#34;: false, &#34;autoplay&#34;: false, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;start&#34;: 0.0, &#34;autoAdvance&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1/handler/publish_completion&#34;, &#34;poster&#34;: &#34;https://mitx-edx-video-meta-storage.s3.amazonaws.com/media/video-images/2a67d46654e2442880736cff58794b37.jpeg?x-amz-security-token=IQoJb3JpZ2luX2VjENX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJHMEUCIQCRYhvUid%2B9cGyhrRVUjmhwoOT3%2Bz7ObPDjeLG%2BrQ2yIwIgXvLJOpDJ2qpp02he8FrkhyezE5%2FCSCbnCdTP5mHjMbUqugUILhADGgw4NTkyMDU2Mzc0MTEiDKVSnD5OaItqp4XQRiqXBcvW2qZLauHemBydfOht3xGFzLwbev9PxzrALE0VpM5Mc1z0jD2WN4gYZtiwYcz8fa77MgZoDSKAYZBMyV5J77BQO71sh0W05Aom90Bm6TQ98MA9hsthyYBiqBWmCD%2F5w48o9NSiKbTAJQ1Jqv7rPYTd6lpW31o2dqxy%2FPQFFR%2BPBcTCiZbFb9it%2FpSM4c6GxtTNOW8c8ctAwfF0KUq8GxUgjW5l%2Fj%2FMhjzfDujp7JJVBYQYPLEqH9lmPcSEZYnDSBoKtSUrck3R7nju5HV3Lg5dxBqypgOvGo8ZLQ4QicdgmunawtCkXKBnZHcJLx1e1IljFrm9rVhGV%2FqMfOtci60E7UCbc6YxyyaOnVnROfCrwmGvXOzVH9SPcVDv25SWJZ6MA8Zgqc1uQFMIY4Uk6DYxvfDqk8NXWUxkCLgLTx0WNE5c7N6Vi1n6uNH4NrVtmpyEuAhNGi9wHG7NGUFrhv%2BlYVbkWY7guwXeQNYiE02yqb4frCVwEGQJxv4EXOp6GFsbipiBz2yrSC0pK6lzuYXAQoaSkQFx%2BmRwf%2Bu5jPmYwNuFDF3VzdBUmzPkmPHH8GugBGY8KaoKbFW0nwNNehIFPnrPh9Kp5ByIran2j8J0DgcooBqvXASe0tBLkwK%2FRN1ElcYRnBNG2KNIyWEY9%2BIAfw0TT2xtDvZ5kx7dwTdKhupg%2BNAjo3x2MtftNnmur79Xy%2FeFnhb1hvnUsiqXT3UPo4jVsofL8KX%2BYBAvOeWibtabUh6CtR0pbcWPUSeJeD5vuS9CQU5q6sQ8kU1G4OjK9%2BdXr43gZDHFBdLvHttnHjC%2FRWJp1Oim%2BsmPuMo%2Bk234vF8IS%2FFfVYtxMrQrQU9ICRt7q3iZRWFjXqwaeH3rZ7aSpssAMjCZro%2B4BjqxAacEHN%2B5ifJ4cdMxH%2BrZ%2FCnyeDlizpERb7x%2B1Lf01w7ffZ1pd1Y7jprxmHcn2vcc7HixRvqQ1b8k9Un%2FZVfic6puVKXDjGWvEN%2BnVsE%2B1sIqMwhyKkFwNIBXn%2FHne0S7J9cSDT25vnqqcNxMRFaQkVT%2BKXkhgEPX6lu%2BXRavMliuHGqYCAiad3G8qWfLUCFo5JP8%2Bvl8n4MNXTtCk9G53RkmjV5YfHlBviHGF3AuXqtTnw%3D%3D&amp;AWSAccessKeyId=ASIA4QDFFSURT3XFQNHH&amp;Expires=1728307554&amp;Signature=sOqJc9xAirRv1vu6VjBiix2C5L8%3D&#34;, &#34;autohideHtml5&#34;: false, &#34;sources&#34;: [&#34;https://d2f1egay8yehza.cloudfront.net/MIT801XX2016-V009200_DTH.mp4&#34;], &#34;recordedYoutubeIsAvailable&#34;: true, &#34;completionEnabled&#34;: false, &#34;streams&#34;: &#34;1.00:EEHIL_PVycI&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;generalSpeed&#34;: 1.0, &#34;captionDataDir&#34;: null, &#34;duration&#34;: 219.63, &#34;speed&#34;: null, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-1/handler/transcript/translation/__lang__&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="W03PS01-1"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. 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Orbital Circular Motion - Velocity</h3> <div id="video_W03PS01-2" class="video closed" data-metadata='{&#34;savedVideoPosition&#34;: 0.0, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;completionPercentage&#34;: 0.95, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/transcript/available_translations&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/xmodule_handler/save_user_state&#34;, &#34;prioritizeHls&#34;: false, &#34;autoplay&#34;: false, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;start&#34;: 0.0, &#34;autoAdvance&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/publish_completion&#34;, &#34;poster&#34;: &#34;https://mitx-edx-video-meta-storage.s3.amazonaws.com/media/video-images/7c938c3df25442e999f923c543d45189.jpeg?x-amz-security-token=IQoJb3JpZ2luX2VjENX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJHMEUCIQCRYhvUid%2B9cGyhrRVUjmhwoOT3%2Bz7ObPDjeLG%2BrQ2yIwIgXvLJOpDJ2qpp02he8FrkhyezE5%2FCSCbnCdTP5mHjMbUqugUILhADGgw4NTkyMDU2Mzc0MTEiDKVSnD5OaItqp4XQRiqXBcvW2qZLauHemBydfOht3xGFzLwbev9PxzrALE0VpM5Mc1z0jD2WN4gYZtiwYcz8fa77MgZoDSKAYZBMyV5J77BQO71sh0W05Aom90Bm6TQ98MA9hsthyYBiqBWmCD%2F5w48o9NSiKbTAJQ1Jqv7rPYTd6lpW31o2dqxy%2FPQFFR%2BPBcTCiZbFb9it%2FpSM4c6GxtTNOW8c8ctAwfF0KUq8GxUgjW5l%2Fj%2FMhjzfDujp7JJVBYQYPLEqH9lmPcSEZYnDSBoKtSUrck3R7nju5HV3Lg5dxBqypgOvGo8ZLQ4QicdgmunawtCkXKBnZHcJLx1e1IljFrm9rVhGV%2FqMfOtci60E7UCbc6YxyyaOnVnROfCrwmGvXOzVH9SPcVDv25SWJZ6MA8Zgqc1uQFMIY4Uk6DYxvfDqk8NXWUxkCLgLTx0WNE5c7N6Vi1n6uNH4NrVtmpyEuAhNGi9wHG7NGUFrhv%2BlYVbkWY7guwXeQNYiE02yqb4frCVwEGQJxv4EXOp6GFsbipiBz2yrSC0pK6lzuYXAQoaSkQFx%2BmRwf%2Bu5jPmYwNuFDF3VzdBUmzPkmPHH8GugBGY8KaoKbFW0nwNNehIFPnrPh9Kp5ByIran2j8J0DgcooBqvXASe0tBLkwK%2FRN1ElcYRnBNG2KNIyWEY9%2BIAfw0TT2xtDvZ5kx7dwTdKhupg%2BNAjo3x2MtftNnmur79Xy%2FeFnhb1hvnUsiqXT3UPo4jVsofL8KX%2BYBAvOeWibtabUh6CtR0pbcWPUSeJeD5vuS9CQU5q6sQ8kU1G4OjK9%2BdXr43gZDHFBdLvHttnHjC%2FRWJp1Oim%2BsmPuMo%2Bk234vF8IS%2FFfVYtxMrQrQU9ICRt7q3iZRWFjXqwaeH3rZ7aSpssAMjCZro%2B4BjqxAacEHN%2B5ifJ4cdMxH%2BrZ%2FCnyeDlizpERb7x%2B1Lf01w7ffZ1pd1Y7jprxmHcn2vcc7HixRvqQ1b8k9Un%2FZVfic6puVKXDjGWvEN%2BnVsE%2B1sIqMwhyKkFwNIBXn%2FHne0S7J9cSDT25vnqqcNxMRFaQkVT%2BKXkhgEPX6lu%2BXRavMliuHGqYCAiad3G8qWfLUCFo5JP8%2Bvl8n4MNXTtCk9G53RkmjV5YfHlBviHGF3AuXqtTnw%3D%3D&amp;AWSAccessKeyId=ASIA4QDFFSURT3XFQNHH&amp;Expires=1728307554&amp;Signature=S29UqE%2BwSMmAK%2BoNRq%2FTF9ruu3U%3D&#34;, &#34;autohideHtml5&#34;: false, &#34;sources&#34;: [&#34;https://d2f1egay8yehza.cloudfront.net/MIT801XX2016-V009100_DTH.mp4&#34;], &#34;recordedYoutubeIsAvailable&#34;: true, &#34;completionEnabled&#34;: false, &#34;streams&#34;: &#34;1.00:cHigceanzsE&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;generalSpeed&#34;: 1.0, &#34;captionDataDir&#34;: null, &#34;duration&#34;: 62.85, &#34;speed&#34;: null, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/transcript/translation/__lang__&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="W03PS01-2"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_W03PS01-2">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W03PS01-2"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-2/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pset_pset4_8c" class="problems-wrapper" role="group" aria-labelledby="pset_pset4_8c-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pset_pset4_8c-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ3-3: Universal Law of Gravitation and Orbital Uniform Circular Motion Part c (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@pset_pset4_8c-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; If the asteroid rotates about its axis with a period [mathjaxinline]T_{\text {a}}[/mathjaxinline], at what radius must the satellite orbit the asteroid so that the satellite appears stationary to the person on the asteroid? &lt;/p&gt; &lt;p&gt; Express you answer in terms of some or all of the following: m_1 for [mathjaxinline]m_1[/mathjaxinline], m_2 for [mathjaxinline]m_2[/mathjaxinline], pi for [mathjaxinline]\pi[/mathjaxinline], T_a for [mathjaxinline]T_ a[/mathjaxinline], and [mathjaxinline]G[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]r_{\text {sat}} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset_pset4_8c_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset_pset4_8c_2_1&#34; id=&#34;input_pset_pset4_8c_2_1&#34; aria-describedby=&#34;status_pset_pset4_8c_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;30&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset_pset4_8c_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset_pset4_8c_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_pset_pset4_8c_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset_pset4_8c_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset_pset4_8c_2_1_dynamath&#34; name=&#34;input_pset_pset4_8c_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pset_pset4_8c_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ3-3: Universal Law of Gravitation and Orbital Uniform Circular Motion Part c (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_pset_pset4_8c&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_pset_pset4_8c&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8c-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8c-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset_pset4_8c-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-5" data-id="block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-3"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-block-type="video" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@video+block@W03PS01-3" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W3PSv1-3: Worked Example - 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-block-type="vertical" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@vertical+block@vert-ls03_06_05" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <h2 class="hd hd-2 unit-title">W3PSQ4: Double Star System (Practice)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-block-type="problem" data-request-token="fb03dbba84ae11ef879c12578eed8dbf" data-usage-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1" data-graded="False" data-course-id="course-v1:MITx+8.01.1x+3T2018"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ls_ls03_ls03_27" class="problems-wrapper" role="group" aria-labelledby="ls_ls03_ls03_27-problem-title" data-problem-id="block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27" data-url="/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ls_ls03_ls03_27-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27-problem-progress&#34; tabindex=&#34;-1&#34;&gt; W3PSQ4: Double Star System (Practice) &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.01.1x+3T2018+type@problem+block@ls_ls03_ls03_27-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;span&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/bf9d6dcdd86f4c615b501379262f3a4c/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls03_27.gif&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; Consider a double star system and the gravitational force between them. Star 1 has mass [mathjaxinline]m_1[/mathjaxinline] and star 2 has mass [mathjaxinline]m_2[/mathjaxinline]. Assume that each star undergoes uniform circular motion and is rotating counterclockwise such that the stars are always a fixed distance [mathjaxinline]s[/mathjaxinline] apart as shown in the figure. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/eb3982984b0305781ac8620462e373f1/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls03_27.svg&#34; width=&#34;220&#34;/&gt; &lt;/center&gt; &lt;p&gt; What is [mathjaxinline]T[/mathjaxinline], the period of the orbit? Express your answer in terms of [mathjaxinline]G[/mathjaxinline], [mathjaxinline]s[/mathjaxinline], m_1 for [mathjaxinline]m_1[/mathjaxinline] and m_2 for [mathjaxinline]m_2[/mathjaxinline]. &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]T =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ls_ls03_ls03_27_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ls_ls03_ls03_27_2_1&#34; id=&#34;input_ls_ls03_ls03_27_2_1&#34; aria-describedby=&#34;status_ls_ls03_ls03_27_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ls_ls03_ls03_27_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ls_ls03_ls03_27_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ls_ls03_ls03_27_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ls_ls03_ls03_27_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ls_ls03_ls03_27_2_1_dynamath&#34; name=&#34;input_ls_ls03_ls03_27_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_ls_ls03_ls03_27_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;W3PSQ4: Double Star System (Practice)&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ls_ls03_ls03_27&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ls_ls03_ls03_27&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_27-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_27-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ls_ls03_ls03_27-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>