{"id":23325,"date":"2026-01-21T16:00:35","date_gmt":"2026-01-21T21:00:35","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23325"},"modified":"2026-04-22T16:26:20","modified_gmt":"2026-04-22T20:26:20","slug":"homework-h1-e-sp-26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/01\/21\/homework-h1-e-sp-26\/","title":{"rendered":"Homework H1.G – Sp 26"},"content":{"rendered":"\n\n\n
Problem statement<\/strong><\/em><\/span><\/a>
\nSolution video<\/a>
\n<\/strong><\/em><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

DISCUSSION THREAD<\/span><\/strong><\/em><\/p>\n

\"\"<\/p>\n

Discussion and hints:<\/strong><\/em><\/p>\n

For this problem, the “Given” information is in terms of the Cartesian kinematical description. The “Find” asks for parameters that are part of the path kinematical description.<\/p>\n

For the Given<\/em> part of the kinematics, you will need to find the first and second derivatives of y<\/em> with respect to time using implicit differentiation of the the path equation: xy = b<\/em>, and using that the first time derivative of x<\/em> is a constant value of c<\/em>.<\/p>\n

Next, you need to relate the Cartesian and path descriptions of the acceleration. There are many approaches in doing this. The most straight-forward approach is to use the projection of acceleration onto the unit tangent vector to find the rate of change of speed: v_dot = a<\/strong>P<\/sub> \u2022 e<\/strong>t<\/sub><\/em>, where the unit tangent is found from e<\/strong>t<\/sub> = v<\/strong>P<\/sub>\/vP<\/sub>. <\/em>The radius of curvature can then be found directly from the magnitude of acceleration equation: aP<\/sub>2<\/sup> = v_dot2<\/sup> + (vP<\/sub>2<\/sup>\/\u03c1 )2<\/sup>.<\/em><\/p>\n

Recall that the sign of v_dot tells us whether P is increasing or decreasing in speed. From the animation below, we see that the acceleration vector has a negative e<\/strong>t\u00a0<\/sub><\/em>throughout the full range of motion. Alternately, you can say that the angle between velocity and acceleration is greater than 90\u00b0 over that motion. So: increasing or decreasing in speed?<\/p>\n

 <\/p>\n

<\/p>\n

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Any questions??<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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