Fall 2008 Quiz #8 PHYS-218Sec Date: Nov. 3, 2008Print NamesThis is your GROUP quiz. Be sure to write all of your assumptions out in words.Draw sketch(es) and derive your equations before coming to an answer. Do NOTwrite the answer alone. Write the answer in a separate paper.1. An object is released on a track with a loop. Find the minimum height of release such that theobject will stay in contact with the track as it loops the loop. In this problem you will considerthe motion of a cylinder of radius rcylthat is rolled from a certain height h so that it ”loops theloop,” that is, rolls around the track with a loop of radius rloopshown in the figure without losingcontact with the track.Unless otherwise stated, assume that friction is sufficient that the cylinder rolls without slipping.The radius rcylof the cylinder is much smaller than the radius rloopof the loop. The moment ofinertia of the cylinder in this motion is Icm=12mr2cyl.(a) Compared to an object that does not roll, but instead slides without friction, should a rollingobject be released from the same, a greater, or a lesser height in order just barely to complete theloop the loop? Explain the reason briefly (without calculation).Find the minimum height hmthat will allow a solid cylinder of mass m and radius rcylto loopthe loop of radius rloopbased on the following steps.(b) In order to stay in contact with the track, the object must have an appropriate centripetalacceleration. Draw the free-body diagram for the object at the top of the loop, and show that thecritical velocity of the object at the top of the loop is√grloop.(c) Use energy conservation obtain the minimum height hmthat will allow a solid cylinder ofmass m and radius rcylto loop the loop of radius rloop.(d) If the rotational motion can be neglected, the cylinder can be treated as a point-like object.What is hmin this case? Compare this results with your expectation in
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