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Physics 1 Problem Solutions 119

Physics 1 Problem Solutions 119 - Chapt 12 Rotational...

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Chapt. 12 Rotational Dynamics 115 13. Dingo the daredevil dog is back—just accept it. He is now on a no-slip track and he curls himself into an exactly spherically symmetric ball (but not necessarily a uniform density one) of radius r Dingo . Starting from REST , he rolls down the track from an initial height y 0 . The track becomes level at y = 0, does a circular loop-the-loop of radius R , and then goes level at y = 0 again. Note r Dingo and R are different radii. a) What is Dingo’s center-of-mass speed at any height y assuming he stays on the track? b) Find a general expression for the normal force on Dingo when he is on the loop as a function of the angle θ between a general radial vector and the radial vector pointing to the top of the loop and radius R . c) For what θ is the normal force expression smallest? What is the normal force expression for this angle? d) What is the condition on y 0 /R for the normal force NOT go less than zero anywhere on the loop? What happens if it did go less than zero?
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