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Midterm_solution-2

Midterm_solution-2 - Statics and Dynamics Me 35b(Winter...

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Statics and Dynamics - Me 35b (Winter 2009) Midterm Examination Solutions Problem 1: A small object of mass m starts sliding down the track (Figure.1) from location A with the height h . The shape of the track to the right of the lowest point of the track is a semicircle with radius h/ 2. Let θ be the angle measured from the horizontal, so that the semicircular part of the track can be described by r = h/ 2 , - π / 2 < θ < π / 2. Assume that the sliding along the track is frictionless. For the semicircular part of the track, determine: 1. The velocity ( v ) of the object as a function of θ , assuming that the object stays on the track. 2. The reaction force ( N ) that the track exerts on the object, assuming that the object stays on the track. 3. The angle at which the object will lose contact with the track and the velocity of the object at that time. 4. The maximum height reached by the object after it loses contact with the track and the velocity of the object at the maximum height.
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