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sp03mech_sol

# sp03mech_sol - PHY6938 Proficiency Exam Spring 2003...

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Unformatted text preview: PHY6938 Proficiency Exam Spring 2003 March 28, 2003 Mechanics 1. The drum of a winch has a mass M and a radius R . A cable wound around the drum suspends a load of mass m . The entire cable has a length L and a density (mass per unit length) λ , with a total mass m c = Lλ . The load starts from rest, at the bottom of the winch, and begins to fall toward the ground, unwinding the cable as it moves. mass=M R m d (a) Write an expression for the change in potential energy of the load and the cable that has been paid out from the drum, between the initial situation and when the load has fallen a distance d . To find the potential, it is useful to choose a reference level or point for which the potential is zero. This selection of the reference point is arbitrary. But it always helps to choose a point which make the solution easier. Below that point the potential energy has negative value and above that point the potential energy is positive. In this problem the center of the drum is chosen as the point with potential energy V = 0. With this choice the potential energy of the drum and the part of the cable wrapped around the drum will be zero. When the V=0 m M d=0 R load is at the highest level, its potential energy is given by V l- initial =- mgR. (1) The initial potential energy of the cable is V c- initial = 0 . (2) When the load has fallen a distance d the final potential energy of the load is V l- final =- mg ( R + d ) . (3) The final potential energy of the cable can be obtained as following. Since the cable is homogeneous the center of the mass of the part paid out from the drum is located at the center of this part.drum is located at the center of this part....
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sp03mech_sol - PHY6938 Proficiency Exam Spring 2003...

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