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Final_Fall03

# Final_Fall03 - Name Rec Section TA Name Problem Score...

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2 Problem 1 Short Problems (15 points) (a) A small child of mass m runs horizontally at speed v o onto a swing of the same mass m , initially at rest. What is the maximum height the child + swing reach as they swing to the right and up? Your answer may contain m, v o , and numerical or physical constants. H = _____ (b) A wooden block of mass M lies on a ramp slanted at an angle θ from the horizontal. With what minimum force F normal to the ramp should the block be pressed against the ramp so that it will slide down the ramp at a constant speed? The coefficients of static and kinetic friction between the block and the ramp are μ s and μ k , respectively. Assume the ramp is fixed in place. Your answer may contain M , μ s , μ k , θ , and numerical or physical constants. F = _________________________ m v o H m θ F
3 (c) A 25 kg mass just barely fits inside a water-filled cylinder and makes a watertight, but frictionless, seal. The cross-sectional area of the cylinder is A = 0.1 m 2 . A small hole exists in the cylinder 1 meter below the mass. Find the velocity of the water leaving the hole. v = _______________________ 25 kg 1 m v A = 0.1 m 2

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4 Problem 2 (10 points) A pendulum consists of two uniform slender rods glued together in a straight line. The length and mass of the upper rod is L and M and of the lower rod is L and 2 M . (a) What is the moment of inertia for the pendulum if it pivots about the end of the upper rod? I = ___________________________ (b) What is the period T of the pendulum for small oscillations? T = ______________________ L L M 2M
5 Problem 3 (10 points) You are asked by the King to determine if her crown is made of pure gold or a mixture of gold and silver. (This is the problem Archimedes was once given.) The crown has a mass M C = 5.0 kg. When you suspend the crown from a spring balance and submerge it completely in water, the balance reads 46 N. The density of water, gold, and silver are ρ w = 1.0 x 10 3 kg/m 3 , ρ G = 20 x 10 3 kg/m 3 , and ρ S = 10 x 10 3 kg/m 3 , respectively.

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