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

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1 Name Rec. Section # / TA Name Physics 112 - Fall 2003 Final Exam Tuesday, December 16, 2003 Instructions and Info : 1. Pencils, pens and calculators are allowed, along with the provided equation sheet; books, notes, etc. are not allowed. 2. Use calculators only for calculating, not text/ equation storage, etc. 3. For the problems, show your work in the space provided so that the grader can understand the reasoning leading to your answers. If you don’t show your work, you will not get credit. For the short answer questions only the answers will be graded. 4. Try all of the problems – don’t get too hung up on any one. 5. Don’t give up if you have trouble with the first part of a problem. Often you can work the later parts even if you didn’t get the earlier parts. 6. Think about your answers – if they do not make physical sense, say so. You’ll get some credit for recognizing this. (You’ll get more for fixing whatever the problem is.) 7. Don’t forget to fill out your name, etc. above. 8. DO NOT GO TO THE NEXT PAGE UNTIL INSTRUCTED TO DO SO. "I am always doing that which I can not do, in order that I may learn how to do it." - Pablo Picasso Problem Score #1 15 #2 10 #3 10 #4 10 #5 10 #6 7 #7 8 #8 10 #9 8 #10 12 Total 100
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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
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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
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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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