PHYSICS 218 EXAM 3 Monday, November 19, 2007

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1 PHYSICS 218 EXAM 3 Monday, November 19, 2007 NAME: SECTION: Note: 525 Recitation Thurs 2: Recitation Tues 9: Recitation Thurs 3: Recitation Tues 12: Recitation Thurs 4: Recitation Tues 3: Recitation Thurs 5: Recitation Tues 6:55 There are a total of 7 problems on this test: Problems 1, 2, and 3 are worth 6 or 7 points each, as specified. For these three problems, points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. Problems 4, 5, 6, and 7 are worth 20 points each. For these four problems, partial credit will be awarded where appropriate. For all 7 problems: You must show your work and/or explain your reasoning to receive any credit for a problem; merely stating the answer is NOT sufficient. Write your final answer(s) in the blanks provided. You may use the backs of the pages for scratch calculations if you wish, but only the work in the spaces provided on the front of the pages will be graded. For numerical values, assume that all specified digits are significant, including trailing zeros. Also remember, an answer CAN NOT be completely correct if it has the wrong units or the wrong number of significant digits. MasteringPhysics for Chapters 8-11: G O O D L U C K!!!!! and H A P P Y T H A N K S G I V I N G!!!!!

2 For problems 1, 2, and 3, do your work in the space provided, and write your final answer in the blank. Points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. 1. (6 points) Four small spheres, each of which you can regard as a point of mass kg, are arranged in a square m on a side and connected by extremely light rods. Find the moment of inertia of the system about the line AB, which is in the plane of the square and passes through the center. Moment of inertia 2. (7 points) A thin-walled hollow sphere of mass M and radius R is rolling without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational? Fraction 3. (7 points) A hunter is initially at rest on a frozen, essentially frictionless pond. The hunter has a rifle that shoots 4.30-g bullets at 975 m/s. The mass of the hunter (including his gun) is 71.5 kg. The hunter fires the rifle horizontally, and holds tight to the gun after firing it. What is the final speed of the hunter? Speed

3 For problems 4, 5, 6, and 7, do your work in the space provided, and write your final answer in the blank. For these problems, partial credit will be awarded where appropriate, based on the work that you show. 4. (20 points) A diving board 3.00 m long is supported at a point 1.00 m from the end. A diver weighing 470 N stands at the free end, as shown in the figure below. The diving board is of uniform cross section and weights 270 N. Find (a) the force at the support point, and (b) the force at the left-hand end. Force at the support point Force at the left-hand end

4 5. (20 points) At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 930 kg traveling east on University collides with a maroon pickup truck with mass 1950 kg that is traveling north on Texas and ran a red light. The two vehicles stick together as a result of the collision, and the wreckage slides at 17.0 m/s in the direction east of north. Calculate the speed of each vehicle before the collision. (The collision occurs during a heavy rainstorm; you can ignore frictional forces between the vehicles and the wet road.) Speed of the car Speed of the pickup truck

5 6. (20 points) The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender, uniform rod pivoting about an axis through its center. When the skater s hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled, hollow cylinder. (See the figures below.) His hands and arms have a combined mass of 8.5 kg. When outstretched, they span 1.9 m; when wrapped, they form a cylinder of radius 27 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.38 kg m 2. If his original angular speed is 0.43 rev/s, what is his final angular speed? Angular speed

6 7. (20 points) In the figure below, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder, passes over the pulley, and has a 4.00-kg box suspended from its free end. There is no slipping between the rope and the cylinder or pulley surfaces. The uniform cylinder has mass 6.00 kg and radius 40.0 cm. The pulley is a uniform disk with mass 2.20 kg and radius 25.0 cm. The box is released from rest and descends as the rope unwraps from the cylinder. Find the speed of the box when it has fallen 1.50 m. Speed

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