PHYSICS 218 EXAM 3 Monday, November 22, 2010

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1 PHYSICS 218 EXM 3 Monday, November 22, 2010 NME: SECTION: Note: 513 Recitation & lab Wed 8:00-10:50 am 514 Recitation & lab Wed 11:30 am - 2:20 pm 515 Recitation & lab Wed 3:00-5:50 pm 516 Recitation & lab Wed 6:10-9:00 pm There are a total of 7 problems on this test: Problems 1, 2, and 3 are worth 6 or 7 points each. 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. lso remember, an answer CN NOT be completely correct if it has the wrong units or the wrong number of significant digits. G O O D L U C K!!!!!

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 connected by massless rods to form a square m on a side. Find the moment of inertia of this system about an axis that crosses the diagonal of the square and passes through two of the spheres, as shown in the figure below. Moment of inertia 2. (7 points) linebacker tackles a fullback on a very muddy football field. Each of the two players has a mass of 100 kg. Immediately before the collision, the linebacker is slipping with a velocity of 8.9 m/s north and the fullback is sliding with a velocity of 7.3 m/s east. What direction do the two players move together immediately after the tackle? Direction 3. (7 points) grindstone in the shape of a solid disk with diameter m and a mass of 55.0 kg is rotating at 850 rev/min. You press an ax against the rim, and the grindstone comes to rest in 7.50 s. Find the friction force between the ax and the grindstone. You can ignore friction in the bearings. Friction force

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) diving board 3.00 m long is supported at a point 1.00 m from the end. diver weighing 480 N stands at the free end, as shown in the figure below. The diving board is of uniform cross section and weights 260 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) Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum from which it is hanging by a thin, very light wire wrapped around the rim. There is no appreciable friction in the axle of the drum, the wire does not slip on the surface of the drum, and everything starts from rest. This system is being tested on earth, but is to be used on Mars, where the acceleration due to gravity is 3.71 m/s 2. In the earth tests, when m is set to 16.0 kg and allowed to fall through 5.70 m, it gives J of kinetic energy to the drum. (a) If the system is operated on Mars, through what distance would the 16.0 kg mass have to fall to give the same amount of kinetic energy to the drum? (b) How fast would the 16.0 kg mass be moving on Mars just as the drum gained J of kinetic energy? Distance Speed

5 6. (20 points) n 8.50 kg ball is hanging from the ceiling by a light wire 140 cm long. The ball is initially at rest. It is struck in an elastic collision by a 2.50 kg ball, which is moving horizontally at 5.00 m/s just before the collision. Find the tension in the wire just after the collision. Tension

6 7. (20 points) uniform, solid sphere with mass 2.00 kg rolls without slipping down an incline plane that makes a angle with the horizontal. Find the acceleration of the center of the sphere, the friction force, and the minimum coefficient of friction needed to prevent slipping. cceleration Friction force Coefficient of friction

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