PHYSICS 218 FINAL EXAM Friday, December 11, 2009

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1 PHYSICS 218 FINAL EXAM Friday, December 11, 2009 NAME: SECTION: Note: 525 Recitation Wed 9:10-10: Recitation Wed 11:30-12: Recitation Wed 1:50-2: Recitation Mon 11:30-12:20 There are a total of 12 problems on this test: Problems 1 through 4 are worth 5 points each. For these four 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 5 through 12 are worth 10 points each. For these seven problems, partial credit will be awarded where appropriate. For all 12 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. G O O D L U C K and H A P P Y H O L I D A Y S!!!!

2 For problems 1-4, 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. In the fastest measured tennis serve, the ball left the racquet at m/s. Assume the tennis ball started from rest and was in contact with the racquet for 29.0 ms, during which time it experienced constant acceleration. How far did the ball travel while in contact with the racquet? Distance A 2. Consider the system shown in the figure below. Block A weights 48.0 N, block B weights 23.0 N, and the pulley is massless. Once block B is set in downward motion, it descends at a constant speed. Calculate the coefficient of kinetic friction between block A and the tabletop. Coefficient of friction 3. A 55.0-g mass moves on the end of a spring with force constant k = 23.0 N/m. Its initial displacement is m. A damping force F x = -bv x acts on the mass, and the amplitude of the motion decreases to m in 5.00 s. Calculate the magnitude of the damping constant b. Damping constant 4. A 3.00-m long, 260-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends, as shown in the figure below. A 110-N howler monkey hangs motionless m from the right end of the rod. Calculate the tension in the left-hand rope. Tension

3 For problems 5-12, 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. 5. A physics book slides off a horizontal tabletop with a speed of 1.20 m/s. It strikes the floor in s. Ignore air resistance. Find: (a) The height of the tabletop above the floor, (b) The horizontal distance from the edge of the table to the point where the book strikes the floor, (c) The magnitude and direction of the book s velocity, just before it reaches the floor. Height Horizontal distance Magnitude Direction A

4 6. A wire with mass 40.0 g is stretched so that its ends are tied down at points 85.0 cm apart. The wire vibrates in its second harmonic mode with frequency Hz and with an amplitude at the antinodes of cm. (a) What is the speed of propagation of transverse waves in the wire? (b) Compute the tension in the wire. (c) Find the maximum transverse velocity and acceleration of particles in the wire. Speed Tension Velocity Acceleration

5 7. Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! (a) With what speed would you need to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it? (b) How long (in hours) after throwing the ball should you be ready to hit it? Speed Time

6 8. A box is sliding with a speed of 4.75 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of kinetic friction is not constant. Rather, it starts at at P and increases linearly with distance past P, reaching a value of at 20.0 m past point P. (a) Find how far this box slides before stopping. (b) How far would the box have slid if the friction coefficient didn t increase, but instead had the constant value of Distance (a) Distance (b)

7 9. A thin-walled hollow sphere with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the sphere so that the sphere can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string. The string doesn t slip over the pulley surface, and the sphere rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest. Acceleration

8 10. A movie stuntman (mass 80.0 kg) stands on a window ledge 5.0 m above the floor. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie s villain (mass 70.0 kg), who is standing directly under the chandelier. (Assume that the stuntman s center of mass moves downward 5.0 m.) The stuntman releases the rope just as he reaches the villain. The two movie characters become intertwined and slide across the floor together. If the coefficient of kinetic friction between their bodies and the floor is 0.200, how far do they slide? Distance

9 11. In the figure below, a uniform rod of mass M and length L hangs vertically downward from a frictionless pivot, which allows the rod to swing freely in the plane of the paper. The lower end of the rod is attached to the neighboring wall by a horizontal, massless spring, with spring constant k. The spring is at its equilibrium length when the rod is hanging straight downward. The rod is displaced to the right of its equilibrium position by a small amount (so that small-angle approximations apply), and released from rest. Find the frequency of the subsequent motion. Frequency

10 12. The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. Assume the height of the block is very small compared to all other distances in the problem. When the system rotates about the axis of the rod, the strings are extended as shown in the figure and the tension in the upper string is 85.0 N. (a) What is the tension in the lower cord? (b) How many revolutions per minute does the system make? Tension Revolutions

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