PHYSICS 218 FINAL EXAM Monday, December 13, 2010
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1 PHYSICS 218 FINAL EXAM Monday, December 13, 2010 NAME: 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 12 problems on this test: Problems 1 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 12 are worth 10 points each. For these eight 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 a n d 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. (5 points) At the instant a traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.70 m/s 2. At the same instant, a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. How far beyond its starting point does the car overtake the truck? Distance 2. (5 points) A person pulls horizontally on block in the figure below. oth blocks A and are seen to move together toward the right. The coefficient of static friction between block and the table is The coefficient of kinetic friction between block and the table is To the right of the figure, draw a free-body diagram for block that would satisfy an Engineering professor. 3. (5 points) In the figure below, the crate full of priceless art objects has a weight w. The diagonal strut is uniform, and also has weight w. The strut is attached to the wall by a frictionless pivot. Find the tension in the horizontal cable. Tension 4. (5 points) In the figure below, your physics professor is demonstrating standing waves on a rope. The rope is 5.0 m long, and has a mass of 1.5 kg. The power drill that is twirling the rope is rotating at 340 rpm. What is the tension in the 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. (10 points) A daring 520-N swimmer dives off a cliff with a running horizontal leap, as shown in the figure. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom? You can ignore air resistance. Speed
4 6. (10 points) A 57-kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axle through its center. The runner s velocity relative to the earth has magnitude 2.9 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.20 rad/s relative to the earth. The radius of the turntable is 3.0 m, and its moment of inertia about the axis of rotation is 75 kg m 2. Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can model the runner as a particle.) Angular velocity
5 7. (10 points) An 8.75 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 2.25 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 8. (10 points) Adjacent antinodes of a standing wave on a string are 12.5 cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude cm and period s. The string lies along the +x axis, and is fixed at x=0. (a) Find the displacement of a point on the string as a function of position and time. (b) Find the speed of propagation of a transverse wave on the string. (c) Find the amplitude at a point 3.00 cm to the right of an antinode. Displacement Speed Amplitude
7 9. (10 points) A 2.00 kg package is released on a incline, 4.00 m from a long spring with force constant 110 N/m that is attached at the bottom of the incline. The coefficients of friction between the package and the incline are μ s = and μ k = The mass of the spring is negligible. (a) What is the speed of the package just before it reaches the spring? (b) What is the maximum compression of the spring? Speed Compression
8 10. (10 points) The figure below shows a Giant Swing. The seat is connected to two cables. The support post is vertical, and the 7.50 m cable is horizontal. The seat swings in a horizontal circle at a rate of 31.5 rpm. Assume the seat weighs 165 N and the person sitting in it weighs 830 N. Find the tensions in the two cables. Tension in diagonal cable Tension in horizontal cable
9 11. (10 points) A landing craft with mass 12,250 kg is in a circular orbit 5.25 x 10 5 m above the surface of a planet. The period of the orbit is 5800 s. The astronauts in the lander measure the diameter of the planet to be 9.40 x 10 6 m. The lander sets down at the north pole of the planet. What is the weight of an 85.0 kg astronaut as he steps out onto the planet s surface? Weight
10 12. (10 points) A square object is constructed of four identical uniform thin sticks, each of length L and mass m, attached together. The object is hung from a hook at its upper corner, as shown in the figure below. If the object is rotated slightly from its equilibrium position and then released, what will be the period of the subsequent oscillatory motion? Period
11
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