PY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I

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1 PY205N Spring 2013 Final exam, practice version MODIFIED This practice exam is to help students prepare for the final exam to be given at the end of the semester. Please note that while problems on this practice exam have come from other sources and thus may be familiar, all final exams questions used in this course are newly constructed each semester. Thus students should not expect to memorize particular problems anticipating seeing them on the final. All problems on final exams (practice or otherwise) appeal to the same physical principles. The skills students develop in solving problems on a practice exam are identical to the skills needed to solve similar (but not identical) problems on the actual final exam. Data: Acceleration of gravity g = 9.8 m/s 2 ; gravitational constant G = N m 2 /kg 2 ; moments of inertia of thin rod about center, sphere, disc, and hoop: (1/12)mr 2, (2/5)mr 2, (1/2)mr 2, and mr 2, respectively; density of water ρ W = 1000 kg/m 3 ; 1 atm = N/m 2 ; (temperature in Kelvin) = (temperature in C) + 273; universal gas constant R = 8.31 J/(K mol); Boltzmann constant k B = J/K. 1. The sun is approximately a sphere of radius m. The surface area of the sun in km 2 is (a) km 2 (b) km 2 (c) km 2 (d) km 2 (e) km 2 2. Two bodies are falling with negligible air resistance, side by side, above a horizontal plane, when one of the bodies is subjected to a horizontal acceleration during its descent that continues until it lands. The correct statement of the following is: (a) The body strikes the plane at the same time as the other body (b) The body strikes the plane earlier than the other body (c) The vertical component of the velocity of the body is altered (d) The vertical acceleration component of the body is altered (e) The body follows a straight-line path along the resultant acceleration vector 3. The vectors a, b, and c are related by c = a b. The diagram below that best illustrates this relationship is (a) I (b) II (c) III (d) IV (e) none of these

2 4. Rain is falling vertically downward with a velocity of 2.0 m/s relative to the ground. A car drives horizontally through the rain. The driver of the car sees raindrops falling at an angle of 72 with respect to the vertical (slanting in at 18 from the horizontal). The speed of the car is (a) 1.9 m/s (b) 5.0 m/s (c) 0.62 m/s (d) 2.0 m/s (e) 6.2 m/s 5. The mass of a bedroom bureau that is loaded with clothing is m = 40 kg. If the coefficients of static and kinetic friction between the bureau and the floor are µ s = 0.46 and µ k = 0.23, respectively, the minimum horizontal force that is required to start the bureau sliding is (a) 4.5 N (b) 45 N (c) 90 N (d) 120 N (e) 180 N 6. A 1000 kg elevator is rising with a speed that is increasing at 3 m/s 2. The tension in the cable lifting the elevator is (a) 6800 N (b) 1000 N (c) 3000 N (d) 9800 N (e) N 7. A passenger weighing 800 N pushes against a car door with a force of 200 N when the car makes a left turn at 13 m/s. The (faulty) door will pop open at a force of 800 N. Supposing the same left turn but at a different speed, the least speed for which the passenger will get thrown out of the car is (a) 14 m/s (b) 19 m/s (c) 26 m/s (d) 36 m/s (e) 54 m/s

3 8. A 5.0 kg cart is moving across a frictionless horizontal surface at 6.0 m/s. In order to change its speed to 10 m/s, the minimum amount of work that must be done on the cart is (a) 40 J (b) 90 J (c) 160 J (d) 400 J (e) 500 J 9. A 1.5 kg crate falls from a height of 2.0 m onto a spring scale where the spring constant is N/m. Ignoring the small amount that the spring compresses when you calculate the gravitational potential energy, at the instant of maximum compression the scale reads (a) 15 N (b) 30 N (c) 1500 N (d) 2100 N (e) 3000 N 10. The diagram below shows a small ball of mass m = 0.45 kg attached to the end of a thin rod of length L = 0.5 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally, as shown, then given enough of a downward push so the ball can swing down and around, then reach the vertical position with zero speed there. The work that gravity did on the ball when it reaches its lowest point is (a) 2.2 J (b) 2.2 J (c) 4.4 J (d) 0.9 J (e) 0.9 J 11. The momentum of a particle is p = 5t 2 î 3 ĵ + 9t kˆ. The force as a function of time is (a) 5tî 3 ĵ + 9 kˆ (b) 10t î + 9 kˆ (c) 10tî 3 ĵ + 9 kˆ (d) 5t î + 9 kˆ (e) 10tî + 3 ĵ + 9t kˆ

4 12. A 5 kg ball collides with a 10 kg ball that is initially stationary. The collision is inelastic. If Δp 5 and Δp 10 are the magnitudes of the changes of momentum of the 5 and 10 kg balls, respectively, then (a) Δp 5 < Δp 10 (b) Δp 5 = Δp 10 (c) Δp 5 > Δp A wheel of an initial angular velocity ω = 18.0 rad/s is slowing at a rate of α = 2.0 rad/s 2. The angle through which it has turned by the time it stops is (a) 81 rad (b) 160 rad (c) 245 rad (d) 330 rad (e) 410 rad 14. A force of a given magnitude is applied to the rim of a wheel that is free to rotate about about a fixed axis through its center that is perpendicular to the plane of the wheel. The torque about the axle is maximized by applying the force (a) near the axle, radially outward from the axle (b) near the rim, radially outward from the axle (c) near the axle, perpendicular to a radius and in the plane of the wheel (d) at the rim, tangent to the rim and in the plane of the wheel (e) at the rim, at 45 to the tangent at that point and in the plane of the wheel 17. A hoop of moment of inertia I = mr 2 rolls along a level stretch of road without slipping. Its rotational kinetic energy is (a) half its translational kinetic energy (b) the same as its translational kinetic energy (c) twice its translational kinetic energy (d) four times its translational kinetic energy (e) one-third its translational kinetic energy 18. A 6.0 kg particle moves to the right at 4.0 m/s as shown. The magnitude of its angular momentum about the point O is (a) 0 kg m 2 /s (b) 288 kg m 2 /s (c) 144 kg m 2 /s (d) 24 kg m 2 /s (e) 249 kg m 2 /s

5 19. A woman is rotating on a frictionless stool with her arms by her side. She then extends her arms horizontally outward. Her rotational kinetic energy (a) increases (b) decreases (c) remains the same (d) may increase or decrease depending on her initial angular velocity (e) may increase or decrease depending on her initial angular acceleration 20. A uniform ladder is 10 m long and weighs 200 N. As shown in the figure below, the ladder leans against a frictionless wall. The point of contact with the wall is h = 8 m above the horizontal pavement. A horizontal force F = 25 N is applied to the ladder at a distance d = 2 m up the ladder from its base. The minimum coefficient of static friction µ s needed to keep the ladder from slipping out is (a) (b) (c) (d) (e) none of the above 21. A uniform plank is 6.0 m long and weighs 80 N. It is balanced on a support at its center. An additional 40 N weight is now placed on its left end. To keep the plank balanced, the plank must be moved to the right a distance of (a) 6.0 m (b) 1.5 m (c) 2.0 m (d) 0.5 m (e) 1.0 m 22. The masses of the moon and earth are m m = kg and kg, respectively, and their radii are r m = m and r e = m, respectively. Given these data, the weight on the moon of an object that weighs 100 N on the earth is (a) 16.5 N (b) 33.7 N (c) 24.1 N (d) 8.3 N (e) 1.7 N

6 23. In simple harmonic motion the magnitude of the acceleration is greatest when (a) the displacement is zero (b) the displacement is maximum (c) the speed is maximum (d) the force causing the acceleration is zero (e) the speed is somewhere between zero and its maximum 24. A 0.20 kg mass is attached to a spring with a spring constant k = 500 N/m and is executing simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is (a) m (b) 0.10 m (c) 0.20 m (d) 25 m (e) 250 m 36. You observe that it takes 16.0 J of energy to raise the temperature of a 200 g object by 10.0 C. The specific heat of the object is (a) J/kg K (b) J/kg K (c) 8.00 J/kg K (d) 1600 J/kg K (e) 115 J/kg K 39. A heat source supplies heat energy at a rate of 187 W to a system doing work at a rate of 131 W. The rate at which the internal energy of the system is changing is (a) 56 W (b) 318 W (c) 187 W (d) 56 W (e) 187 W

7 Key: 1a, 2a, 3c, 4e, 5e, 6e, 7c, 8c, 9e, 10a, 11b, 12b, 13a, 14d, 15b, 16b, 17b, 18c, 19b, 20a, 21e, 22a, 23b, 24b, 25c, 26e, 27b, 28d, 29e, 30d, 31e, 32c, 33b, 34a, 35b, 36c, 37a, 38e, 39a, 40c