Physics 201, Final Exam, Fall 2006 PRACTICE EXAMINATION Answer Key The next three problems refer to the following situation: Two masses, m 1 and m 2, m 1 > m 2, are suspended by a massless rope over a pulley (disk) 2 of mass m P and radius r P. ( I = m P r P / 2 ) At time t = 0, the masses are released from rest. m P m 1 m 2 1. The tensions T 1 (in the segment of rope attached to m 1 ) and T 2 (in the segment of rope attached to m 2 ) are related by a. T 1 < T 2 b. T 1 = T 2 c. T 1 > T 2 2. What is the initial acceleration, a, of m 1 (take down as the positive direction)? ( m + m ) 1 2 a. a = g mp b. a = ( m1! m2 ) g m p c. a = ( m! m ) 2 1 2 2 m d. a = 1! m 2 g m p + 2m 1 + 2m 2 g ( ) e. a = m p 2 g
3. In terms of the acceleration, a, what is the work, W, done on the pulley for the period t = 0 to t = t 1? 2! a$ 2 a. W = m p " # 2% & t 1 ( m 2 b. 1! m2 ) W = at1 mp c. W = m1arp The next two problems refer to the following situation A string is wrapped around a disk of radius R (I=1/2 MR 2 ) that sits on a frictionless incline with angle θ as shown. The string is pulled up the plane with tension T in such a way that it unwinds without slipping from the disk and the disk rolls without slipping down the incline. M T θ 4. What is the linear acceleration, a, of the disk down the plane? a. a = 2 3g sin! b. a = 3 2g sin! c. a = 1 2g sin! d. a = 5 3g sin! e. a = g tan!
5. If the tension, T, exceeds Mgsin! a. the disk will move up the plane while spinning. b. the disk will move down the plane but not obey v=wr. c. the disk will spin in place. 6. During simple harmonic motion, there is no time at which the position, velocity, and acceleration all have the same sign (+,-, or 0). (T) True (F) False The next three problems refer to the following situation: A block of mass m = 0.5 kg slides initially without friction in a circular path on a horizontal table top with angular momentum L i = 4.7 kg m 2 /s as shown in the figure below. The initial radius of motion is r i = 0.41 m. m 7. If the string is pulled down, reducing the radius to r f = 0.19 m, what is the final angular speed, ω f? a. ω f = 97 rad/s b. ω f = 116 rad/s c. ω f = 130 rad/s d. ω f = 180 rad/s e. ω f = 260 rad/s
8. How much work, W, must be done in decreasing the radius to r f above? a. W = 96.1 J b. W = 227 J c. W = 340 J d. W = 480 J e. W = 546 J 9. If someone now sprinkled sand on the table (causing friction) and it was observed that the angular momentum of the block decreased to 3.9 kg m 2 /s over the first 0.5 seconds, what is the average torque, τ avg, on the block over that time? a. τ avg = 0.18 N m b. τ avg = 0.80 N m c. τ avg = 1.6 N m 10. A pitcher throws a ball past a stationary batter. If the ball has no spin and is thrown straight, then the ball has no angular momentum with respect to the batter. (T) True (F) False 11. A rotating object necessarily has a net torque on it. (T) True (F) False 12. A rotating object necessarily has a net force on it. (T) True (F) False
The following two problems refer to the situation described below: A block of mass 5 kg is placed on top of a block of mass 10 kg, which in turn sits on a frictionless horizontal surface, as shown in the figure. A force F = 98 N is applied to the 10 kg block, and the 5 kg block is held in place by a string attached to the wall. The coefficient of friction between the two blocks is 0.15. 13. What is the tension in the string? (a) 45.0 N (b) 7.35 N (c) 0 N (d) 27.2 N (e) 55.7 N 14. What is the acceleration of the 10 kg block? (a) 2.72 m/s 2 (b) 9.06 m/s 2 (c) 19.06 m/s 2 (d) 3.42 m/s 2 (e) 1.56 m/s 2 15. If you double the amplitude of a simple harmonic oscillator, the period of the oscillator (a) decreases by a factor of 2 (b) decreases by a factor of 2 (c) does not change (d) increases by a factor of 2 (e) increases by a factor of 2
16. A glider on an air track is attached to one end by a spring. If it takes 0.30 sec for the glider to travel the distance of 12 cm from one turning point to the other, its amplitude is: (a) 12 cm (b) 6 cm (c) 24 cm (d) 3.6 cm (e) not enough information 17. A pine tree in a high wind sways back and forth. You note that every 5 sec it is exactly upright. The frequency of this oscillation is: (a) 5 Hz (b) 10 Hz (c) 0.2 Hz (d) 0.1 Hz (e) 6.28 Hz 18. A magnesium atom (molar mass is 24 gm) in a crystal is measured to oscillate with a frequency of about 10 13 Hz. What is the effective spring constant of the forces holding that atom in the crystal? (a) 158 N/m (b) 1.6 x 10 3 N/m (c) 16 N/m (d) 4 x 1013 N/m (e) 6.28 Hz
19. What would be the natural oscillation period of a 30 kg child on a swing whose seat is 3.2 m below the bar from which the chains of the sear are attached? (a) 5.5 s (b) 6.28 s (c) 1 s (d) 3.14 sec (e) 3.6 s 20. Refer to the points A-D marked in the figure below. At which of those points is the pressure maximum? A. Point A B. Point B C. Point C D. Point D E. Pressure is the same at all four of those points 21) The pressure on the roof of a tall building is 0.985 x 10 5 Pa and the pressure on the ground is 1.000 x 10 5 Pa. The density of air is 1.29 kg/m 3. What is the height of the building? A. 100 m B. 118 m C. 135 m D. 114 m E. None of the above
22) Refer to the figure below. What can you conclude about pressure P in the bulb and the atmospheric pressure P 0? (The tube is filled with mercury with density ρ Hg ) A. P < P 0 B. P = P 0 C. P = ρ Hg g h D. P = ρ Hg g h + P 0 E. None of the above 23) Which of the following statements is false about Bernoulli's equation (BE)? A. BE is a consequence of conservation of energy B. BE is applicable for any flow speed, v C. BE is applicable in a space ship D. BE is applicable even if the net work done by the fluid is zero E. BE is applicable even when viscosity of fluid is large
24) A bullet strikes a ballistic pendulum as shown in the figure. If the mass of the wooden block with embedded bullet is measured to be 0.50% larger than original and the pendulum swings up by 5.00 cm, what is the speed of the bullet when it struck it? A. ~100 m/s B. ~200 m/s C. ~250 m/s D. ~500 m/s E. It is not possible to determine the answer with the information provided. 25. The acceleration of any object sliding down an incline that makes an angle θ with the horizontal is (µ k is the coefficient of kinetic friction) A. g cos θ µ k g sin θ B. g sin θ µ k g cos θ C. g tan θ µ k g cot θ D. g cot θ µ k g tan θ E. Not possible to compute without knowing the mass of the object