( ) Physics 201, Final Exam, Fall 2006 PRACTICE EXAMINATION Answer Key. The next three problems refer to the following situation:

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1 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 ) m d. a = 1! m 2 g m p + 2m 1 + 2m 2 g ( ) e. a = m p 2 g

2 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!

3 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

4 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

5 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 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) m/s 2 (d) 3.42 m/s 2 (e) 1.56 m/s 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

6 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 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.

7 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 x 10 5 Pa and the pressure on the ground is 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

8 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

It is not possible to determine the answer with the information provided. 25.

9 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

Figure 1 Answer: = m

Figure 1 Answer: = m Q1. Figure 1 shows a solid cylindrical steel rod of length =.0 m and diameter D =.0 cm. What will be increase in its length when m = 80 kg block is attached to its bottom end? (Young's modulus of steel