# 1. When the terminal velocity is reached, what is the acceleration of mass m 2?

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1 N3) Masses m 1 and m 2 are connected by a massless rope slun over a massless, frictionless pulley. Assume m 2 >m 1. The pulley and the masses are inside a vat containin water, and each of the masses experiences a dra force equal in manitude to F DRAG = bv 2 ; b is the same for both masses. The dra forces cause the masses to reach a terminal velocity, v T. You may nelect any effects due to buoyancy. 1. When the terminal velocity is reached, what is the acceleration of mass m 2? a. The acceleration of m 2 is upward. b. The acceleration of m 2 is downward. c. The acceleration of m 2 is zero. 2. Find an expression for the terminal velocity, v T. a. v T 2 m 2 m1 2b b. v T m 2 m1 2b c. v T m 2 m1 2b d. v T m 2 m1 b e. v T m 2 m1 b

2 N5) A block M 1 with mass 3k sits atop a frictionless inclined plane. The inclined plane is at an anle of =30 from the horizontal. Block M 1 is connected to block M 2 (mass=2k) throuh a massless strin around an ideal, frictionless pulley. M 1 =3k 1. Which way is block M 2 acceleratin? A. upwards B. downwards C. it is not movin =30 M 2 =2k 2. With a defined as the manitude of the acceleration ( a ³ 0 ) and = m/s 2, which is the correct expression for the manitude of the tension in the strin? A. 0 N B. M 2 (-a) C. M 2 (a+) D. M 2 a/(a+) E. M 1 sin

3 N7) Two blocks A and B are connected by a strin named strin 2. A hand pulls strin 1, which is attached to block A, so that the blocks move upward and radually slow down. The strins remain taut at all times. Assume the strins are massless and do not stretch. The mass of block B is reater than that of block A. 1. Three students drew the free-body diarams below for block A. Choose the diaram that is most nearly correct. Tension in strin 1 Tension in strin 2 Pullin force of hand Weiht of block B Tension in strin 1 A B strin 1 strin 2 Weiht of A Weiht of A Weiht of A (a) (b) (c) 2. Is the upward force on block B by strin 2 reater than, less than, or equal to the weiht of block B? (a) reater than (b) less than (c) equal to

4 N8) Two masses m and 4m are connected by a strin that runs over a massless pulley. The pulley can either be locked in place so that it cannot rotate or unlocked to allow it to rotate freely. The pulley is suspended from a force probe, much like one used in Phys 211 Lab 2, which measures the upward force on the pulley. The force probe reads a positive force when it is pulled. y pulley Force probe x strin 4m m 1. What will the force probe read when the pulley is locked and the whole system is motionless? a. m b. 2m c. 3m d. 4m e. 5m 2. Which of the followin statements best describes the tension in the strin T when the pulley rotates freely? a. T > m b. T = m c. T < m

5 N16) A satellite is put into a uniform circular orbit around the earth. The radius of the satellite s orbit is R s = 6.3 x10 7 m (measured from the center of the earth). The satellite has a mass of 145 k. G=6.7x10-11 m 3 k -1 s -2 M e =6.0x10 24 k R e =6.4x10 6 m Earth: mass M e R e R s satellite mass = 145 k 1. What is the period of the satellite s orbit? (Note: 1 day = 86,400 s) A. 0.2 days B. 1.0 days C. 1.8 days D. 4.7 days E days 2. Suppose the satellite were in orbit about the moon (M moon = M earth /81 ). At what radius, compared to R s above, would the satellite have the same orbital period as in the previous problem? A. R = 81R s B. R = R s /9 3 C. R = Rs 81

6 N19) A roller coaster car of mass m is at the top of a loop-the-loop section of the track as shown in the diaram. 1. What speed, v, is required for the roller coaster car to have a normal force exerted on it by the track which is equal to the car s weiht? Note that this normal force acts in the direction of. v r a. v r / m b. v r c. v 2r d. v r / 2 e. v 0 2. If the speed of the car is twice as lare as v calculated above, the manitude of the normal force is a. larer than the car s weiht. b. equal to the car s weiht. c. smaller than the car s weiht.

7 N27) A block of mass m = 0.5 k rests on top of a block of mass M = 2.0 k. A strin attached to the block of mass M is pulled so that its tension is T = 6.0 N at a 20 o anle to the horizontal as shown. The blocks move toether. The coefficient of static friction at the surface between the blocks is s = 0.4; there is no friction at the surface between block M and the floor. s = 0.4 m M 20 T = 0 1. What is the acceleration, a, of the two-block system? a. a = 1.63 m/s 2 b. a = 2.26 m/s 2 c. a = 3.18 m/s 2 d. a = 3.72 m/s 2 e. a = 4.89 m/s 2 2. The tension T is now increased - what is the maximum tension, T max, with which the strin can be pulled such that the blocks continue to move toether (i.e. that the block of mass m does not start to slide on top of the block of mass M)? a. T max = 7.67 N b. T max = 8.31 N c. T max = 8.94 N d. T max = 9.36 N e. T max = N

8 N28) Two blocks of mass m = 2 k and M = 5 k are positioned as shown on top of an inclined plane. There is no friction at the surface between the two blocks, but there is friction on the surface between the lare block and the incline. The strin attached to the block of mass m is parallel to the incline. The system is in equilibrium with both blocks stationary. = 0 s = What are the forces exerted on each block? a. Forces on m: Tension, weiht Forces on M: Weiht, friction, normal force due to incline, normal force due to m b. Forces on m: Tension, weiht, friction Forces on M: Weiht, friction, normal force due to incline, normal force due to m c. Forces on m: Tension, weiht, normal force due to M Forces on M: Weiht, friction, normal force due to incline, normal force due to m d. Forces on m: Tension, weiht, normal force due to M Forces on M: Weiht, friction, normal force due to incline e. There are no forces on either mass because they are both in equilibrium m 30 o M 2. What is the manitude of the net force, F net, on the block of mass m? a. F net = 0 N b. F net = 9.8 N c. F net = 12.3 N d. F net = 19.6 N e. F net = 47.3 N

9 E3) The next two questions relate to the followin situation In lab 4 a cart of mass M = 700 is attached to a sprin with force constant k = 3 N/m and suspended on a frictionless incline plane that makes a 30 anle with respect to the horizontal. With the sprin in the unstretched position, the cart is released from rest at x = 0. motion detector k M 1. What is the maximum extension of the sprin when the cart is at its lowest point on the incline? x=0 x 30 a. 1.1 m b. 3.8 m c. 4.5 m d. 1.7 m e. 2.3 m 2. For what value of x does the cart have the larest kinetic enery? a. 1.1 m b. 0.5 m c. 2.3 m d. 5.2 m e. 0.9 m

10 E8) The next two questions refer to the followin situation. A block is on a plane inclined at an anle = 30 from the horizontal. The coefficient of the kinetic friction between the block and the incline is k = A force is applied alon the incline to a block of mass m = 2 k as shown in the fiure, and the mass moves up the incline at constant velocity v = 2 m/s. 1. How much work does force F do in 0.6 seconds? a J b J c J d J e J 2. Considerin all forces actin on the block, which force does zero work on the block? a. The normal force of the incline b. The ravitational force of the Earth c. The friction force between the block and the incline

11 E11) The next two problems concern identical blocks that initially have the same velocity V at the bottom of two ramps. The first ramp inclined at a shallower anle ( 1 ) with respect to the horizontal than the second ramp ( 2 ). The maximum heihts reached by the blocks are h 1 and h 2, respectively. V V 1. Assume that both ramps are frictionless. Which statement is most correct concernin the maximum heihts reached by the blocks? a. h 2 = h 1 b. h 2 > h 1 1 h 1 2 h 2 c. h 2 < h 1 2. Now assume instead that in both cases there is the same (non-zero) kinetic coefficient of friction between the blocks and the ramps. Which statement is most correct concernin the maximum heihts reached by the blocks? a. h 2 = h 1 b. h 2 > h 1 c. h 2 < h 1

12 E13) The next two questions are about the followin situation: 2m h? A small box of mass M=10 k is released from rest at a heiht of 2 meters on a frictionless incline as shown. At the bottom of the ramp, it encounters a 1 meter lon rouh surface with k =0.25, and then a frictionless circular rise. 1. At what heiht, h, does the box stop on the circular rise? a. 2 meters b meters c meters d meters e. 1.0 meters 1m 2. Compare the manitude of the work done by ravity to the manitude of the work done by friction in the above problem at the moment when the mass has reached its maximum heiht, h, on the circular rise. a. W ravity > W friction b. W ravity < W friction c. W ravity = W friction

13 E14) The next two questions are about the followin situation: A 6 k box is pulled across a rouh floor by a rope. There is friction between the box and the floor. The tension in the rope is T=5 N. Consider a time interval durin which the box moves a distance of 2 m, and its velocity decreases from 1.5 m/s to 0.8 m/s. v T 1. How much work is done on the box by the rope? a. 0 J b. 10 J c. -10 J 2. How much work is done on the box by friction? a J b J c J d J e J

14 E15) The next two questions are about the followin situation: A 6 k box is pulled across a horizontal floor by a rope. The tension in the rope is T = 5 N. Consider a time interval durin which the velocity of the box increases from 0.8 m/s to 1.5 m/s. v T 1. If the floor is frictionless, how far has the box moved? a m b m c m d m e m 2. Suppose now that there is friction between the box and the floor. The box now has to be pulled for 2 m to increase its speed from 0.8 m/s to 1.5 m/s (still with tension T = 5N). How much work is done on the box by friction? a Joules b Joules c Joules d Joules e Joules

15 E17) The next two questions are about the followin situation: A planet of mass M and radius R and a smaller planet of radius R/2 and mass M/8 are separated by a distance 6R between their centers. M 6R R R/2 1. Where is the center of mass of this two-body system with respect to the center of the larer planet? a. R/3 b. R/2 c. 2R/3 d. 5R/6 e. R 2. If a missile is launched from the north pole of the larer planet, what is the escape velocity, V, for the missile (takin into account the ravitational force from both planets)? a. V < b. V = c. V > 2GM R 2GM R 2GM R

16 E20) The next two problems refer to the followin situation: A block of mass m=100 is launched horizontally on a frictionless track by compressin a sprin of constant k=78n/m. After 1m (from the position of the sprin at equilibrium) the track turns upward at a 30 anle as shown in the fiure below. The heiht difference between the lower and upper level is 1.4m. 1. If you compress the sprin by a distance of 20cm, what is the horizontal rane of the block x shown in the fiure? a. 12cm b. 33cm c. 67cm d. 93cm e. 123cm 2. Let x be the answer to the previous question. If there is friction between the track and the block, the horizontal rane of the block is now: a. reater than x b. equal to x c. smaller than x

17 P1) The next three questions refer to the followin situation A frictionless ramp of mass 3m is initially at rest on a horizontal frictionless floor. A small box of mass m is placed at the top of the ramp and then released from rest. After the box is released, it slides down the ramp and onto the horizontal floor, where it is measured to have a speed v, havin fallen a total distance h. 1. What is the speed V of the ramp after the box has left the ramp? A. 3h 1 B. 6 h 1 C. 3 h D. 6h 1 E. 2 h 2. If there were kinetic friction between the ramp and the floor, but none between the block and the ramp, the speed V of the ramp after the box has left the ramp, compared to its speed when both the ramp and the floor are frictionless, would be A. Less B. The same C. More

18 P3) The next three questions are about the followin situation: A 5 k block slides on a horizontal, frictionless surface with a velocity of 2 m/s. It collides with an ideal, massless sprin which is attached to a 15 k block which is initially at rest. The sprin has a sprin constant of k = 50 N/m. 1. At the instant the sprin is maximally compressed, both masses will be travelin with a common velocity of a m/s b. 0.5 m/s c. 1 m/s d. 1.5 m/s e. 2 m/s 2. When the sprin is maximally compressed, how do the manitudes of the acceleration of the two blocks compare? a. The acceleration of the 5 k block is 3 times the acceleration of the 15 k block. b. The acceleration of the 15 k block is 3 times the acceleration of the 5 k block. c. The acceleration of the 5 k block equals the acceleration of the 15 k block.

19 P7) The next two questions are about the followin situation: A block of mass M 1 slides on a horizontal, frictionless surface with a velocity of V 1. It collides with an ideal, massless sprin which is attached to a block of mass M 2 which is initially at rest. The sprin has a sprin constant of k = 20 N/m. 1. At the instant the sprin is maximally compressed, both masses will be travelin with a common velocity, V, of a. M 1 V 1 / M 2 b. M 1 V 1 / (M 1 +M 2 ) c. (M 1 +M 2 )V 1 / M 1 2. Assumin M 1 = 5 k, M 2 = 25 k, and V 1 = 3 m/s, what is the maximal compression of the sprin durin the collision? a m b m c m

20 P11) The next two questions refer to the followin situation A car of mass 2000 k is travellin alon a straiht road at 60 km/hr. It collides completely inelastically with another car, of mass 2600 k, that is initially stationary in the middle of the road. 1. What is the ratio of the final kinetic enery of the two-car system after the collision to its initial kinetic enery? A. 10/13 B. 13/20 C. 23/10 D. 13/23 E. 10/23 2. What is the speed, in km/hr, of the two cars (stuck toether) immediately after the collision? A B C D E. 15.3

21 P13) The next two questions refer to the followin situation: A pendulum is made by attachin a piece of putty of mass 0.24 k to the end of a massless strin of lenth L = 1 m. The putty is swun out until it is at a heiht h = 0.2 m above the round and released from rest. When the putty is at the lowest point in the swin, it collides with and sticks to another, stationary piece of putty of mass 0.36 k, and the resultin mass of putty continues swinin to the riht. L=1 m 1. What is the kinetic enery, K, of the pendulum just before it strikes the putty restin on the round? a. K = 0.34 J b. K = 0.39 J c. K = 0.47 J d. K = 0.53 J e. K = 0.87 J m=0.24 K h=0,2 m m=0.36 K 2. How does the new maximum heiht reached by the center of mass of the two-putty system, H, compare to the oriinal heiht h? a. H = (0.16)h b. H = (0.24)h c. H = (0.08)h d. H = (0.44)h e. H = (0.12)h

22 P14) The next four questions refer to the followin situation. Consider the followin two cases: v 0 v 0 m v f M V 1 m M V 2 Case 1 Case 2 In case 1 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is movin to the riht with V 1 and the ball is movin to the left with speed v f. In case 2 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is movin to the riht with speed V 2. In both cases the box slides without friction. Assume all motion is horizontal. 1. In case 2 it is observed that V 2 = v 0 /3. What is the ratio of masses M/m? a. M/m = 1/2 b. M/m = 3/4 c. M/m = 4/3 d. M/m = 3/2 e. M/m = 2 2. In case 1 it is observed that v f = v 0 /2. What V 1 /v 0? a. V 1 /v 0 = 3M/2m b. V 1 /v 0 = 2M/3m c. V 1 /v 0 = 3m/2M d. V 1 /v 0 = 2m/3M e. V 1 /v 0 = m/2m

23 P15) The next two questions are about the followin situation: A small steel ball of mass 2 k is attached to the end of a massless strin of lenth 0.5 m which is fixed at the opposite end. The strin is pulled taut and held horizontally, as shown above. The ball is then released from rest. At the bottom of the path, the ball strikes a steel block of mass 6 k initially at rest on a horizontal frictionless surface. x 1. What is the speed of the steel ball just before the collision? a m/s b m/s c m/s d m/s e m/s 2. In the x-direction, if the velocity of the ball just before the collision is v and the velocity of the ball just after the collision is -v/3, what is the velocity of the block just after the collision? a. 4v/9 b. 2v/3 c. 3v/4 d. 3v/2 e. v

24 P20) The next two questions are about the followin situation. A spherical object of mass M, initially at rest, explodes into 3 pieces with masses M/2, M/4 and M/4. After the explosion, the pieces move in the x-y plane. 1. Suppose the final velocity of the lare piece is v = v j. In this case, after the explosion, the total momentum of the two smaller pieces, P small, is a. P small = 0 b. P small = (Mv/2) j c. P small = - (Mv/2) j 2. Suppose in a different situation that the manitudes of the final momenta of all three pieces were the same all equal P. If the final momentum of the larer piece is aain in the j direction, what is the component, p x, of the final momentum of one of the smaller framents in the i direction? 1 a. p x P 2 1 b. p x P 2 3 c. p x P 4 3 d. p x P 5 e. p x P

25 M3) The next three questions refer to the followin situation. Two blocks of mass m A and m B are placed side by side on a frictionless table. At time t 0 both blocks are at rest and a constant force of the same manitude is applied to each of the blocks. Block A has a smaller mass than block B (m A < m B ). top view m A F m B F 1. How do the momenta of the two blocks compare 5 seconds after t 0? a. p A < p B b. p A > p B c. p A = p B 2. After each block has traveled the distance of 1 m, which is correct? a. p A = p B b. K A = K B c. all of the above

26 M7) The next three questions refer to the followin situation: A small block of mass m slides down a frictionless ramp that makes an anle of 60 º with the horizontal. The ramp joins smoothly onto a circular track of radius R which ends where it is vertical, as shown in the fiure. The block is released from rest at a distance 3R above the horizontal and leaves the track at point A. m 3R A 60 R R 1. After the block leaves the track, how hih above the lowest point of the track does the block rise? a. 3 3 R b. 3R/2 c. 3R 2. What is the manitude of the net acceleration on the block just before the block leaves the track? a. b. 2 5 c. d. 4 e. 17

27 M8) The next two problems to the followin situation: top A skier is on top of a frictionless, spherical mountain of radius R=300m. cos = (R-h)/R R-h R 1. From rest, she beins to slide down the hill. What is the vertical distance between the top of the mountain and the place where she leaves the round? a. 10m b. 40m c. 100m d. 166m e. 300m 2. Let h be the answer to the previous problem. If the skier had a non-zero initial velocity, the vertical distance between the top of the mountain and the spot where she would leave the round would be a. smaller than h b. equal to h c. reater than h

28 M9) The next three questions refer to the followin situation: A small block of mass m slides down a frictionless ramp that makes an anle of 60 º with the horizontal. The ramp joins smoothly onto a circular track of radius R which ends where it is vertical, as shown in the fiure. The block is released from rest at a distance 3R above the horizontal and leaves the track at point A. m 3R A 60 R R 1. What is the manitude of the net acceleration on the block just before the block leaves the track? a. b. 2 c. 5 d. 4 e If the flat section had a coefficient of kinetic friction μ k =0.2 (and all other surfaces are frictionless), what is the maximal lenth of the flat section in order for the block to reach point A? a. 3R b. 6R c. 10R

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