UP Diliman Physics 71 Long Exam#2 Sample Exam

Name

Section

Student Number

Set

University of the Philippines College of Science

Physics 71 Set A 2nd Sem AY 2011-2012 Second Exam

A

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

  Part I. Instructions: Choose the letter of the best answer. Use g = 9.81 sm2 for the acceleration on Earth due to gravity. Ignore air friction unless otherwise stated.

1. Spring box. You apply a 50.-[N] horizontal force to a 5.0-[kg] block on a rough horizontal surface. The block moves 1.0 [m] at a constant velocity. What can you say about the total work done on the block? (a) It is zero. (b)It is equal to the work done by you. (c) It is equal to the work done by friction. (d)It increases the kinetic energy of the block. (e) It decreases the kinetic energy of the block. 2. Varying force. A box is moving in a line, and is acted upon by a net force whose component along the line is given by Fx . Fx varies with the position of the box as given in the figure. What is the work done on the particle as it moves from x=6 to x=0? (a)−6 [J] (b)−4 [J] (c)−2 [J]

(d)2 [J] (e)4 [J]

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

3. Balikbayan Box. A 20.0-[kg] balikbayan box is on a ramp inclined at 30.0◦ above the horizontal. If the balikbayan box moves down the ramp at constant speed, what is the work done by friction on the box after it slides 2.00-[m] on the ramp? (a) zero

(b)-98.1 [J]

(c)-170 [J]

(d)-196 [J]

(e)-340 [J]

4. Wish. You dropped a coin from rest at the top of an empty well that is 3.0 [m] deep. What is the speed of the coin just before it reaches the bottom of the well?           (a)3.0 ms (b)5.4 ms (c)7.7 ms (d)29 ms (e)59 ms 5. WaKE up! A box of mass 1.0 [kg] is strapped to a chair inside  ma car traveling on a straight highway that accelerates from rest a constant rate of 5.0 s2 . What is the total work done on the box after 1.0 [s]? (a)48 [J] (b)25 [J] (c)13 [J] (d)2.5 [J] (e)zero 6. Home Run. A conservative force acts on a particle, causing the latter to move on a trajectory as shown. The work done by the force when the particle moved from point A to B, B to C and C to D are 1 [J], 2 [J] and 3 [J] respectively. What is the work done by the force when the particle moved from D to A? (a)6 [J] (b)4 [J] (c)0 [J]

(d)−4 [J] (e)−6 [J]

  7. To Pass. You throw a rock straight up from the ground with an initial speed 30.0 ms . At what height above the ground will the rock have kinetic energy equal to the potential energy? Assume that the potential energy on the ground is zero. (a)11.5 [m]

(b)22.9 [m]

(c)15.0 [m]

(d)45.9 [m]

(e)91.7 [m]

8. Skiing. Skiers Brian and May slide from rest down the same slippery slope. Brian’s mass is twice that of May. Who will reach the bottom of the slope with a higher speed? (a) Brian (b)May (c) Both of them will have the same speed at the bottom of the slope.

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

9. Valley. A sled is at the top of one of the peaks (peak A) in an icy valley that is 50. [m] above the ground. If the sled is to go down the valley from peak A to peak B, which is 60. [m] above the ground, with what minimum speed must the sled leave peak A? Treat the sled as a single particle.     (a)34 ms (d)10. ms     (b)31 ms (e)3.0 ms   (c)14 ms 10. Box-spring. At t = 0, a 2.0-[kg] box slides down a ramp from rest at point A, 2.0 [m] above the horizontal surface, as shown in the figure. After reaching the bottom of the ramp, it continues to move on a flat horizontal surface where the box compresses a spring   2 N of spring constant k = 2.0 × 10 m . The spring compresses by 0.50 [m] before the box momentarily comes to rest at t = tf . What is the work done by friction on the box from t = 0 to t = tf ? (d)14 [J]

(a) zero (b)12 [J] (c) -12 [J]

(e)-14 [J]

11. Stable. A mass on a frictionless level surface is attached to a horizontal spring. The other end of the spring is attached to a fixed wall. How many stable equilibrium positions are there in this spring-mass system? (a) 0

(b)1

(c)2

(d)3

(e)4

12. U from F. The magnitude of the force you applied on a spring is 32 [N] after you stretched it by 0.020 [m] from its unstretched position. What is the corresponding elastic potential energy stored at this instant? (a) 0.32 [J]

(b)0.64 [J]

(c)1.3 [J]

13. Count. How many unstable equilibrium points are there in the potential energy diagram on the right? (a) zero (b)1 (c) 2

(d)3 (e)4

(d)2.0 [J]

Physics 71/Second LE Set A

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14. What? Three point masses are placed in different locations along the x-axis. What should be the unknown mass located at x = 2a for the center of mass to be located at x = 0? (a)2M (d)M/4 (b)M (e)Zero (c)M/2 15. Explosion. A bomb of mass M is initially lying on a smooth horizontal ground. Upon detonation, it disintegrates into three parts, each moving along the same plane. The first part  mass m1 = M/4 moves  mwith with velocity 5.27 s ˆi. The second part of mass   m2 = M/4 moves with velocity 4.86 ms ˆj. What is the velocity of the third part, m3 ?     (a)−5.27 ms ˆi − 4.86 ms ˆj     (b)−4.68 ms ˆi − 5.27 ms ˆj     (c)−2.63 ms ˆi − 2.43 ms ˆj     (d)−2.43 m ˆi − 2.63 m ˆj s

s

16. Bounce. A ball hits the floor with speed v0 at an angle 45◦ from the normal, as shown in the figure. It bounces with the same speed, also at an angle 45◦ from the normal. In which direction does the floor exert a force on the ball? (a) upward (b)downward (c) to the left (d)to the right (e) The floor does not exert a force on the ball. 17. Final speed. You apply a horizontal and varying force on a box that is moving in a straight line on a frictionless horizontal surface. The net horizontal force changes with time as shown in the figure. If the box weighs 0.50 [kg] and started from rest at t = 0, what is its speed at t = 2 [s]?     (a) 4.0 ms (d)11 ms     (b)6.0 ms (e)13 ms   (c) 9.6 ms

2nd Sem AY 2011-2012

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

18. In elastic. Which of the following statements is ALWAYS TRUE for systems on which the net external force is zero? (a) In an inelastic collision, kinetic energy is conserved. (b)In an inelastic collision, linear momentum is conserved. (c) In an inelastic collision, linear momentum and kinetic energy are conserved. (d)In an elastic collision, linear momentum is not conserved. (e) In an elastic collision, kinetic energy is not conserved. 19. Collision point again. During  m  a test of airbags, a car with mass 500. [kg] moving along a straight line at 60.0 s collides with a stationary obstacle of mass 100. [kg]. Upon collision, the obstacle sticks to the car. What is the final speed of the composite car-obstacle object?           (b)50.0 ms (c)40.0 ms (d)20.0 ms (e)10.0 ms (a) 60.0 ms 20. Bounce back. Ball A (mass = mA ) is traveling at a speed v straight towards ball B (mass = mB ) that is at rest. If the collision is elastic, which of the following conditions will make ball A bounce back at half its initial speed? (a)mA = 31 mB (b)mA = 21 mB (c)mA = mB

(d)mA = 2mB (e)mA = 3mB

21. GNav. A disk is rotating with decreasing angular speed about the axis perpendicular to the disc and passing through its center. Which of the following is true about the angular velocity and angular acceleration about the axis before the disk comes to rest? (a) Angular velocity is in the same direction as the angular acceleration. (b)Angular velocity is in a direction opposite to that of the angular acceleration. (c) Angular velocity is perpendicular to the angular acceleration. (d)Angular acceleration is zero. (e) Angular velocity is zero. 22. Power of Two. A particle is rotating abouta fixed  axis of  radradius  2 r = 2.0 [m] according rad to the angular position θ = 4.0 [rad] − 2.0 s t + 1.0 s2 t . What is the magnitude of the tangential acceleration of the particle at t = 2.0 [s]?           (a)1.0 sm2 (b)2.0 sm2 (c)4.0 sm2 (d)8.0 sm2 (e)16. sm2

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

23. Direction of rotation. A circular disk rotates on the y-z plane as specified in the figure. What is the direction of the angular velocity vector? (a) Clockwise (b)Counterclockwise (c)ˆi (d)-ˆi (e) The angular velocity is zero.

24. Bugs. Two ants are on the surface of a DVD spinning at a constant angular speed about an axis passing through its center and perpendicular to its surface. Ant A is located 2.0 [cm] from the axis, while Ant B is located 5.0 [cm] from the axis. Which of the following quantities is/are the same for both ants? I. angular speed II. angular acceleration III. radial acceleration (a) I only (b)II only (c) III only

(d)I and II only (e)I, II and III

  inside a DVD player, 25. DVD. A DVD, initially rotating at an angular speed of 13.0 rad s slows down at a uniform rate until it comes to rest. If it took the DVD 3.00 [s] to stop rotating, by how many radians did the DVD rotate during this time interval? (a) 4.33 [rad]

(b)19.5 [rad]

(c)28.2 [rad]

(d)39.0 [rad]

(e)58.5 [rad]

26. Circular track. A car, initially at rest, moves around  m a circular track of radius 50. [m]. Its linear speed increases at a uniform rate of 0.50 s2 . What is the magnitude of the car’s angular velocity after the car completes one revolution?    rad   rad   rad   rad  (b)0.13 (c)0.35 (d)18 (e)310 (a) 0.010 rad s s s s s

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

27. Door. You apply a constant torque of magnitude 4.0 [N · m]when opening your room’s door. If the door rotated at an angular acceleration of 2.0 rad s2 , what is the door’s moment of inertia about the hinge?     (a)1.0 kg · m2 (d)8.0 kg · m2     (b)2.0 kg · m2 (e)16 kg · m2   (c)4.0 kg · m2 28. Frame. A huge square frame is constructed from four 1.0 [m] long rods each with mass 3.0 [kg]. What is the moment of inertia of the frame about an axis passing through the center of the frame and perpendicular to the plane of the frame?     (a)1.0 kg · m2 (d)4.0 kg · m2     (b)2.0 kg · m2 (e)12.0 kg · m2   (c)3.0 kg · m2 29. Fiesta. Two point masses, m1 = 1.0 [kg] and m2 = 2.0 [kg], are attached on opposite ends of a very light rod of length L = 1.0 [m], forming a baton. A girl twirls this baton around while holding it at a point L/4 away fromtheheavier mass. You observe that the rod’s rotation is slowing down at a rate of 0.091 rad s2 . What is the magnitude of the net torque acting on the rod? (a)0.063 [N · m] (b)0.091 [N · m] (c)1.7 [N · m]

(d)7.6 [N · m] (e)13 [N · m]

30. Rod. The center of a slender uniform rod (mass 0.250 [kg], length 0.200 [m]) is nailed to a horizontal tabletop, forming a pivot where the rod can rotate. If the rod is made to  rad rotate at 5.00 s , what is the kinetic energy of the rod? (a)2.08 × 10−4 [J] (b)8.33 × 10−4 [J] (c)2.60 × 10−3 [J]

(d)1.04 × 10−2 [J] (e)3.13 [J]

31. Tissue. You pull the end of a very thick tissue roll, initially at rest, that can rotate about its core, which is  fixed. The moment of inertia of the roll about this axis is I = −3 2 1.125 × 10 kg · m . If you pull the tissue with a constant force of 0.10 [N], what is the angular speed of the tissue roll after you have pulled 0.20 [m] of tissue?    rad   rad   rad   rad  (a) 0.63 rad (b)5.3 (c)6.0 (d)36 (e)40. s s s s s

Physics 71/Second LE Set A

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2nd Sem AY 2011-2012

32. Seesaw. Two girls, Camille and Rita, weighing 30. [kg] and 40. [kg] respectively are on a uniform seesaw. If they both sat 1.0 [m] away from the middle at opposite ends, what is the magnitude and direction of the net torque on the seesaw at the moment when the seesaw is level? (a) 98.1 [N · m] into the page (b)10.0 [N · m] into the page (c) zero (d)10.0 [N · m] out of the page (e) 98.1 [N · m] out of the page 33. Rolling on. A uniform 15-[kg] object, whose radius is 0.60 [m], is released from rest at the top of a 1.2 [m] high ramp. It then rolls without slipping and reaches the bottom with its center of mass moving at a speed of 3.4 ms . What is the moment of inertia of the object about an axis passing through its center of mass?   (a)2.7 kg · m2   (b)5.6 kg · m2   (c)16 kg · m2   (d)11 kg · m2   (e)22 kg · m2 34. Total KE. A uniform object of mass M and radius R is rolling without slipping. It has a rotational kinetic energy that is half its translational kinetic energy. What is the object’s moment of inertia about an axis passing through its center? (a) 12 M R2

(b) 32 M R2

(c) 52 M R2

(d)2M R2

(e)3M R2

35. Roll. A solid sphere of mass m and radius r rolls without slipping on a horizontal surface at a constant translational speed v. What is the magnitude of its angular momentum about its center of mass? (d) 53 mrv (e) 25 mrv (a) zero (b)mrv (c) 52 mrv  rad  36. Ice Princess. An iceskater is spinning at angular speed 11.3  s with her hands stretched  2 outwards such that her moment of inertia is 2.60 kg · m  . She  then draws her arms to 2 her chest so that her moment of inertia changes to 1.30 kg · m . What is the change in her rotational kinetic energy?

Physics 71/Second LE Set A

(a)14.7 [J]

(b)22.6 [J]

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(c)44.1 [J]

2nd Sem AY 2011-2012

(d)83.0 [J]

37. Tipid. Consider two uniform disks attached about a frictionless shaft as shown in the figure. About the axis passing through the center, the top disk is initially rotating at angular speed ω1 , angular momentum (magnitude) Li and moment of inertia I1 . It then drops to the bottom disk which is initially at rest with moment of inertia I2 about the same axis. After collision, the two disks stick together, rotating with a combined angular momentum (magnitude) Lf about the same axis. What is Li − Lf ? Assume that the net external torque of the system is zero. (a) 21 (I1 + I2 )ω1 (d)(I1 − I2 )ω1 (b) 12 (I1 − I2 )ω1 (e)zero (c)(I1 + I2 )ω1 38. Disks. Three thin uniform disks (each with mass, M = 0.300 [kg], radius, r = 0.240 [m] and moment of inertia, I = 12 M r2 ) are connected side to side such that their centers are falling along the same line. If the system is made to rotate clockwise with respect to an axis passing through the center of mass perpendicular to the plane of the disks, what is the moment of inertia about this axis?   (a)2.33 × 10−1 kg · m2   (b)1.64 × 10−1 kg · m2   (c)7.78 × 10−2 kg · m2   (d)2.59 × 10−2 kg · m2   (e)8.64 × 10−3 kg · m2 39. kaPAg Tumibok. Consider a thin, uniform rod located from position xL to xR as shown in the figure. It is rotated about an axis that is always perpendicular to the plane of the rod, as shown by the dot. As one moves the axis from x = 0 to x = xR , which of the graphs below best represents the moment of inertia about this axis?

(e)166. [J]

Physics 71/Second LE Set A

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40. Si! A Mexican (mass 60.0 [kg]), initially at the right side of a 2.00-meter boat (mass 100. [kg]), decided to move to the left side as shown in the figure (top view). By how much distance did the boat move from its initial position? Assume that there is no net force acting on the system composed of the Mexican and the boat. (a)5.33 [m] (d)1.20 [m] (b)3.33 [m] (e)0.75 [m] (c)2.00 [m] 41. Rotating Pulley. Two masses mA = 1.0 [kg] and mB = 2.0 [kg] are attached by a lightweight string that passes over a pulley (solid cylinder, M = 0.25 [kg],R = 0.30 [m]) that rotates about a frictionless axle. Mass mB , initially at rest, starts to move downwards, rotating the pulley. The string does not slip on the pulley. What is the angular speed of the pulley after mass mB has gone down by a distance of 0.50 [m]?    rad  (a) 2.51 rad (d)10.2 s s  rad   rad  (b)8.19 s (e)10.6 s   (c) 8.35 rad s

2nd Sem AY 2011-2012

Physics 71/Second LE Set A

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42. Slide. A 0.500-[kg] block starts from rest on top of a frictionless incline oriented at 30.0◦ with respect to the horizontal as shown. At the bottom of the in- N cline lies a spring with spring constant k = 1250 m and relaxed length L = 0.250 [m]. The block slides down, compressing the spring by a distance L/2 before momentarily coming to rest. What is the initial height, h, of the block? (a) 31.9 [m] (b)16.0 [m] (c) 2.05 [m]

(d)1.99 [m] (e)0.250 [m]

End of Exam

2nd Sem AY 2011-2012