Name Section

Student Number Set A

University of the PhilippinesCollege of Science

Physics 71

Set A2nd Sem AY 2011-2012

Second Exam

Physics 71/Second LE Set A – Page 2 of – 2nd Sem AY 2011-2012

Part I. Instructions: Choose the letter of the best answer. Use g = 9.81[ms2

]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 hori-zontal surface. The block moves 1.0 [m] at a constant velocity. What can you say aboutthe 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 com-ponent along the line is given by Fx. Fx

varies with the position of the box as givenin the figure. What is the work done on theparticle 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 – Page 3 of – 2nd Sem AY 2011-2012

3. Balikbayan Box. A 20.0-[kg] balikbayan box is on a ramp inclined at 30.0◦ above thehorizontal. If the balikbayan box moves down the ramp at constant speed, what is thework 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 a car traveling on a

straight highway that accelerates from rest a constant rate of 5.0[ms2

]. 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 movedfrom 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 theforce 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 potentialenergy? 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’smass 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 – Page 4 of – 2nd Sem AY 2011-2012

9. Valley. A sled is at the top of one of the peaks (peakA) in an icy valley that is 50. [m] above the ground.If the sled is to go down the valley from peak A topeak B, which is 60. [m] above the ground, with whatminimum speed must the sled leave peak A? Treatthe sled as a single particle.

(a)34[ms

](b)31

[ms

](c)14

[ms

](d)10.

[ms

](e)3.0

[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 hori-zontal surface, as shown in the figure. After reachingthe bottom of the ramp, it continues to move on a flathorizontal surface where the box compresses a springof spring constant k = 2.0 × 102

[Nm

]. The spring

compresses by 0.50 [m] before the box momentarilycomes to rest at t = tf . What is the work done byfriction on the box from t = 0 to t = tf?

(a)zero(b)12 [J]

(c)-12 [J]

(d)14 [J]

(e)-14 [J]

11. Stable. A mass on a frictionless level surface is attached to a horizontal spring. The otherend of the spring is attached to a fixed wall. How many stable equilibrium positions arethere 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 stretchedit by 0.020 [m] from its unstretched position. What is the corresponding elastic potentialenergy stored at this instant?

(a)0.32 [J] (b)0.64 [J] (c)1.3 [J] (d)2.0 [J]

13. Count. How many unstable equilibrium points arethere in the potential energy diagram on the right?

(a)zero(b)1(c)2

(d)3

(e)4

Physics 71/Second LE Set A – Page 5 of – 2nd Sem AY 2011-2012

14. What? Three point masses are placed in differentlocations along the x-axis. What should be the un-known mass located at x = 2a for the center of massto be located at x = 0?

(a)2M(b)M(c)M/2

(d)M/4

(e)Zero

15. Explosion. A bomb of mass M is initially lying on asmooth horizontal ground. Upon detonation, it disin-tegrates into three parts, each moving along the sameplane. The first part with mass m1 = M/4 moveswith velocity 5.27

[ms

]i. The second part of mass

m2 = M/4 moves with velocity 4.86[ms

]j. What is

the velocity of the third part, m3?(a)−5.27

[ms

]i− 4.86

[ms

]j

(b)−4.68[ms

]i− 5.27

[ms

]j

(c)−2.63[ms

]i− 2.43

[ms

]j

(d)−2.43[ms

]i− 2.63

[ms

]j

16. Bounce. A ball hits the floor with speed v0 at anangle 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 floorexert 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 varyingforce on a box that is moving in a straight line ona frictionless horizontal surface. The net horizontalforce changes with time as shown in the figure. If thebox weighs 0.50 [kg] and started from rest at t = 0,what is its speed at t = 2 [s]?

(a)4.0[ms

](b)6.0

[ms

](c)9.6

[ms

](d)11

[ms

](e)13

[ms

]

Physics 71/Second LE Set A – Page 6 of – 2nd Sem AY 2011-2012

18. In elastic. Which of the following statements is ALWAYS TRUE for systems on whichthe 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 a test of airbags, a car with mass 500. [kg] movingalong a straight line at 60.0

[ms

]collides with a stationary obstacle of mass 100. [kg].

Upon collision, the obstacle sticks to the car. What is the final speed of the compositecar-obstacle object?(a)60.0

[ms

](b)50.0

[ms

](c)40.0

[ms

](d)20.0

[ms

](e)10.0

[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 willmake ball A bounce back at half its initial speed?

(a)mA = 13mB

(b)mA = 12mB

(c)mA = mB

(d)mA = 2mB

(e)mA = 3mB

21. GNav. A disk is rotating with decreasing angular speed about the axis perpendicular tothe disc and passing through its center. Which of the following is true about the angularvelocity 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 about a fixed axis of radius r = 2.0 [m] accordingto the angular position θ = 4.0 [rad] − 2.0

[rads

]t + 1.0

[rads2

]t2. What is the magnitude

of the tangential acceleration of the particle at t = 2.0 [s]?(a)1.0

[ms2

](b)2.0

[ms2

](c)4.0

[ms2

](d)8.0

[ms2

](e)16.

[ms2

]

Physics 71/Second LE Set A – Page 7 of – 2nd Sem AY 2011-2012

23. Direction of rotation. A circular disk rotates on they-z plane as specified in the figure. What is the di-rection of the angular velocity vector?(a)Clockwise

(b)Counterclockwise

(c) i

(d)-i

(e)The angular velocity is zero.

24. Bugs. Two ants are on the surface of a DVD spinning at a constant angular speed aboutan 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 followingquantities 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

25. DVD. A DVD, initially rotating at an angular speed of 13.0[rads

]inside a DVD player,

slows down at a uniform rate until it comes to rest. If it took the DVD 3.00 [s] to stoprotating, 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 a circular track of radius 50. [m].Its linear speed increases at a uniform rate of 0.50

[ms2

]. What is the magnitude of the

car’s angular velocity after the car completes one revolution?

(a)0.010[rads

](b)0.13

[rads

](c)0.35

[rads

](d)18

[rads

](e)310

[rads

]

Physics 71/Second LE Set A – Page 8 of – 2nd Sem AY 2011-2012

27. Door. You apply a constant torque of magnitude 4.0 [N ·m] when opening your room’sdoor. If the door rotated at an angular acceleration of 2.0

[rads2

], what is the door’s moment

of inertia about the hinge?

(a)1.0[kg ·m2

](b)2.0

[kg ·m2

](c)4.0

[kg ·m2

](d)8.0

[kg ·m2

](e)16

[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 frameabout an axis passing through the center of the frame and perpendicularto the plane of the frame?

(a)1.0[kg ·m2

](b)2.0

[kg ·m2

](c)3.0

[kg ·m2

](d)4.0

[kg ·m2

](e)12.0

[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 batonaround while holding it at a point L/4 away from the heavier mass. You observe that therod’s rotation is slowing down at a rate of 0.091

[rads2

]. 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 nailedto a horizontal tabletop, forming a pivot where the rod can rotate. If the rod is made torotate at 5.00

[rads

], 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 rotateabout its core, which is fixed. The moment of inertia of the roll about this axis is I =1.125 × 10−3

[kg ·m2

]. 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?

(a)0.63[rads

](b)5.3

[rads

](c)6.0

[rads

](d)36

[rads

](e)40.

[rads

]

Physics 71/Second LE Set A – Page 9 of – 2nd Sem AY 2011-2012

32. Seesaw. Two girls, Camille and Rita, weighing 30.[kg] and 40. [kg] respectively are on a uniform see-saw. If they both sat 1.0 [m] away from the middleat opposite ends, what is the magnitude and directionof the net torque on the seesaw at the moment whenthe 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 is0.60 [m], is released from rest at the top of a 1.2 [m] highramp. It then rolls without slipping and reaches the bottomwith its center of mass moving at a speed of 3.4

[ms

]. What

is the moment of inertia of the object about an axis passingthrough 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’smoment of inertia about an axis passing through its center?

(a) 12MR2 (b) 32MR2 (c) 5

2MR2 (d)2MR2 (e)3MR2

35. Roll. A solid sphere of massm and radius r rolls without slipping on a horizontal surfaceat a constant translational speed v. What is the magnitude of its angular momentum aboutits center of mass?(a)zero (b)mrv (c) 2

5mrv (d) 35mrv (e) 52mrv

36. Ice Princess. An iceskater is spinning at angular speed 11.3[rads

]with her hands stretched

outwards such that her moment of inertia is 2.60[kg ·m2

]. She then draws her arms to

her chest so that her moment of inertia changes to 1.30[kg ·m2

]. What is the change in

her rotational kinetic energy?

Physics 71/Second LE Set A – Page 10 of – 2nd Sem AY 2011-2012

(a)14.7 [J] (b)22.6 [J] (c)44.1 [J] (d)83.0 [J] (e)166. [J]

37. Tipid. Consider two uniform disks attached about a fric-tionless shaft as shown in the figure. About the axis pass-ing through the center, the top disk is initially rotatingat angular speed ω1, angular momentum (magnitude) Li

and moment of inertia I1. It then drops to the bottomdisk which is initially at rest with moment of inertia I2about the same axis. After collision, the two disks sticktogether, 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) 12(I1 + I2)ω1

(b) 12(I1 − I2)ω1

(c)(I1 + I2)ω1

(d)(I1 − I2)ω1

(e)zero

38. Disks. Three thin uniform disks (each with mass,M = 0.300 [kg], radius, r = 0.240 [m] and momentof inertia, I = 1

2Mr2) are connected side to side suchthat their centers are falling along the same line. Ifthe system is made to rotate clockwise with respectto an axis passing through the center of mass perpen-dicular to the plane of the disks, what is the momentof 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 lo-

cated from position xL to xR as shown in the figure.It is rotated about an axis that is always perpendicularto the plane of the rod, as shown by the dot. As onemoves the axis from x = 0 to x = xR, which of thegraphs below best represents the moment of inertiaabout this axis?

Physics 71/Second LE Set A – Page 11 of – 2nd Sem AY 2011-2012

40. Si! A Mexican (mass 60.0 [kg]), initially at the rightside of a 2.00-meter boat (mass 100. [kg]), decidedto move to the left side as shown in the figure (topview). By how much distance did the boat move fromits initial position? Assume that there is no net forceacting on the system composed of the Mexican andthe boat.

(a)5.33 [m]

(b)3.33 [m]

(c)2.00 [m]

(d)1.20 [m]

(e)0.75 [m]

41. Rotating Pulley. Two masses mA = 1.0 [kg] and mB =2.0 [kg] are attached by a lightweight string that passes overa pulley (solid cylinder, M = 0.25 [kg],R = 0.30 [m]) that ro-tates about a frictionless axle. MassmB, initially at rest, startsto move downwards, rotating the pulley. The string does notslip on the pulley. What is the angular speed of the pulley aftermass mB has gone down by a distance of 0.50 [m]?

(a)2.51[rads

](b)8.19

[rads

](c)8.35

[rads

](d)10.2

[rads

](e)10.6

[rads

]

Physics 71/Second LE Set A – Page 12 of – 2nd Sem AY 2011-2012

42. Slide. A 0.500-[kg] block starts from rest on top ofa frictionless incline oriented at 30.0◦ with respectto the horizontal as shown. At the bottom of the in-cline lies a spring with spring constant k = 1250

[Nm

]and relaxed length L = 0.250 [m]. The block slidesdown, compressing the spring by a distance L/2 be-fore momentarily coming to rest. What is the initialheight, 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