Name _______________________________Student ID ______________________ Score ________
Last
First
40 multiple choice questions, 5 points each
Use the scenario below for the next two questions.
Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the
position in 𝑥 vs. time 𝑡 graph below. Different instants are labeled by letters P through T.
1. At what instant are the speeds of Car 1 and Car 2 approximately the same?
A) P
B) Q
C) R
D) S
E) T
2. At what instant are the directions of Car 2’s velocity and acceleration both negative?
A) P
B) Q
C) R
D) S
E) T
Phys 114 A Fall 2016 Final Exam Page 1 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next two questions.
A projectile is fired from the ground at position A with an initial velocity of 𝐯$ as shown below.
The horizontal component of the launching velocity is 15 m/s. The projectile reaches the
maximum height at position B, 1.5 seconds after the launch. It then lands on the ground at
position C. Neglect air resistance.
3. How high above the ground is position B?
A) 44 m
B) 22 m
C) 88 m
D) 3.7 m
E) 11 m
4. How far is position C from position A?
A) 89 m
B) 0.86 m
C) 140 m
D) 45 m
E) 30 m
Phys 114 A Fall 2016 Final Exam Page 2 Name _______________________________Student ID ______________________ Score ________
Last
First
5. Suppose that an ocean current has a velocity of 1.8 m/s that makes an angle of 40° from the
positive x-direction with respect to the earth. A boat is sailing in the ocean current with a
velocity of 5.2 m/s in the positive x-direction with respect to the earth. What is the x-component
of the velocity of the ocean current with respect to the boat?
A) 6.6 m/s
B) -6.6 m/s
C) -4.0 m/s
D) 3.8 m/s
E) -3.8 m/s
Use the scenario below for the next two questions.
Suppose you are in an ascending elevator that is slowing down with an acceleration whose
magnitude is 2.5 m/s2. The elevator floor exerts a normal force of 450 N on your feet.
6. What is the magnitude of the force that your feet exert on the elevator?
A) 62 N
B) 600 N
C) 450 N
D) 150 N
E) 760 N
7. Then the elevator starts to descend, speeding up with an acceleration whose magnitude is
2.5 m/s2. What is the normal force on your feet by the elevator floor now?
A) 62 N
B) 600 N
C) 450 N
D) 150 N
E) 760 N
Phys 114 A Fall 2016 Final Exam Page 3 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next three questions.
Two boxes, each with a mass of 𝑀 = 80 kg, are connected by an inextensible massless rope and
sitting on a flat floor. The right box is then pulled to the right with a constant force F = 290 N
causing the boxes to accelerate with a constant acceleration.
8. If there is no friction between the boxes and the floor, what is the tension in the rope, T?
A) 0 N
B) 1.5 × 102 N
C) 2.9 × 102 N
D) 73 N
E) 5.8 × 102 N
9. If there is no friction between the boxes and the floor, what is the kinetic energy of the boxes
when they are pulled over a distance of 58.0 m?
A) 1.7 × 104 J
B) 8.4 × 104 J
C) 2.5 × 104 J
D) 9.1 × 104 J
E) 4.5 × 104 J
10. Suppose now that there is friction between the boxes and the floor. The coefficient of kinetic
friction between the boxes and the floor is 0.62. If the boxes still have the same acceleration,
what is the magnitude of the force, F, in this case?
A) 6.8 × 102 N
B) 3.9 × 102 N
C) 7.8 × 102 N
D) 1.3 × 103 N
E) 2.9 × 102 N
Phys 114 A Fall 2016 Final Exam Page 4 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next three questions.
Block 1 (with a mass of 𝑚* = 5.0 kg) is connected to Block 2 with a massless inextensible string
that goes over a massless pulley with a frictionless axle. The string does not slip on the pulley.
Block 1 is on top of a rough horizontal table. The coefficients of static friction and kinetic friction
between the table and Block 1 are 𝜇, = 0.65 and 𝜇- = 0.45, respectively.
11. If the mass of Block 2 is 𝑚. = 2.0 kg, the blocks do not move. What is the frictional force on
Block 1 by the table surface?
A) 49 N
B) 32 N
C) 26 N
D) 45 N
E) 20 N
12. If the mass of Block 2 is 𝑚. = 7.0 kg, the blocks move. If they start from rest, what is the speed
of the blocks when Block 2 has fallen by a distance 1.2 m?
A) 2.7 m/s
B) 3.1 m/s
C) 4.9 m/s
D) 4.7 m/s
E) 3.7 m/s
13. Now suppose that the pulley in question 12’s set-up is replaced with one with a mass while
everything else is the same. Both blocks still move from rest. Which of the following statement
regarding the tensions in the string labeled 𝑇* and 𝑇. in the figure correct?
Statement I: 𝑇* is greater than 𝑇. .
Statement II: 𝑇* is larger now than its original value of 𝑇* .
Statement III: 𝑇. is larger now than its original value of 𝑇. .
A) Statement I only
B) Statement II only
C) Statement III only
D) Both Statements II and III
E) All statements are correct.
Phys 114 A Fall 2016 Final Exam Page 5 Name _______________________________Student ID ______________________ Score ________
Last
First
14. A block of mass 𝑚 initially at rest at position A slides down on a frictionless incline of angle 𝜃.
During the descend, the block encounters a relaxed spring with a spring constant of 𝑘 and comes
to rest momentarily at position B as shown in the figure. The distance between positions A and
B is 𝑑. What is the work done on the block by the spring as it moves from position A to position
B?
A) 𝑚𝑔𝑑 sin 𝜃
B) −𝑚𝑔𝑑 sin 𝜃
C) *89:
.
D) −*89:
.
E) −𝑚𝑔𝑑
15. A uniform disk with a radius 𝑅 is free to rotate about its central axle. The moment of inertia of
the disk about the axle is 𝐼. The disk is initially stationary. A clay of mass 𝑚 approaches the rim
of the disk with a speed 𝑣 as shown. What is the angular velocity of the disk after the clay lands
and sticks to the rim of the disk?
A) 𝑚𝑣𝑅
𝐼
B) 𝑣
𝑅
𝑚𝑣𝑅
C)
𝐼 + 𝑚𝑅 .
D) 𝑚𝑣
𝐼
E) 0
Phys 114 A Fall 2016 Final Exam Page 6 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next two questions.
Initially, Puck 1 with a mass of 1.0 kg is moving with a velocity of 𝐯*D = 13 m s 𝐱 while Puck 2
is moving with a velocity of 𝐯.D = 26 m s 𝐲, both on a frictionless ice. After they collide, they
stick together and move in the direction that makes 45° from both positive 𝑥- and positive 𝑦directions.
16. What is the mass of Puck 2?
A) 1.0 kg
B) 0.50 kg
C) 2.0 kg
D) 1.4 kg
E) 0.74 kg
17. If the impulse that Puck 1 imparts on Puck 2 during the collision is 𝐈, what is the impulse that
Puck 2 imparts on Puck 1?
A) 𝐈
B) 2𝐈
C) 𝐈 2
D) −𝐈
E) − 𝐈 2
18. Suppose you are standing on a flat sheet of plywood that is initially at rest on a frictionless flat
ice surface. If your mass is 60 kg, and the mass of the plywood sheet is 15 kg, as you move to
the left on the plywood with a speed of 2.0 m/s relative to the plywood, how fast and to which
direction is the center of mass of the you-plywood system move relative to the ice surface?
A) 2.0 m/s to the left
B) 2.0 m/s to the right
C) 1.5 m/s to the left
D) 1.5 m/s to the right
E) Actually, the center of mass does not move.
Phys 114 A Fall 2016 Final Exam Page 7 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next two questions.
A uniform horizontal disk with a radius of 𝑅 = 1.5 m and a mass of 𝑀 = 25 kg is initially at rest,
and its axle is frictionless. A force with a constant magnitude F is applied at a point on the disk,
always making an angle 𝜃 = 25° from tangent to the rim of the disk as shown. This causes the
disk to start rotating, and 12 second later, its angular speed is 54 rad/s. The moment of inertia of a
*
uniform disk about an axis through its center is given by 𝐼 = 𝑀𝑅 . .
.
19. What is the magnitude of the applied force, 𝐹?
A) 93 N
B) 190 N
C) 200 N
D) 130 N
E) 140 N
20. What is the angular momentum of the disk about its center 12 s after the force started being
applied on the disk?
A) 0 kg ∙ m. s
B) 3.0 × 10U kg ∙ m. s
C) 4.1 × 10V kg ∙ m. s
D) 2.1 × 10V kg ∙ m. s
E) 1.5 × 10U kg ∙ m. s
Phys 114 A Fall 2016 Final Exam Page 8 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the scenario below for the next two questions.
You decided to put up a sign against a wall using a uniform horizontal rod and a string as shown
on the right. The mass of the rod is 25 kg. The tension in the string is 840 N, and the string makes
an angle of θ = 21° from the horizontal.
21. What is the mass of the sign?
A) 31 kg
B) 67 kg
C) 18 kg
D) 59 kg
E) We need to know the length of the rod to answer this question.
22. What is the horizontal component of the force exerted by the wall on the rod?
A) 0.0 N
B) 780 N
C) 300 N
D) 460 N
E) 700 N
Phys 114 A Fall 2016 Final Exam Page 9 Name _______________________________Student ID ______________________ Score ________
Last
First
Use the following scenario for the next two
problems.
A uniform solid ball, initially at rest, rolls down
on an incline without slipping from position A to
position B as shown in the figure. The height
difference between positions A and B is 𝐻. The
radius and the mass of the ball are 𝑅 and 𝑀,
respectively. At the bottom of the incline, the ball
has a linear speed of 𝑣. The moment of inertia of a
.
solid sphere about its center of mass is 𝐼 = 𝑀𝑅 . .
X
23. What is the kinetic energy of the ball at the bottom of the incline at position B?
A) *𝑀𝑣 .
B)
.
*
𝑀𝑣 .
.
*
+ X𝑀𝑅 . 𝑣 .
C) 𝑀𝑔𝐻
D) *𝑀𝑣 . + *𝑀𝑅 . 𝑣 . − 𝑀𝑔𝐻
.
X
E) 𝑀𝑔𝐻 + *𝑀𝑣 . + *𝑀𝑅 . 𝑣 .
.
X
24. While the ball is rolling down, is there any torque on the ball about an axis through its center of
the ball? If so, which force provides the torque?
A) No.
B) Yes. The normal force by the incline surface on the ball.
C) Yes. The weight of the ball.
D) Yes. The static friction by the incline surface on the ball.
E) Yes. The kinetic friction by the incline surface on the ball.
Phys 114 A Fall 2016 Final Exam Page 10 Name _______________________________Student ID ______________________ Score ________
Last
First
25. Assuming that the moon is orbiting around in a circular orbit, calculate the centripetal
acceleration of the moon. The mass of the earth is 6.0 × 1024 kg, the mass of the moon is
7.3 × 1022 kg, and the radius of the moon’s orbit is 3.9 × 108 m.
A) 1.9 × 1020 m/s2
B) 3.2 × 10-5 m/s2
C) 1.0 × 106 m/s2
D) 9.8 m/s2
E) 2.6 × 10-3 m/s2
Use the following scenario for the next three problems.
A comet is orbiting around the sun in an elliptical orbit from
position P to Q. The distance between the sun and position P is
0.59 AU, and the distance between the sun and position Q is
35 AU. 1 AU (astronomical unit) is the mean distance between
the sun and the earth.
26. Which of the following statements is or are correct as the comet moves from position P to
position Q?
Statement I: the sun does negative work on the comet.
Statement II: the sun does positive work on the comet.
Statement III: the sun provides non-zero torque on the comet about the sun.
A) Statement I only
B) Statement II only
C) Statement III only
D) Statement I and III
E) Statement II and III
27. If the comet is moving with a speed of 54 km/s at position P, how fast is it moving at position
Q?
A) 3.2 × 103 km/s
B) 54 km/s
C) 1.8 km/s
D) 28 km/s
E) 0.91 km/s
28. What is the orbital period of the comet?
A) 0.45 years
B) 75 years
C) 100 years
D) 210 years
E) Not enough information is given.
Phys 114 A Fall 2016 Final Exam Page 11