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- 1. Multiple Choice
At time t=0 ,a cart is at x=10 m and has a velocity of 3 m/s in the -xdirection. The cart has a constant acceleration in the +x-direction with magnitude 3 m/s2 < a < 6 m/s2 . Which of the following gives the possible range of the position of the cart at t=1 s?
4 m < x < 5.5 m
8.5 m < x <10 m
. 11.5 m < x < 13 m
14.5 m < x < 16 m
- 2. Multiple Choice
A launcher with mass m1 is suspended from the ceiling by a string, as shown. A block with mass m2<m1 is launched horizontally. At the moment of launch, the block has unknown speed v2 and the launcher has unknown speed v1 in the opposite direction. Which of the following is a true statement about the forces exerted between the launcher and block?
The launcher exerts a greater force on the block than the block exerts on the launcher
The block exerts a greater force on the launcher than the launcher exerts on the block
The block and the launcher exert forces of equal magnitude on each other
The relative magnitude of the force exerted on the spring by the block and launcher cannot be determined without knowing v1 and v2 .
- 3. Multiple Choice
At time t=0s, an object is moving to the right with a velocity v that can be modeled by the equation𝑣 = (4.2 𝑚/𝑠 ) − (1.4 𝑚/𝑠 2 ) 𝑡. At what time, if any, does the object change its direction of motion?
0.33 s
3.0 s
5.6 s
At no time; the object never changes direction.
- 4. Multiple Choice
A distant planet has an acceleration due to gravity of 4 m/s2 near its surface. An object is released from rest from the top of a tall cliff on the planet, and the object lands at the bottom of the cliff in 20 seconds. A second object is then thrown upward from the edge of the same cliff with a speed of 4 m/s. The time it takes the second object to reach the bottom of the cliff is most nearly
19 s
21 s
22 s
80 s
- 5. Multiple Choice
Blocks 1 and 2 are connected by a light string that passes over a pulley with negligible mass and friction, as shown in the figure. Block 1 is on a table covered with two different materials, A and B. The two-block system is released from rest, and the speed of block 1 begins to increase. When block 1 reaches material B, its speed increases at a greater rate. Which of the following correctly compares the coefficient of kinetic friction μ between block 1 and the two materials and describes the change in the magnitude of the net force on block 2 as block 1 slides from material A to material B?
- 6. Multiple Choice
A toy doll and a toy robot are standing on a frictionless surface facing each other. The doll has a mass of 0.20 kg, and the robot has a mass of 0.30 kg. The robot pushes on the doll with a force of 0.30 N. The magnitude of the acceleration of the robot is
- 7. Multiple Choice
A box of mass m is released from rest and accelerates down a ramp that is at an angle θ to the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is μ. As the box is sliding down the ramp, how are the magnitudes of the horizontal and vertical components of the box’s velocity changing, if at all?
- 8. Multiple Choice
An engineer measures the velocity v of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t=0 s?
3 s ≤ t < 5 s
5 s ≤ t < 7 s
7 s ≤ t < 10 s
10 s ≤ t < 12 s
- 9. Multiple Choice
On another planet, a ball is in free fall after being released from rest at time t=0 . A graph of the height of the ball above the planet’s surface as a function of time t is shown. The acceleration due to gravity on the planet is most nearly
- 10. Multiple Choice
An amusement park ride consists of a large vertical wheel of radius R that rotates counterclockwise on a horizontal axis through its center, as shown above. The cars on the wheel move at a constant speed v. Points A and D represent the position of a car at the highest and lowest point of the ride, respectively. A person of weight Fg sits upright on a seat in one of the cars. As the seat passes point A, the seat exerts a normal force with magnitude 0.8 Fg on the person. While passing point A, the person releases a small rock of mass m, which falls to the ground without hitting anything.
What is the normal force exerted on the rider when passing point D?
- 11. Multiple Choice
Three blocks, A, B, and C are pushed by a constant force F that is applied on block A as shown. There is negligible friction between the blocks and the surface. When a small object is attached to the top of block B, the normal force between blocks A and B is FAB and the normal force between blocks B and C is FBC. How will the values of FAB and FBC change if the small object is moved to the top of block C and the experiment is repeated?
- 12. Multiple Choice
The graph shows the acceleration as a function of time for an object that is at rest at time t=0s . The distance traveled by the object between 0 and 2s is most nearly
1 m
2 m
3 m
4 m
- 13. Multiple Choice
At time t=0, a projectile is launched from the top of a cliff at an angle of 30 degrees below the horizontal. Which of the following pairs of graphs best represents the horizontal displacement (Δx) and the vertical velocity component (vvert) of the projectile as a function of time t?
- 14. Multiple Choice
Three blocks are pushed along a rough surface by a force with magnitude P, as shown above. FC is the magnitude of the contact force between blocks 2 and 3, and Ff, FN, and FG are the magnitudes of the friction, normal, and gravitational forces on block 3, respectively. Which of the following is a correct free-body diagram for block 3?
- 15. Multiple Choice
The graph shows the force exerted on a ball by the floor as a function of time as the ball bounces off the floor. If the positive direction is upward, which of the following graphs could represent the force exerted on the floor by the ball?
- 16. Multiple Choice
In Figure 1, cart Y is connected to cart X by a tight string and is also connected to the hanging block of mass m0 by a light string that passes over a pulley. Figure 2 shows a system that is identical except for one change: cart Y and X are connected by a spring at its equilibrium length. Both systems are released from rest. Is the hanging block’s acceleration as a function of time the same in both systems, and why or why not?
Yes, because the net external force exerted on both systems is the same.
Yes, because the tension in the string connecting the block to cart Y is determined by the masses of cart Y and the block.
No, because the net external force exerted on each system is different.
No, because the tension in the string connected to the block is constant in one system but not in the other.
- 17. Multiple Choice
A box of mass m slides up a ramp with initial velocity +v0. The kinetic friction force on the box has magnitude f. Which of the following is a correct equation that could be used to determine the acceleration a of the box?
−𝑓 = 𝑚a
𝑚𝑔𝑠𝑖𝑛𝜃 − 𝑓 = 𝑚a
𝑓 − 𝑚𝑔𝑠𝑖𝑛𝜃 = 𝑚a
−𝑓 − 𝑚𝑔𝑠𝑖𝑛𝜃 = 𝑚a
- 18. Multiple Choice
A block is attached to the end of a string and initially moves at a constant speed in a horizontal circle of constant radius, as shown. The radius is then increased slowly while the speed remains the same. Which of the following graphs best represents the force exerted on the block by the string as a function of the radius?
- 19. Multiple Choice
A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?
Zero
10 m/s
17 m/s
20 m/s
- 20. Multiple Choice
An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
F = mg
F > mg
F can be greater than or less than mg, depending on the speed of the elevator.
- 21. Multiple Choice
The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?
0.5 m/s2
1.6 m/s2
2.0 m/s2
2.5 m/s2
- 22. Multiple Choice
Two students need to move two identical boxes of mass M0 across a room where friction between the floor and the boxes cannot be neglected. One student moves the first box by pushing with a force of magnitude F0 at an angle θ from the horizontal, as shown in the figure for scenario 1. The other student moves the second box by pulling with a force of magnitude F0 at the same angle θ from the horizontal, as shown in the figure for scenario 2.
Which of the following graphs could describe the motion of the two boxes as they are moved across the room?
- 23. Multiple Choice
A block slides down an inclined plane in a classroom. Which of the following pieces of information are needed to determine whether the velocity of the block will be constant? Select two answers.
The mass of the block
The angle of the inclined plane
The acceleration due to gravity in the classroom
The coefficient of kinetic friction between the block and the inclined plane
- 24. Multiple Choice
A block of mass m is at rest on a rough incline, as shown in the figure above. Which of the following forces must have a magnitude equal to mg? Select two answers.
The total force exerted on the block by the incline
The normal force exerted on the block by the incline
The force of friction exerted on the block by the incline
The gravitational force exerted on Earth by the block
- 25. Multiple Choice
A test car and its driver, with a combined mass of 600 kg, are moving along a straight, horizontal track when a malfunction causes the tires to stop rotating. The car skids to a halt with constant acceleration, leaving skid marks on the road during the whole time it skids. Which two of the following measurements, taken together, would allow engineers to find the initial speed of the test car? Select two answers.
The length of the skid marks
The contact area of each tire with the track
The coefficient of static friction between the tires and the track
The coefficient of kinetic friction between the tires and the track
- 26. Multiple Choice
A 50.0 N box is at rest on a horizontal surface. The coefficient of static
friction between the box and the surface is 0.50, and the coefficient of kinetic
friction is 0.30. A horizontal 20.0 N force is then exerted on the box. The
magnitude of the acceleration of the box is most nearly
0 m/s2
.5 m/s2
1.0 m/s2
4.0 m/s2
- 27. Multiple Choice
Assume the elevator has upward acceleration a, and consider the stack that has two boxes of mass M. What is the magnitude of the force exerted on the top box by the bottom box?
Mg
Ma
M(a - g)
M (a + g)
- 28. Multiple Choice
How does the magnitude of the force exerted by the top box on the bottom box compare with the magnitude of the force exerted by the bottom box on the top box for each of the stacks?
The two magnitudes are always equal in each of the stacks.
The two magnitudes are always different in each of the stacks.
The two magnitudes are equal when the boxes have equal mass and different when the boxes have different masses
The two magnitudes are equal when the elevator is moving at constant speed and different when it is accelerating.
- 29. Multiple Choice
An engineer measures the velocity v of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t=0 s?
3 s ≤ t < 5 s
5 s ≤ t < 7 s
7 s ≤ t < 10 s
10 s ≤ t < 12 s
- 30. Multiple Choice
Three blocks are pushed along a rough surface by a force with magnitude P, as shown above. FC is the magnitude of the contact force between blocks 2 and 3, and Ff, FN, and FG are the magnitudes of the friction, normal, and gravitational forces on block 3, respectively. Which of the following is a correct free-body diagram for block 3?
- 31. Multiple Choice
Two objects, A and B, move toward one another. Object A has twice the mass and half the speed of object B. Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?
The force exerted by A on B will be twice as great as the force exerted by B on A because A has twice the mass of B.
The force exerted by A on B will be half as great as the force exerted by B on A because A has half the speed of B.
The forces exerted by each object on the other are the same, because the product of mass and speed is the same for both objects.
The forces exerted by each object on the other are the same, because interacting objects cannot exert forces of different magnitude on each other.
- 32. Multiple Choice
Blocks A and B, of masses mA and mB, are at rest on a frictionless surface, as shown above, with block A fixed to the table. Block C of mass mC is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B?
- 33. Multiple Choice
An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
F = mg
F > mg
F can be greater than or less than mg, depending on the speed of the elevator.
- 34. Multiple Choice
At time t=0, a projectile is launched from the top of a cliff at an angle of 30 degrees below the horizontal. Which of the following pairs of graphs best represents the horizontal displacement (Δx) and the vertical velocity component (vvert) of the projectile as a function of time t?
- 35. Multiple Choice
An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is 10 N directed due north, and another is 10 N directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
10√3 N, directed northwest
10√3 N, directed southeast
10√2 N, directed northwest
10√2 N, directed southeast
- 36. Multiple Choice
An object begins at position x = 0 and moves one-dimensionally along the xaxis with a velocity v expressed as a function of time t according to the graph above. At what time does the object pass through x = 0 again?
Between 10 s and 20 s
Between 20 s and 30 s
At 30 s exactly
Between 30 s and 40 s
After 40 s
- 37. Multiple Choice
A box of mass m hangs from massless strings, as shown in the figure above. The angle between strings 1 and 2 is 90°, and the angles that the strings make with the ceiling are θ1 and θ2, respectively. If T1 is the tension in string 1, which of the following are the magnitudes of the horizontal and vertical components of the tension in string 2?
- 38. Multiple Choice
Object A is released from rest at height h. At the same instant, Object B is thrown downward from the same location. Which of the following graphs of speed of v as a function of time t is correct for the two objects?
- 39. Multiple Choice
A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is
200 N
800 N
1000 N
1200 N
2200 N
- 40. Multiple Choice
The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?
0.5 m/s2
1.6 m/s2
2.0 m/s2
2.5 m/s2
- 41. Multiple Choice
A box is given a sudden push up a ramp. Friction between the box and the ramp is not negligible. Which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?
- 42. Multiple Choice
Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for twice the time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration?
Object X is moving at the same speed as object Y.
Object X is moving four times faster than object Y.
Object X has traveled twice as far as object Y
Object X has traveled four times as far as object Y.
- 43. Multiple Choice
A rock attached to a string swings in a vertical circle, as shown to the right, with negligible air resistance. Which of the following diagrams could correctly show all the forces on the rock when the string is in the position above?
- 44. Multiple Choice
Which of the following expressions correctly relates the magnitudes Ff and FT?
Ff < FT
Ff = FT
FT < Ff < 2 FT
Ff = 2 FT
- 45. Multiple Choice
Which of the following correctly ranks the displacement ∆x for the three segments of the object’s motion?
∆x3 > ∆x2 > ∆x1 > 0
∆x1 = ∆x2 = ∆x3 > 0
(∆x1 = ∆x3) > ∆x2 > 0
(∆x1 = ∆x3) > 0 > ∆x2
- 46. Multiple Choice
A student throws a rock horizontally from the edge of a cliff that is 20 m high. The rock has an initial speed of 10 m/s. If air resistance is negligible, the distance from the base of the cliff to where the rock hits the level ground below the cliff is most nearly
10 m
20 m
40 m
200 m
- 47. Multiple Choice
A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?
Zero
10 m/s
17 m/s
20 m/s
- 48. Multiple Choice
A block of mass m is at rest on a rough incline, as shown in the figure above. Which of the following forces must have a magnitude equal to mg? Select two answers.
The total force exerted on the block by the incline
The normal force exerted on the block by the inclin
The force of friction exerted on the block by the incline
The gravitational force exerted on Earth by the block
- 49. Multiple Choice
A block slides down an inclined plane in a classroom. Which of the following pieces of information are needed to determine whether the velocity of the block will be constant? Select two answers.
The mass of the block
The angle of the inclined plane
The acceleration due to gravity in the classroom
The coefficient of kinetic friction between the block and the inclined plane
- 50. Multiple Choice
A test car and its driver, with a combined mass of 600 kg, are moving along a straight, horizontal track when a malfunction causes the tires to stop rotating. The car skids to a halt with constant acceleration, leaving skid marks on the road during the whole time it skids. Which two of the following measurements, taken together, would allow engineers to find the initial speed of the test car? Select two answers.
The length of the skid marks
The contact area of each tire with the track
The coefficient of static friction between the tires and the track
The coefficient of kinetic friction between the tires and the track
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