PASSAGE 1 (Questions 1 – 5 pertain to this passage.)
A student performs a series of experiments to determine the coefficient of static friction and the coefficient of kinetic friction between a large crate and the floor. The magnitude of the force of static friction is always less than or equal to msN, where <ms denotes the coefficient of static friction, and N denotes the normal force exerted by the floor on the crate:
fs £ msN.
Static friction exists only when the crate is not sliding across the floor.
The force of kinetic friction is given by
fk = mkN,
where µk denotes the coefficient of kinetic friction. Kinetic friction exists only when the crate is sliding across the floor.
The crate has mass 100 kg. In this situation, the normal force points upward.
Experiment 1
The student pushes horizontally (rightward) on the crate, and gradually increases the strength of this push force. The crate does not begin to move until the push force reaches 400 N.
Experiment 2
The student applies a constant horizontal (rightward) push force for 1.0 seconds and measures how far the crate moves during that time interval. In each trial, the crate starts at rest, and the student stops pushing after the 1.0-second interval. The following table summarizes the results.

Trial | push force (N) | distance (m) |

1500 | 1.0 |  |

2600 | 1.5 |  |

3700 | 2.0 |  |

1. | The coefficient of static friction between the crate and floor is approximately:

A. | 0.25

B. | 0.40

C. | 2.5

D. | 4.0

2. | In experiment 1, when the rightward push force was 50 N, the crate didn't move. Why didn't it move?

A. | The push force was weaker than the gravitational force on the crate.

B. | The push force had the same strength as the gravitational force on the crate.

C. | The push force was weaker than the frictional force on the crate.

D. | The push force had the same strength as the frictional force on the crate.

3. | The coefficient of kinetic friction between the crate and the floor is approximately:

A. | 0.20

B. | 0.30

C. | 0.40

D. | 0.50

4. | In trial 3, what is the crate's speed at the moment the student stops pushing it?

A. | 1.0 meters per second

B. | 2.0 meters per second

C. | 3.0 meters per second

D. | 4.0 meters per second

5. | For trial 3, which of the following graphs best shows the position of the crate as a function of time? The student first starts pushing the crate at time t = 0 s.

A. | A

B. | B

C. | C

D. | D

PASSAGE 2 (Questions 6 – 10 pertain to this passage.)
A moving company uses the pulley system in figure 1 to lift heavy crates up a ramp. The ramp is coated with rollers that make the crate's motion essentially frictionless. A worker piles cinder blocks onto the plate until the plate moves down, pulling the crate up the ramp. Each cinder block has mass 10 kg. The plate has mass 5 kg. The rope is nearly massless, and the pulley is essentially frictionless. The ramp makes a 30° angle with the ground. The crate has mass 100 kg.
Let W1 denote the combined weight of the plate and the cinder blocks piled on the plate. Let T denote the tension in the rope. And let W2 denote the crate's weight.

6. | What is the smallest number of cinder blocks that need to be placed on the plate in order to lift the crate up the ramp?

A. | 3

B. | 5

C. | 7

D. | 10

7. | Ten cinder blocks are placed on the plate. As a result, the crate accelerates up the ramp. Which of the following is true?

A. | W1 = T = W2sin 30°

B. | W1 = T > W2sin 30°

C. | W1 > T = W2sin 30°

D. | W1 > T > W2sin 30°

8. | The ramp exerts a "normal" force on the crate, directed perpendicular to the ramp's surface. This normal force has magnitude:

A. | W2

B. | W2sin 30°

C. | W2cos 30°

D. | W2(sin 30° + cos 30°)

9. | The net force on the crate has magnitude:

A. | W1 – W2sin 30°

B. | W1 – W2

C. | T – W2sin 30°

D. | T – W2

10. | After the crate is already moving, the cinder blocks suddenly fall off the plate. Which of the following graphs best shows the subsequent velocity of the crate, after the cinder blocks have fallen off the plate? (Up-the-ramp is the positive direction.)

A. | A

B. | B

C. | C

D. | D

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