Kinetic & Static Friction (College Board AP® Physics 1: Algebra-Based): Exam Questions

A force is applied to move a box of mass across a rough horizontal surface at velocity . The magnitude of the force of kinetic friction between the box and the surface is . The applied force is removed and the box slows to a stop.

Derive an expression for the distance travelled after the applied force is removed in terms of , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

A student pushes a wooden box of mass up a rough inclined plane at a constant velocity. The incline makes an angle to the horizontal, and the coefficient of kinetic friction between the box and the surface is ​.

The box is pushed a distance up the incline by a constant force ​ applied parallel to the surface.

The student derived the following expression for the applied force:

The experiment is repeated with a different block of the same mass. The coefficient of kinetic friction between the new block and the surface is increased by a factor of compared to the original block, where . The new block still moves up the incline at a constant velocity.

Indicate whether the magnitude of the new applied force increases by less than , exactly , or more than .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ less than

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ exactly

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ more than

Justify your reasoning using the student's derived expression.

Figure 1

A sled of mass slides down a rough ramp with constant speed . The angle between the ramp and the horizontal is , as shown in Figure 1. The ramp smoothly transitions to a horizontal surface. The coefficients of static and kinetic friction between the sled and the ramp are and , respectively. The ramp and the horizontal surface are made of identical materials.

The dot in Figure 2 represents the sled when it is sliding down the ramp at a constant speed. Draw and label arrows that represent the forces (not components) that are exerted on the sled. Each force must be represented by a distinct arrow starting on and pointing away from the dot.

Figure 2

Express your answers for b)i) and b)ii) in terms of , , , , and physical constants, as appropriate.

i) Starting with Newton's second law, derive an expression for the frictional force exerted on the sled. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

ii) Derive an expression for the coefficient of kinetic friction between the sled and the ramp. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 3

From time to , the sled slides down the ramp at a constant speed. At , the sled reaches the bottom of the ramp, and from to , the sled continues to slide on the horizontal surface, as shown in Figure 3. The sled comes to rest some time after .

On the axes shown in Figure 4, sketch a graph of the velocity of the sled as a function of time from to .

Figure 4

Indicate how the shape of the graph between and sketched in part c) would change, if at all, if the angle of the ramp were increased. Justify your claim.