Question

A box slides down a plank of length d that makes an angle of θ with the horizontal, as shown. The kinetic and static coefficients of friction are μk and μs, respectively. Option A: The box will slide down the plank. Option B: The answer depends on the value of μk. Option C: The answer depends on the value of μs. Option D: The box will not slide down the plank.

Answer 1

The box will slide down a plank with constant velocity if the kinetic frictional force is equal to the component of the box's weight down the slope. Hence, it depends on the value of the kinetic friction coefficient (μk).

Step-by-step explanation:

Whether a box will slide down a plank depends on the component of the weight down the slope and the kinetic friction opposing this motion. The component of the weight pulling the box down the plank is mg sin θ, where m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the plank with the horizontal. This force competes with kinetic friction, which is defined as μk mg cos θ.

For a box to slide at a constant velocity, the down slope force and frictional force must be equal, which means that the kinetic friction coefficient μk determines this balance. Therefore, if μk is large enough to create a frictional force equal to the weight component down the slope, the box will not accelerate, implying the correct answer is Option B: The box will slide down the plank, as the question strictly indicates that the box will either slide or not, without the consideration for initial movement.

Answer 2

The box will slide down the plank.

Step-by-step explanation:

When an object slides down an inclined plane, the force of friction opposes its motion. The coefficient of friction, denoted as μ, determines the amount of friction between the object and the plane. In this case, we have the kinetic and static coefficients of friction, μk and μs respectively.

If the box is sliding down the plank, it means that the force of friction, which is given by μk times the normal force, is less than or equal to the force component down the plane, which is given by mgsin(θ). Therefore, the answer is option A: The box will slide down the plank.

The answer does not depend on the value of μs, as the static coefficient of friction is only relevant when the box is at rest and not sliding down the plank.