Question

Which of the following statements is true regarding the motion of the block?

A. The block will move with constant velocity if the slope angle θ is equal to the arctan of the coefficient of kinetic energy.
B. The block will move with constant velocity if the slope angle θ is equal to the arctan of the coefficient of friction.
C. The block will move with constant velocity if the slope angle θ is equal to the arctan of the gravitational force.
D. The block will move with constant velocity if the slope angle θ is equal to the arctan of the acceleration.

Answer 1

When an object slides down an inclined plane at constant velocity, the net force on the object is zero. The block will move with constant velocity if the slope angle θ is equal to the arctan of the coefficient of friction.

Step-by-step explanation:

When an object slides down an inclined plane at constant velocity, the net force on the object is zero. The force of gravity acting along the slope can be divided into two components: mg sin(θ) acting down the slope and mg cos(θ) acting perpendicular to the slope. The frictional force acting up the slope is given by μk mg cos(θ), where μk is the coefficient of kinetic friction.

For an object to move with constant velocity, the magnitude of the component of the weight down the slope (mg sin(θ)) must be equal to the magnitude of the frictional force (μk mg cos(θ)). Therefore, the correct statement is:

The block will move with constant velocity if the slope angle θ is equal to the arctan of the coefficient of friction (Option B).