Question

A girl pushes on a crate with a force as great as the frictional force existing between the crate and the floor. Which of the following statements is true?

A) The net force on the crate is zero.
B) The crate may be at rest or it just starts to slide.
C) The crate is not accelerating.
D) All of the above.

Answer 1

Hint: When the applied force overcomes the frictional force between the crate and the floor, the crate moves. The frictional force is a resistive force that opposes the motion of the crate.

Complete step by step answer.
Step 1: List the data provided in the question.
A girl is pushing a crate against the floor with some force. This force is said to be equal to the frictional force existing between the crate and the floor.
i.e., ${\text{applied force}} = {\text{frictional force}}$
Step 2: Discuss the effect of the applied force on the crate.
Initially, the crate is at rest. When the girl applies a force on the crate, friction between the crate and the floor opposes this force. It is only when the exerted force becomes greater than the frictional force that the crate moves. So for the crate to move, the net force on the crate must have some value.
Then the net force is the resultant force acting on the crate and it is given by, ${\text{net force}} = {\text{applied force}} - {\text{friction}}$. The negative sign corresponds to the difference in the direction of the two forces. Since it is given that the applied force is only as great as the frictional force, the net force on the crate will be zero.
Now as the net force acting on the crate is zero, the crate must be at rest or it just starts to slide.
Also, we know the force is the product of mass and acceleration i.e., $F = ma$ . Here the net force is zero. This implies that the acceleration of the crate must be zero too. (Mass of the crate cannot be zero).
Therefore, all statements are true. D is correct option

Additional information: In addition to the applied force and the frictional force, the weight of the crate exerts a force downward. But this is balanced by an equal and opposite force called normal force. The normal force acts upward.

Note: The frictional force discussed here is the static friction. It is the force that keeps the crate from moving. It only comes into play when an external force is applied. If there is no external force then there will be no static friction.