Question

A block is resting on a rough horizontal surface. A force is applied horizontally, but the block does not move. What can be said about the frictional force acting on it?

• A. It is zero
• B. It is equal to the limiting friction
• C. It is more than the applied force
• D. It is equal to the applied force

Hint:

Static friction adjusts to match the applied force until it reaches the limiting value. If the object is at rest, static friction equals the applied force, not the maximum possible friction.

Answer 1

The Correct Option is D

When a horizontal force is applied to a block on a rough horizontal surface, friction opposes the applied force.
As the block remains stationary, it is in equilibrium, meaning the net force is zero.
Consequently, the frictional force equals the applied force:
\[ f_{\text{friction}} = F_{\text{applied}} \]
This is known as static friction, a force that self-adjusts to match the applied force up to a maximum value called limiting friction.
The limiting friction is calculated as:
\[ f_{\text{limiting}} = \mu_s N \] where \( \mu_s \) represents the coefficient of static friction and \( N \) is the normal force.
If the applied force does not exceed the limiting friction, the static friction will be equal to the applied force, and the object will remain at rest.
In this scenario, with the block immobile, it is established that:
\[ f_{\text{friction}} = F_{\text{applied}} \]
Therefore, the frictional force acting on the block is equal to the applied force.