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 block is placed on a rough horizontal surface and a horizontal force is applied, friction acts to oppose the applied force.
Since the block does not move, it is in equilibrium. This means the net force on it is zero.
Therefore, the frictional force must exactly balance the applied force:
\[ f_{\text{friction}} = F_{\text{applied}} \]
This friction is called static friction. It is a self-adjusting force, meaning it increases or decreases to match the applied force—up to a maximum value called limiting friction.
The limiting friction is given by:
\[ f_{\text{limiting}} = \mu_s N \] where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force.
If the applied force is less than the limiting friction, the static friction equals the applied force and the object remains at rest.
In this case, since the block does not move, we conclude:
\[ f_{\text{friction}} = F_{\text{applied}} \]
So, the frictional force acting on the block is equal to the applied force.