A block of mass m is kept on a horizontal table. If the static friction coefficient is u, find the frictional force acting on the block.

To determine the frictional force acting on a block resting on a horizontal table, we need to consider the forces at play, particularly the static friction. Static friction is the force that prevents an object from moving when it is at rest. It acts in the opposite direction to any applied force trying to move the object. The maximum static frictional force can be calculated using the coefficient of static friction and the normal force acting on the block.

Understanding the Forces Involved

When a block of mass m is placed on a horizontal surface, the weight of the block exerts a downward force due to gravity, which can be calculated as:

• Weight (W) = m × g

Here, g represents the acceleration due to gravity, approximately 9.81 m/s² on Earth. This weight creates a normal force (N) acting perpendicular to the surface, which, in this case, is equal to the weight of the block since there are no vertical forces acting on it. Therefore:

• Normal Force (N) = m × g

Calculating the Maximum Static Friction

The maximum static frictional force (F_s) can be calculated using the coefficient of static friction (u) and the normal force:

• F_s = u × N

Substituting the expression for the normal force, we get:

• F_s = u × (m × g)

Determining the Actual Frictional Force

It’s important to note that the actual frictional force acting on the block will depend on any external forces trying to move it. If there are no external forces applied to the block, the frictional force will be zero. However, if a force is applied, the frictional force will adjust up to its maximum value, which is F_s.

For example, if you apply a horizontal force F on the block that is less than or equal to F_s, the frictional force will equal the applied force, preventing the block from moving. If the applied force exceeds F_s, the block will start to move, and kinetic friction will take over, which is typically less than static friction.

Summary of Key Points

• The static frictional force can be calculated as F_s = u × (m × g).
• The actual frictional force depends on the applied force and can range from 0 up to the maximum static friction.
• If no external force is applied, the frictional force is zero.

In essence, the frictional force acting on the block is contingent upon the forces applied to it, and it will adjust accordingly, up to its maximum limit defined by the coefficient of static friction and the weight of the block. This interplay of forces is fundamental in understanding how objects behave on surfaces.