The force of friction can be calculated by multiplying the coefficient of friction by the normal force.

In more detail, the force of friction is a force that opposes the motion of one surface sliding over another. It is expressed using the formula:

where:

• $F$ is the force of friction,
• $\mu$ (mu) is the coefficient of friction, and
• $N$ is the normal force.

The normal force is defined as the force exerted by a surface that supports the weight of an object resting on it, acting perpendicular to that surface.

The coefficient of friction is a numerical value that quantifies the amount of friction between two objects. This value is determined experimentally and varies based on the materials in contact. There are two types of coefficients of friction: static and kinetic. The static coefficient of friction, denoted as $\mu_s$, represents the frictional force that must be overcome to initiate motion from rest. In contrast, the kinetic coefficient of friction, denoted as $\mu_k$, pertains to the frictional force that must be overcome to maintain a constant velocity while the object is in motion.

To calculate the force of friction, you first need to determine the normal force. For an object resting on a flat surface and not experiencing vertical acceleration, the normal force equals the weight of the object, which can be calculated using the equation:

where:

• $m$ is the mass of the object, and
• $g$ is the acceleration due to gravity.

Next, you must identify the appropriate coefficient of friction, which depends on whether the object is at rest or in motion, as well as the materials involved in the contact. Once you have both the coefficient of friction and the normal force, you can compute the force of friction by using the formula:

It’s important to note that the force of friction always acts in the direction opposite to the motion or potential motion of the object. For instance, if an object is moving to the right, the force of friction acts to the left. Similarly, if an object is stationary but is being pushed to the right, the force of friction still opposes this motion by acting to the left. This principle is why overcoming friction is necessary to either initiate the motion of an object or to maintain its movement.