How to Calculate Contact Force

By Thomas Bourdin; Updated April 24, 2017

Newton's Three Laws of Motion provide the basis for understanding the source of movement for many macroscopic objects. One important implication of these laws is that any changes in motion of an object is caused by a force (such as a push or pull). These interactions where two (or more) bodies are in contact are called contact forces. Contact forces are ubiquitous and are the cause of most everyday interactions that are explained by Newton's Laws.

Determine the total mass of the system by combining the masses of the individual bodies. For example, if the system consists of two blocks with masses of 4 kilograms (kg) and 8 kg, respectively, then the total mass is 12 kg.

Calculate the acceleration of the system, given the total force and the total mass of the system--for example, the two bodies are being pushed by a force of 30 Newtons (N). The acceleration can be calculated by dividing the force of 30 N by the combined mass of the bodies, which is 12 kg. Completing this calculation yields 2.5 meters per second square (m/s^2) as the acceleration.

Multiply the acceleration of the bodies by the mass of the larger body to find the contact force. In this example, multiplying 2.5 m/s^2 by 8 kg gives 20 N. This is the contact force between the two blocks.

Tip

If the system of objects is not accelerating, then the contact force between the bodies is just the initial force.