Newton's Second law: The law of acceleration

An object subject to an unbalanced force will accelerate in the direction of the unbalanced force. The magnitude of the acceleration is proportional to the force and inversely proportional to the mass.

This law is usually expressed as F = ma. If an unbalanced force is applied to a mass, the mass will accelerate in the direction of the applied force. The difficulties occur when there are multiple masses involved and people do not know how to separate the forces in the system out to investigate each mass. Consider the system below.

The acceleration of the system is found by dividing the total force (40 N) by the total mass (8 kg). Both blocks will accelerate at 40 / 8 = 5 m s^-2.

If asked to find the force that the 3 kg block applies to the 5 kg block we need to consider the 5 kg block in isolation.

The force is 25N.

If asked to find the force of the 5 kg block on the 3 kg block, the correct approach is not to immediately apply Newton's third law. Especially since we have not even introduced it yet. The correct approach is to apply Newton's first law and identify the unbalanced force.

If there were no FB on A force then the acceleration would be; a = F / m = 40 / 3 = 13.33 m s^-1. Given that we know the acceleration is only 5 m s^-2, we solve by summing the two forces: