Newton’s Second Law of Motion

Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system and inversely proportional to its mass. This means that a net force will produce an acceleration in its own direction and that the acceleration will be bigger the stronger the force is. Likewise, the same force will produce a lesser acceleration on an object the greater the mass of the object is.

In equation form, Newton’s Second Law is

a = ΣF /m A is equal to sum of F divided by m,

where a is the acceleration, ΣF the sum of F is the vector sum of all forces acting on the body, the net force; and m is the mass. This is often written in the more familiar form ΣF = m awhere the vector sum of forces is equal to the mass times acceleration.

For problems in more than one dimension, the component form of Newton's Second Law of Motion is used.

Three panels show similar scenes. In the first scene, a person pulls a cart of mass m with force F. The acceleration of the cart is a. In the second scene, two people are pulling on the same cart. Together, they pull with a force of 2 F and the acceleration of the cart is 2 a. In the third panel, a person pulls a bigger cart with a mass of 2 m with a force of F. The acceleration of the cart is one half of a.

Figure 1: A person pulls on a cart of mass m with force F and, as a result, the car accelerates in the direction of the pulling force. If twice the force is applied, the acceleration of the cart is multiplied by two. If the mass of the cart being pulled is multiplied by a factor of two, its acceleration is divided by a factor of two.