Difference Between Gravitational Potential Energy and Elastic Potential Energy

Gravitational Potential Energy vs Elastic Potential Energy

Gravitational potential energy and elastic potential energy are two important quantities discussed in mechanics. This article will try to compare and contrast what are their definitions, their similarities and differences.

What is Gravitational Potential Energy?

To understand the gravitational potential energy, background knowledge in gravitational fields is required. Gravity is the force that occurs due to any mass. Mass is the necessary and the sufficient condition for gravity. There is a gravitational field defined around any mass. Take masses m1 and m2 placed in a distance r from one another. The gravitational force between these two masses is G.m1.m2/r², where G is the universal gravitational constant. Since negative masses are not present, the gravitational force is always attractive. There are no repulsive gravitational forces. It must be noted that gravitational forces are also mutual. That means, the force m1 exerts on m2 is equal and opposite to the force m2 is exerting on m1. The gravitational potential at a point is defined as the amount of work done on a unit mass when bringing it from infinity to the given point. Since the gravitational potential at infinity is zero and the amount of work has to be done is negative, the gravitational potential is always negative. The gravitational potential energy of an object is defined as the work done on the object when the object is taken from infinity to the said point. This is also equal to the product of gravitational potential and the mass of the object. Since the mass of the object is always positive and gravitational potential of any point is negative, the gravitational potential energy of any object is also negative.

What is Elastic Potential Energy?

Elasticity is a very useful property of matter. It is the ability of the materials to return to their original shape after the external forces are removed. It is observed that the force required to keep an elastic rod stretched is proportional to the stretched length of the rod. The proportionality constant is known as the spring constant and is denoted using k. This gives us the equation F=-kx. The minus sign stands for the reverse direction of x to the force. The elastic potential energy is the amount of work that is required to stretch the elastic object by a given length x. Since the force applied F(x)=kx, the work done is equal to the integration of F(x) from zero to x, with respect to dx, that is equal to kx²/2. Therefore, the potential energy is kx²/2. It must be noted that the potential energy of any object attached to the end of the rod does not depend on the mass of the object but only on the spring constant, and the stretched length.