Force-Potential Energy Relation

The physical world can be broken down into interactions between different types of forces, and it is these interactions that give meaning to all the phenomena we witness. In our daily lives, too, all our activities involve the application of force in some form or other.

But, all activities ranging from the movement of particles to the change in motion of a body require energy. Energy is an important factor in trying to do any kind of work. It is the very fundamental requirement of being able to do work. The manipulation of energy is also important for the development of civilisation.

What is Force?

Force is the fundamental concept that gives the cause behind any phenomenon that we observe. From the most trivial of observations, like moving a glass of water to the movement of celestial bodies, everything is explained and controlled by force.

Force is born from the interaction of two bodies with each other. As long as these two bodies interact with each other, there is a force acting on both the bodies. When the interaction between these two bodies ceases, the force acting on these two bodies also ceases. 

Force can be of two types: contact force and non-contact force. Contact forces are those forces that require physical interaction between the two bodies for the force to have an effect on them. For example, the frictional force is a contact force. For friction to act upon two bodies, the two bodies should be in touch with each other. If they are not in touch with each other, there will be no frictional force between them.

Non-contact forces are those forces that do not require physical interaction between the two bodies. The effect of these forces can be felt in a given region around a certain body responsible for the force. Examples of these forces include gravitational force and electrostatic forces. In the case of gravitational force, two bodies attract each other by virtue of their masses and the distance between them. It does not require the two bodies to be in contact with each other; instead, they only need to be within the region around each other where the effect of their forces can be felt.

What is Potential Energy?

When force is applied on a body, displacement is produced in the body. In order to produce this displacement and to apply force on a given body, the applicant of the force must be spending a certain amount of energy. But whenever energy is spent, it cannot be destroyed rather it must take up some other form.

When force is applied on a body and the body gets displaced from its initial position, then it is said that work is done on the body. In order to do work, energy has to be used. When energy is used, it must get expedited in a different form of energy. This different form is called potential energy. 

When work is done on a body, the work done gets stored in the form of potential energy of the body. This potential energy of the body is by virtue of the force acting upon it. Therefore if no force were to act on a body, there would be no potential energy of the body. For a body to apply force on a different body, or to do some work , it must have a certain amount of potential energy in it. Without potential energy, if there is no external source of energy, a body would not be able to do any work.

The unit of potential energy is Joule (J).

Force Potential Energy relation

We have seen that potential energy is stored in a body by virtue of the work that is done on the body. But work is an effect of force; therefore, it becomes clear that force and potential energy share a relation between them. But force is a vector quantity, and potential energy a scalar quantity, so what relation do these have with each other?

Let us consider the example of a tennis ball thrown in the air. To throw the ball, some force has to be applied on it. If the mass of the ball is m and it reaches a height h when it is thrown in the air, then we can tell the potential energy that the ball will have when it reaches the pinnacle of its motion.

The force on the ball will be F and the height gained by the ball is h. Therefore, the work done on the ball is W = F x h. Now the work done on the ball is stored as the potential energy of the body. Therefore we can say that the potential energy of the body is U = W = F x h.

In general, if a force F is acting on a body to produce a displacement Δy, then the potential energy of the body can be given as,

ΔU=F × Δy

Rearranging the equation, we can get,

F=ΔU/ Δy

Therefore, the force can be described as the slope of the graph that plots the potential energy of a body at different points in its path.

Conclusion

Force is the fundamental concept that gives the cause behind any phenomenon we observe. From the most trivial of observations, like moving a glass of water to the movement of celestial bodies, everything is explained and controlled by force.

When force is applied to a body, and the body gets displaced from its initial position, it is said that work is done on it. In order to do work, energy has to be used. When energy is used, it must get expedited in a different form of energy. This different form is called potential energy.

We have seen that potential energy is stored in a body by virtue of the work that is done on the body. But work is an effect of force. Therefore, it becomes clear that force and potential energy share a relation between them.