Work Done By A Variable Force

Introduction

We all are familiar with the term ‘work’; However, work is related to energy in scientific terms. Energy is transferred from one form to another when work is done.

The product of the force and displacement leads us to the formula of work, which is:

W = (F cos θ) d

Work

In physics, work means mechanical work. Work is done when a body is displaced in a direction in which the force is applied, for example, when you push a rock, work is said to be done only when the rock moves and not when you apply pressure on the rock. The formula for work is W= Fs (Where w stands for work, F for force, and s for displacement). The standard unit of work is the joule. There are three types of work: positive work, negative work, and zero work.

Work done = Force × Displacement

W = Fs

• Work has only the value of magnitude, and there is no direction.
• The S.I. unit of work is joule:

1 joule = 1 Newton × 1 mètre.

• Work can only be done if two requirements are met:

1. An item should be subjected to force.
2. The object needs to be displaced.

• A force’s work on an object would be zero if the object’s displacement were zero.
• A force’s output might be either positive or negative.
• When a force works in the opposite direction of displacement, the work done is negative.
• When the force is in the direction of displacement, the work done is positive.
• To summarise, no work is complete if:

1. There is no displacement.
2. There is no force.
3.  Both the force and the displacement are perpendicular to one another.

Types of Forces

• Constant force – A constant force is the force when the direction and magnitude remain constant during the journey of a certain body.
• Variable force- This is the force when the direction and amplitude vary during the body’s motion, for example, spring force, magnetic force, and electrostatic force.

Work done by a Variable Force

It is more difficult to calculate the variable force’s work than a constant force. As mentioned above, a variable force is constantly changing. The dot project of a variable force is calculated for elemental displacement. During the fundamental changes in displacement, the force will be considered constant. When the integration is performed on the full displacement by the variable, we will calculate the total work done by the variable force.

Let us understand this concept by integration.

Integration is used to calculate the work executed by constant and variable forces, indicating that the particular method of determining the work executed by a static strength on a moving body is to integrate the product of distance and force in the equation.

Let us assume that gas is wrapped in the piston. We need to calculate the work done by a gas on the piston. As a result, the pressure equals the force on the surface area is constant and may be removed from the integral equation.
dW = Fds = pAds = pdV

W =abPdV where ab is the area

W =PabdV

W = PV

Where P is the pressure

V is the volume change.

The product derived from this equation is similar to that obtained from force and distance.

Conclusion

Work executed by a variable force indicates that when a force displays an object and does work on the object, the force might change its magnitude or direction or both. Calculating the work executed by variable force is more complex than a constant force. In variable forces, the work done is calculated with the integration method.