Work done by a content force and a variable force

We all are familiar with the term work, but the scientific meaning of the term is entirely different from the meaning of this term. In scientific terms, work is related to energy. When any work is done, energy is transferred from one form to another.

 For any work to be done scientifically, some energy has to be exerted, and there has to be displacement of energy in the direction that the energy is applied.

 We can conclude that the product of the force applied in a particular direction leads to displacement and the magnitude of displacement.

 The formula for work is as follows.

W = (F cos θ) d = F. d

So in this article, we will discuss work done by a constant force and a variable force. But before this, let’s talk about constant force and variable force.

Constant force 

A constant force does not change in regard to the time when applied to an object. 

A constant force assists in maintaining an object’s steady speed and enables uniform motion. A force given to a stationary object is also considered to be constant if it aids in maintaining its balance. A constant force is a force that tends to act on an item for an infinitely long period, assuming the physical conditions stay constant. When the force is constant, the work done by the constant force is equal to the product of the force and the distance travelled in the force’s direction.

Some examples of constant forces are gravity, the force of friction, upthrust, pendulum, and many more. 

Gravity pulls on an object regardless of the passage of time, and that is why it is classified as a constant force. 

Another example of constant force is cycling. While cycling, a person exerts a force that makes the cycle constantly work. It makes it constantly work, hence making cycling a constant force. 

Hydrostatic force can be determined as a constant force, unlike buoyancy. This is because hydrostatic force exerts a force on the object from each side of the respective object, and in the case of buoyancy, the force is exerted only in the upward direction. Therefore, hydrostatic force is also classified as a constant force. 

Variable force

Most of the forces that we encounter every day are variable forces. Variable forces abound in nature. Examples of variable forces are electrostatic force, magnetic force, spring force, gravitational field force, etc.

We can say that a force is working when there is a displacement in the direction that the force is applied. The displacement determines the work done by a variable force. Its displacement can be divided into smaller intervals. Integration is essential to calculate the work done by a variable force. 

This article will explain the different types of variable forces present in nature and understand how to calculate these forces.

There are many examples of variable forces in nature. Spring force is the most common example of variable force, electrostatic force, magnetic force, and drag force. 

Work done by a constant force

Work done by a constant force: when a constant force works on displacement, the force remains the same during the whole process. Therefore, the calculation of such a kind of displacement is very easy. To calculate the work done by a constant force, we need to calculate the dot product of force and the displacement vector.

If a body is held on a frictionless surface and a force of constant magnitude of 10 N acts on it, the body will finish a distance of 5 metres due to the action of the forces, and the formula of the work done will be given as W = F x s ( W= work done, F = Force applied, s = distance travelled)

So work done W = 10 N x 5m = 50 J.

Work done by a variable force

Work done by a variable force: calculating the work done by the variable force is a bit more difficult than calculating work done by a constant force. As we learned in the article above, a variable force constantly changes. The dot product 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 total the work done by the variable force.

The work done by variable force formula is : 

W =  F(x).dx

Integration is used in the calculation of the work executed by constant forces.

The same integration method used to calculate the work executed by the variable force may also be used to calculate the work executed by the constant force. This indicates 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 into the equation.

Let us assume that gas is wrapped in the piston. Thermodynamics is concerned with the study of this phenomenon. As a result, the pressure equals the force on the surface area is constant and may be removed from the integral equation. 

 W = abPdV

W =P abdV

W = P(Vb-Va)

Where P is the pressure 

Vb-Va is the volume change.

Conclusion

Work executed by a variable force means when a force displays an object and does work on the object, the force might change its magnitude or direction or both. The forces of such kinds are known as variable forces. Calculating the work executed by variable force is more complex than finding out the work executed by a constant force.