Work Formula

Every day we do work that requires energy. Also, to do work we have to use force so that we can push an object to a distance. Besides, the work formula helps us to find out the energy we use to move an object.

Work

When a force act on a body or object, it causes the object to move to cover a distance. Furthermore, sometimes it happens that the direction of the moving object is not as same as the direction of the force. Moreover, in these cases the component of force that acts in the direction of the movement causes work to be done.

In simple words, work refers to the force you apply to an object to cause a change in its position or when the object moves and cover some distance. Besides, the S.I unit of work is Joules (J). Most noteworthy, joule and newton-meter (N) is the same thing. In this way, the unit for work and energy is the same.

Transfer of Energy

When we do work we transfer energy from one object to another. Also, work links with expansion and contraction of gases. Moreover, when gas tries to expand it exerts an increasing force on the surface of the container and might make that surface move.

For example, suppose you heat a balloon then the air molecule inside the balloon will gain energy and strike each other. Also, this will cause the molecule to hit the surface of the balloon with more force causing its surface to expand. In this way, the air does work and transfer energy to the balloon.

 Formula for Work 

Work = Force × Distance × Cosine (refers to the angle between movement direction and force)
W = F × d × cosθ

Derivation of Work Formula

W = work done
F = the force which we express in Newton’s
d = distance that the object or body covers
Cosθ = refers to the angle amidst the force and movement direction

Solved Examples on Work Formula 

Example 1

Suppose a tractor-pulled a wagon full of hay to a distance of 1000 m. For doing so the force exerted on the wagon to cover this distance was 12,000 N. Also, the force acted in the same direction as the movement of the tractor. Calculate the work done by the tractor to pull the wagon.

Solution: In this question, the movement and force that acted on the wagon are in the same direction, thus the angle between them was 0^o. Now we can apply the work formula to calculate the work done by the tractor.

W = F × d × cosθ
W = F × d (1)
W = (12,000 N) (1,000 m)
W = 1,20,00,000 N∙m = 1,20,00,000 J

Besides, we can state it as Mega Joules 12.0 MJ. So, the work done by tractor to move the wagon in the given distance is 1,20,00,000 J or 12.0 MJ.

Example 2

Let’s consider a man is pushing a lawnmower across a yard and the force that he is applying to the handle is angled down at 60^o from the horizontal plane. Besides, the force has a magnitude of 900 N. So, if he pushes the mower 30 m. Then calculate the work done by the person to move the lawnmower.

Solution: In this situation, the force is at the angle of 60^o with respect to its movement. Now we can find the work done by using the work formula.

W = F × d × \(cos60^o\)
W = F × d (0.5)
W = (900 N) (30 M) (0.5)
W = 13,500 N∙m = 13,500 J

In the given distance the work done by the person while mowing the land was 13,500 J.