# Calculation of Work done in Physics – formula

Work is one of the popular words in our daily life. The word work means to do something. We need some energy to do work for us. Physics also says that some external energy is required to do a work. But, the Work done in Physics is different from the work we know in our daily life. In this article, we are going to explain the concept, formula and calculation of work done in Physics or science.

1. Definition of work done in Physics
2. Formula of work done
3. Units of work done
4. Dimension of work done
5. Calculation of work done
6. At what condition does the work done become zero?
7. Is work done energy?

## Definition of work done in Physics

In Physics, when a body moves some distance due to the application of net external force, then it is said that the external force has done a work. This type of work is nothing but mechanical work.

So, it is important that the body must have some displacement. It is not essential that the body always moves in the same direction of applied force. We have discussed that below. The work done is a scalar quantity.

## Formula of Work done

Work done is the multiplication between the net applied force and the displacement of the object.

Work done = Net force × Displacement

If a net force F displaces a body by r in the direction of applied force, then the equation of work done is, $\color{Blue} W = F.r$

But, this is not the general formula. Because the object may not move exactly in the same direction of force. If a net force F displaces an object by r in the direction making an angle $\color{Blue}\theta$, then the general formula of work done is

$\color{Blue} W = F.rcos\theta$………….(1)

This is the general equation of work done in Physics.

## Concept of positive work and negative work

If the object moves in the same direction of the net force, the work done is positive work and if the object moves in the opposite direction then the work done is negative work.

The work done against the friction force is always negative work.

## Units of work done

The SI unit of work done is Newton.meter (N.m) which has another name Joule (J). The CGS unit is dyne.cm or erg.

1 Joule = 107 erg.

## Dimension of Work done

$cos\theta$ do not have any dimension. So, the dimensional formula of work done is [ML2T-2].

## Calculation of Work done in Physics

One can calculate the amount of work done by using equation-(1). You need to know the three variables –

• The net force acting on the object
• Amount of displacement of the object
• The angle between the net force and the displacement

After finding these three, put these values in the formula of work done $\color{Blue} W = F.rcos\theta$ to calculate it.

Again, one can find the amount of work done by using the work done calculator directly. Here also you need to know the values of the above three quantities.

## At what condition the work done by the applied force becomes zero?

There are two conditions at which the work done by an applied force becomes zero.

1. If the displacement of the object becomes zero then the work done also becomes zero. For example: If an object starts its journey from a point and finishes it at the same point after traveling a distance, then its displacement is zero. Hence, the work done by the object is zero.
2. If a particle moves perpendicular direction to the applied force, then the work done becomes zero. Because, the cos90° = 0.

## Are Energy and work done are same in Physics?

Energy and work done are not the same in Physics in terms of the physical quantity. However, the dimensional formula and units are the same for these two quantities. Energy is the ability to do the work.

The work done on a body is stored as the potential energy inside the body and to do work, a system needs to have some energy. So, the work done is the phenomenon in which mechanical energy is transferred from an external system to the target body.