# Work Formula

## Work Formula Physics

In Physics, work is energy transferred to or from an object through the application of forces along with a displacement. In other words, the work formula is the product of force and displacement. Work can be either positive or negative. Work is said to be positive work when both displacement and force are in the same direction. Work is said to be negative work when both displacement and force are in the opposite direction. Work is a scalar quantity as it has only magnitude and no direction. The SI unit of work is Joule. The explanation of the work formula will cover the concepts of work done by an object along with the formula of work done, and work formula Physics.

### What is Work in Physics?

Work, in Physics, is a measure of the transfer of energy that occurs when an object is moved over a distance by an external force at least partially, in the direction of displacement. If the force that is applied is constant, work can be calculated by multiplying the length of the path with the component of force acting along the path. To express the work formula mathematically, the work (W)  is equal to the force (f) time the distance.

W = Force × Distance

If the force is been exerted at an angle θ to  the displacement, then the work done will be calculated as:

W = F d Cos θ

### Work Examples

There are many examples of work in everyday life. Let us discuss a few: a boy pulling a grocery cart down the corridor of a grocery store, a horse pulling a plough through the field, a student lifting his bag full of books upon her shoulder, etc. In general, for work to occur, a force has to exert on an object causing it to move. A person pushing against a wall is not considered as work because the wall does not move. But, a child’s toy falling from a table and hitting the ground is considered as work because the force acting on the toy causes it to be displaced in a downward direction.

### Work Equations

The work equations or work formulas is articulated as:

W = F d Cos θ

In the above work equation

W = Amount of work.

F = Vector of force.

D = Magnitude of displacement.

θ = Angle between the vector of force and vector of displacement

The SI unit of work is joules and its dimensions are kg.m²/s².

### Work Done

Work done is the amount of energy transferred. In other words, work is said to be done when a force is applied. If that force is constant, then the formula for work done by the force is the dot product of the displacement.

$W = \overrightarrow{F} . \overrightarrow{D}$

The net work done on an object is equal to the energy added to the object. This is the reason for both the unit of work being Joules, J.

$W = \triangle K$

The formula for work done in constant force can also be given as:

$W = F \triangle K Cos \theta$

This implies that for work to be done, an object must have changed its position by an amount $\triangle \overrightarrow{k}$, while a force $\overrightarrow{F}$ is acting on it such that there include some non-zero components in the direction of the force. Hence, the formula for work done is:

$W = F \triangle K Cos \theta$

W = Work done (Joules)

F = Magnitude of force for which the work is calculated in Newtons

$\triangle K$ = Magnitude of displacement in meters

θ = Angle between the force and the direction of the displacement.

It should be noted that F Cos θ is the magnitude of the component of $\overrightarrow{F}$ in the direction of $\triangle \overrightarrow{k}$. if the value of θ is greater than 90° (> 90°), then the component is said to be parallel in the direction of displacement but indicates in the opposite direction and force is opposing the motion.

### Work Formula Examples with Solutions:

1. A school bus is travelling along a straight horizontal road. A force of 700 N is applied on the bus in the direction that it is travelling. As the bus increases its speed, it covers a distance of 10 m. Calculate the work done on a car.

Solution:

• The magnitude of the force applied, F = 700 N.

• The total distance travelled by the bus $(\triangle K)$ = 20 meters.

• The applied force and the distance covered by the bus are in the same direction. Hence, the angle between displacement and force is θ = 0°.

To calculate the work done a car, we will use the formula for work done, and that is:

$W = F \triangle K Cos \theta$

Substituting the value in the above work equation, we get

$W = F \triangle K Cos \theta$

(700 × 20 × Cos 0)

(700 × 20 × 1)

14000 Joules

The answer is positive because the applied force and displacement both are in the same direction.

2. Calculate the work done if 20 N of force acts on a body showing a displacement of 3 m.

Solution:

Force (F) = 20 N

Displacement  (D) = 3 m

Applying the formula of work done, we get:

Work Done = Force × Displacement

Substituting the values, we get

Work = F × D

W = 20 × 3

W = 60 Joules

Hence, the work done is 60 joules.

### Conclusion

At last, it is concluded that work is an energy that transforms from one system to another. In simple terms, it is expressed as a dot product of fòrce and displacement. Work formulas given here will help you to solve problems based on work in Physics.

Q1. What is Displacement?

Ans. Displacement is defined as the change in the position of an object or body. For example, if an object moves from point X to point Y, then its position changes. This change in position is considered as displacement. It is considered as a vector quantity and has both magnitude and direction.

Q2. What is the SI Unit of Work?

Ans. The SI unit of work is joules. The word joule is introduced after the 19th century English Physicist James Prescott Joule. The term joule is defined as the work required to exert a force of one newton through a displacement of one meter.

Q3. What is the Difference Between Distance and Displacement in Physics?

Ans. Distance and displacement are the two important terms used in Physics to describe the length between two points. Both the terms, distance and displacement, have some differences. Distance is defined as the length of the actual path between two points whereas displacement is the length of the shortest distance between two points.