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Work Formula Physics

In science, work is defined as a force causing the displacement of an object. In the case of a constant force, work is the scalar product of the applied force and the displacement due to this force. Due to the nature of scalar product work is a scalar quantity besides the fact that both force and displacement are vector quantities. In many occasions, we need to calculate the amount of work done by an object in motion. This article of physics will give the concept of work done with work formula physics and example. Let us begin it!

Work Formula Physics

What is Work?

Thus, work is a very important phenomenon in science as well as in our life. There are many examples of work done in our everyday life. For example, a horse pulling a plow through the field, a father pushing a grocery cart in a shopping mall, or a student lifting a bag on his back or his shoulder full of books and many more.

In general, for work to occur, a force is a must which will cause a movement in the object. For work done, displacement of the object is a must, otherwise, according to science no work will be done even if force is applied.

So, if a person pushing against a wall, will only exhaust himself because there is no work will be performed. This is because the wall does not move at all.

The formal definition of work:

The product of the component of the force in the direction of the displacement with the magnitude of this displacement will give the value of work done.

Mathematically we can write,

\(W= F × d × cos\theta\)

Where,

W It is the work done by the force.
F F is the force applied.
d It is the displacement caused by the force
\(\theta\) It is the angle between the force vector and the displacement vector.

Also if force and displacement are in the same direction, then

W = F × d

The dimension of work is the same as that of energy. It is given as, \([ML²T^-²].\)

Unit of Work:

The SI unit for the work is joule (J), and it is defined as the work done by a force of 1 Newton in moving an object for a distance of one unit meter in the direction of the force.

Work formula is used to compute work done, force or displacement in any problem. It is written as in Newton meter or Nm.

Solved Examples

Q.1: Compute the work done if 10 N of force acts on the body showing the displacement of 2m in the direction of the force.

Solution:

As given in the question:

Force, F = 10 N,

Displacement, d = 2 m,

\(So, W (Work done) = F \times d \)

i.e. \(W= 10 N \times 2 m\)

i.e. W = 20 N m or 20 joule.

Example-2: Compute work done for 2-newton force and 3-meter displacement and angle between force and displacement is 45 degree?

Solution:

As given in the question:

Force, F = 2 N,

Displacement, d = 3 m,

θ = 45°

Work done,

\(W = Fd cos\theta\)

\(i.e. W = 2N \times 3m \times cos 45°\)

\(It is because, cos 45°=\frac{1}{\sqrt{2}} \)

W   = 3.51 Nm. 

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