Dimensional Formula of Work

“Work” and “energy” are two terms we often hear and use in our daily lives. Work is a type of activity that involves a certain amount of physical as well as mental effort. To perform any work, you need energy. However, work and energy are not defined in such a way in physics. For example, suppose we push or pull a box, and it moves; it means work is performed. On the contrary, suppose a woman is carrying many pots on her head but is standing still on the spot. In such cases, it is said that work is not performed. In terms of physics, energy is also closely related to work. The capacity of a specific object to perform a certain work is termed energy. Before we understand the meaning of the dimensional formula of work, let’s go over some basic concepts.

Definition of the dimension of work

There are physical quantities that are measured in specific units. There are seven different types of base units that are used to describe a physical quantity.

Work is a quantity that cannot be described in terms of length as well as time. It is important to understand that the dimensions of work are the same or equal to the dimensions of energy.

Temperature, mass, and electric charge are some fundamental quantities that cannot be expressed in terms of other units.

In terms of physics, work is a process through which the transfer of the motion of an object takes place because of an applied force. This work is represented with the help of the product of the force as well as displacement.

Definition and Formula of Work Done

• Work is considered to be done when a force applied to an object produces a specific motion in the specified object.

• Work is defined in terms of the force applied to a specific object and the displacement of said object.

Example: A notebook is placed on a frictionless horizontal table. The notebook will be acted on with a constant force, termed “F”. The action of this force is to push the book through a distance D in a straight line in the specific direction of the force applied.

Note: The work done with the application of force is the product of the displacement of the specific object and the magnitude of the applied force

W = F*D

Where F = Applied force, and

D = Distance travelled by the object.

There are two important things you must keep in mind:

1. The work done is positive when the force applied to the specific object displaces the object in the same direction as the force applied.

2. The work done is negative when the force applied to the object displaces said object in the opposite direction.

Dimensional Formula of Work

To understand the dimensional formula of work or any physical quantity, you must consider the formula and the definition with specific known dimensions.

You must also understand that work is a scalar quantity because work does not have any direction. Moreover, we previously explained that work is the product of force as well as displacement. Now, you must understand that the displacement of the object may or may not be because of the applied force.

Let us consider an example. Force is applied when a ball is thrown upwards; however, when the ball returns to the ground, it is the gravitational force that acts on it. Hence, a force equal to the weight of the ball is applied to it.

Now, let us understand the meaning of the dimensional formula of work and its derivation.

When a constant force F is applied to an object, it causes a displacement known as s in the specific object. Let us take the angle between the displacement and the force as θ 

Then the work done by the force would be 

W = Fs cosθ

Now, the work was done either to transfer or displace energy from one place to the other or change its form.

You must know that the SI unit of work is the joule, represented as J.

W = F. Δx

Now, this can be represented as 

W = F Δx cos(θ)

Here 

θ = The angle between the force as well as the displacement vector

cos = Cosine of the angle is dimensionless, and the dimension of the displacement is of length.

Force is measured in newtons, represented as

1 N = kg. m/s2

The dimension of the work is

Work = Force x Displacement

This can be represented as

W = F x s

Here 

s: Displacement

F: Force applied

W: Work done by the force

Now, the dimension of the displacement will be L1

Let us derive the dimension of force

F= m.a

Here 

m = Mass of the object

a = Acceleration produced in the object

The dimension of the mass = [M1]

Acceleration will be represented as 

a = Δv/t = Δvt-1

Hence, the dimension of velocity is [M0L1T−1]

The dimension of time = [T1]

= [M0L1T-2]

Hence, the dimension of the force is given by

Dimension of the force = [ M1] × [M0L1T−2] = [M1L1T−2]

Hence the dimension of the work = Dimension of the force x Dimension of Displacement

= [M1L1T−2] × [L1]

= [M1L2T−2]

And the unit of work done is the joule.

So, the dimensional formula of work done is [M1L2T−2]

Conclusion

To understand how we can derive the dimensional formula of work using the dimensions of force and displacement, we first need to understand the formula used to calculate work and the factors on which the magnitude of work depends. Moreover, you should also be familiar with the procedure to conduct different operations involving the use of base units. Thus, before you completely understand the concept of the dimensional formula of work, it is essential that you have thorough knowledge regarding force, mass, displacement, and work done. The formula and dimensional formula of work is explained elaborately in the article. The dimensional formula of work done is [M1L2T−2].