Concept of Work in Physics

In this article, we are going to understand the basic concepts of Work.

Table of Contents

• What is Work?
• Formal Definition of Work
• Understanding Work Formula in depth

What is Work?

When we apply force or torque on a body, then energy gets transferred from one body to another. This energy transfer is the work done by that force or torque.

During this energy transfer, the energy may change its form. For example, frictional force that applies on a sliding ice cube, changes the mechanical energy (kinetic energy to be precise) of the ice cube into thermal energy (that is dissipated in the surroundings).

So, frictional force does the work of:

• transferring the kinetic energy of ice cube to the surroundings (i.e. from one body to another)
• changing the form of the energy from kinetic energy to thermal energy

So, Energy and Work are related to one another. They are inter-convertible. They even have the same unit, i.e. Joule.

Note

Sum of Energy and Work is conserved in Newtonian Physics.

Concept of Positive and Negative Work

Let’s consider an example.

If a person is holding a bag above his head, without moving it, then potential energy of that bag is not increasing. So, as no energy is being transferred by the person to the bag, we can say that No Work is being done by the person on that bag.

However, if the person raises the bag a bit, then it means that potential energy of the bag increases. That’s because the person has transferred his muscular energy to the bag by applying force. So, a Positive Work has been done by the person on the bag.

But we know that, as per Newtonian principal, every force has an equal and opposite reaction. So, the bag will also apply the same but opposite reaction force on the person. Also, by principal of conservation of energy and work, if the force exerted by the person does W positive work, then the reaction force by the bag will do -W negative work.

So, Positive Work is done by the object exerting force. Its energy will get transferred to the other object. So, the energy of the object doing Positive Work will get reduced.

And, the object on which the force is exerted, will gain energy. So, we can say that it does Negative Work on the object which is exerting force.

Summary

A force increasing the energy of some other body is said to be doing Positive Work.
A force decreasing the energy of some other body is said to be doing Negative Work.

Some more examples of Positive and Negative Work:

• When a horse pulls a cart on a level road – The horse does positive work on the cart, as it transfers its muscular energy into kinetic energy of the cart.

• If an object slides over a rough surface, then negative work is done by friction force – Friction force reduces the kinetic energy of the object and changes it to heat energy.

Now, let’s have a look at the formal definition of Work.

Formal Definition of Work

Definition of Work: If a force acting on some object moves it by some distance in the same direction in which the force is acting, then that is called work.

Mathematically, it is given by the following formula.
Work = Force × Distance, i.e., W = \(\overrightarrow{F} . \overrightarrow{s}\)

So, Work is a dot product of two vectors, Force and Displacement. It’s a scalar quantity.

SI unit of Work is Joule (J)

Understanding Work Formula in depth

Now, let’s try to understand the Work formula in detail.

W = \(\overrightarrow{F} . \overrightarrow{s}\) = F s cos θ

Here, θ is the angle between the Force and Displacement vectors.

So, work is said to be done only if:

• There is a force. No force (i.e. F = 0) means no work. For example, an object sliding on a horizontal and frictionless surface. It will keep on sliding forever without any external force.

• That force displaces the object. No displacement (i.e. s = 0) means no work. For example, a person exerting force on a heavy concrete slab without moving it even a bit. Or a person holding a weight over his head, without raising it.

• All or some of the movement must be in the direction of the force. If the direction of the force and displacement are mutually perpendicular (i.e. θ = 90°), then net work done will be zero (as cos 90° = 0). For example, when a stone is tied to a thread/string and moved along a circular path. Here, the centripetal force acting on the stone is perpendicular to the direction of motion of that stone. Therefore, work done by or against centripetal force in circular motion is zero.