 # Work: Factors On Which It Depends

## What is Work?

Quite often we use terms such as overworked and hard worker to describe the quantity of effort put by a person. But what is the meaning of work and how do we quantize it? In this section, we will learn about the physical meaning of work and the factors on which it depends. We can define work as:

The product of the component of the force in the direction of the displacement and the magnitude of this displacement.

### Work Formula

Mathematically we can write,

#### W = (F cos θ) d = F. d

Where,

• W is the work done by the force.
• F is the force, d is the displacement caused by the force
• θ is the angle between the force vector and the displacement vector

Work dimension is the same as that of energy and is given as, [ML2T–2].

### Unit of Work

The SI unit of work is joule (J), which is defined as the work done by a force of 1 Newton in moving an object through a distance of 1 metre in the direction of the force. A weightlifter lifts a barbell weighing 25 kg and displaces it from the ground by 2 m. Here, the work done upon the barbell is against gravity.

The work done upon the weight against gravity can be calculated as follows:

Work Done = (Mass × acceleration due to gravity) × Displacement

= (25 × 9.8) × 2 J

## Factors Affecting Work

Let us now consider the factors on which work done on an object by a force depends.

### Force:

Force is defined as a push or a pull that can cause any object with a mass to change its velocity and acceleration. Force is a vector quantity and has both a magnitude and a direction. If the force acting on an object is zero irrespective of the state of the object (dynamic or static) that work done by the force is zero.

### Displacement:

Displacement is a vector quantity that gives the shortest distance between the initial position and the final position of any object. If the resulting displacement in the direction of force, due to force acting on any object is zero, the net work done by that force on that object is zero. For e.g., if we push a rigid wall with all our might and still fail to displace it, then we can say no work has been performed by us on the wall.

## The Angle between the Force Vector and the Displacement Vector The work done by a force on an object can be positive, negative or zero, depending upon the direction of displacement of the object with respect to the force. For an object moving in the opposite direction to the direction of force, such as friction acting on an object moving in the forward direction, the work is done due to the force of friction is negative. Similarly, an object experiences a zero force when the angle of displacement is perpendicular to the direction of the force. Consider an example of a coolie lifting a mass on his head moving at an angle of 90˚ with respect to the force of gravity. Here, the work done by gravity on the object is zero.