# Work in Physics | Definition | Examples

## Work-

In physics, work may be defined as-

 The work is said to be done when a force acting on the body causes a displacement it in the direction of force.

### Essential Conditions for Work-

The following conditions must be satisfied for work to be done-

• A force must act on the body.
• The point of application of the force must have some displacement in the direction of force.

### Work Done By A Constant Force-

The work done by a constant force is calculated by using the formula-

OR

Consider-

• A body is acted upon by a force ‘F’ acting at an angle θ with the horizontal.
• The body suffers a displacement ‘d’ as shown.

Here, the force F can be resolved into two rectangular components-

• Fsinθ, which is perpendicular to the direction of displacement
• Fcosθ, which is along the direction of displacement

The component Fcosθ causes the displacement d in its own direction whereas the component Fsinθ does not cause any displacement.

By the above definition, the work done by force F is given by-

W = Force in the direction of displacement x Displacement

W = Fcosθ x d

W = F x d x cosθ

W = F.d

Thus, work done is the dot product of force and displacement vectors.

### Characteristics of Work done-

• Work is a scalar quantity.
• The SI unit of work is joule (J).

1 J = 1 Nm

• The work done is said to be one joule if a force of 1 N causes a displacement of 1 m in the direction of force.
• The work done by a force may be positive, negative or zero.

### Nature of Work Done-

The work done by a force may be positive, negative or zero.

### Positive Work-

 When the angle between force and displacement is an acute angle (<90°), then the work done by force is positive.

The positive work signifies that the force favors the motion of the body.

#### Examples-

• When a body falls freely under gravity (θ=0°), the work done by gravity is positive.
• When a horse pulls a cart, the applied force and displacement are in the same direction (θ=0°), the work done by horse is positive.

### Negative Work-

 When the angle between force and displacement is an obtuse angle (>90°), then the work done by force is negative.

The negative work signifies that the direction of force is such that it opposes the motion of the body.

#### Examples-

• When a body is thrown upwards under gravity (θ=180°), the work done by gravity is negative.
• When brakes are applied to a moving vehicle (θ=180°), the work done by the braking force is negative.
• The work done by friction is usually negative.

### Zero Work-

 When the angle between force and displacement is 90°, then the work done by force is zero.

#### Examples-

• The work done by a coolie carrying a suitcase on his head and moving on a horizontal platform (θ=90°) is zero.
• The work done by centripetal force (θ=90°) is zero.