IGCSE Physics - 1.7.2 Work

Objective

Understand that mechanical or electrical work done is equal to the energy transferred.

What is Work?

In physics, work is done when a force causes displacement of an object. It is a measure of the energy transferred to or from an object by the application of a force over a distance.

Mathematically, work (W) is defined as the dot product of the force (F) and the displacement (d):

$$W = F \cdot d$$

This means that work is only done if the object moves in the direction of the force.

Mechanical Work

Mechanical work involves forces and displacements in the mechanical systems. Examples include:

• Pushing or pulling an object
• Lifting an object vertically
• The work done by a spring

The work done by a constant force over a displacement is given by:

$$W = F \times d \times \cos{\theta}$$

where:

• $F$ is the magnitude of the force
• $d$ is the magnitude of the displacement
• $\theta$ is the angle between the force and the displacement

If the force and displacement are in the same direction ($\theta = 0^\circ$), then $\cos{0^\circ} = 1$, and the formula simplifies to:

$$W = F \times d$$

If the force is perpendicular to the displacement ($\theta = 90^\circ$), then $\cos{90^\circ} = 0$, and no work is done.

Electrical Work

In electrical circuits, work is done by the electric field on moving charges (electrons). When a current flows through a resistor, electrical energy is transferred to the resistor, causing it to heat up.

The electrical work done ( $W_{electrical}$) is the electric potential difference ( $V$) multiplied by the charge ( $q$) that moves:

$$W_{electrical} = V \times q$$

The unit of electrical work is the joule (J), which is equivalent to the unit of energy.

Energy Transfer

The fundamental concept is that work done is equal to the energy transferred. This energy transfer can take various forms, such as:

• Kinetic energy (energy of motion)
• Thermal energy (heat)
• Potential energy (stored energy)
• Light energy

In any process where work is done, energy is either transferred to the system or transferred from the system.

Examples

Scenario	Work Done	Energy Transfer
Lifting a box vertically	$W = F \times d$ (where F is the force applied and d is the distance lifted)	Potential energy of the box increases
Pushing a block across a floor	$W = F \times d \times \cos{0^\circ} = F \times d$	Kinetic energy of the block increases (assuming friction is negligible)
Current flowing through a resistor	$W_{electrical} = V \times q$	Thermal energy is transferred to the resistor