Work

Work is the product of force and distance moved in the direction of the force. The SI unit of work is the joule (J).

Illustration of work done

Work done formula

The work done is calculated using the formula:

$W = F \times d$

Where:

• $W$ = work done (joules)
• $F$ = force applied (newtons)
• $d$ = distance moved in the direction of the force (metres)

Gravitational potential energy

The formula for gravitational potential energy is:

$E_p = m \times g \times h$

Where:

• $E_p$ = gravitational potential energy (joules)
• $m$ = mass (kilograms)
• $g$ = gravitational field strength (9.8 m/s²)
• $h$ = height (metres)

Compressing spring

Kinetic energy

The formula for kinetic energy is:

$E_k = \frac{1}{2} \times m \times v^2$

Where:

• $E_k$ = kinetic energy (joules)
• $m$ = mass (kilograms)
• $v$ = speed (metres per second)

Battery connected to a charging unit

Example 1

Question: how much work is done to first lift a 7 kg object a distance of 2 m and then hold it at that height for 10 seconds?

Solution:

Lifting the object:

• Mass of the object: 7 kg

• Gravitational force ($g$): 10 N/kg

• Force applied:

  $F = \text{mass} \times \text{gravitational force} = 7 \, \text{kg} \times 10 \, \text{N/kg} = 70 \, \text{N}$

• Distance lifted ($d$): 2 m

• Work done:

  $W = \text{Force} \times \text{Distance} = 70 \, \text{N} \times 2 \, \text{m} = 140 \, \text{J}$

Holding the object:

While holding the object, the distance moved is zero.

$W = \text{Force} \times \text{Distance} = 70 \, \text{N} \times 0 \, \text{m} = 0 \, \text{J}$

So work done while lifting = 140 J, work done while holding = 0 J.

Example 2

Question: a force of 80 N pulls a box along a smooth and level ground through a distance of 5 m. Calculate the work done by the force.

Solution:

• Force applied ($F$): 80 N

• Distance moved ($d$): 5 m

• Work done:

  $W = \text{Force} \times \text{Distance} = 80 \, \text{N} \times 5 \, \text{m} = 400 \, \text{J}$

Work done = 400 J.