Energy

Work and Power

1st Year · 2nd Year · 3rd Year (Junior Cert)

✓Define work and state its SI unit.
✓Calculate the work done by a force using the formula W = Fd.
✓Define power and state its SI unit.
✓Calculate power using the formula P = W/t.
✓Explain the difference between work and power.

Key concepts

Work

Work is done when a force causes an object to move a certain distance (displacement) in the direction of the force. If there is no movement, or if the movement is perpendicular to the force, no work is done by that specific force. Work is a measure of energy transferred.

W = Fd

Power

Power is the rate at which work is done, or the rate at which energy is transferred. It tells us how quickly work is being performed.

P = W/t

Key facts to remember

1Work is done when a force causes displacement in the direction of the force.
2The formula for work is W = Fd, where W is work, F is force, and d is displacement.
3The SI unit for work is the joule (J).
4Power is the rate at which work is done.
5The formula for power is P = W/t, where P is power, W is work, and t is time.
6The SI unit for power is the watt (W).
71 J = 1 N m.
81 W = 1 J/s.

Worked examples

Example 1

A student pushes a trolley with a force of 50 N over a distance of 10 m. Calculate the work done by the student.

IIdentify the given values: Force (F) = 50 N, Distance (d) = 10 m.

IIState the formula for work done: W = Fd.

IIISubstitute the values into the formula: W = 50 N × 10 m.

IVCalculate the result: W = 500 J.

Answer

The work done by the student is 500 J.

Example 2

A crane lifts a load, doing 1200 J of work in 10 seconds. Calculate the power of the crane.

IIdentify the given values: Work (W) = 1200 J, Time (t) = 10 s.

IIState the formula for power: P = W/t.

IIISubstitute the values into the formula: P = 1200 J / 10 s.

IVCalculate the result: P = 120 W.

Answer

The power of the crane is 120 W.

Example 3

A person climbs a flight of stairs. If the person has a weight of 600 N and climbs a vertical height of 3 m in 5 seconds, calculate: (a) the work done against gravity, and (b) the power developed by the person.

I(a) Calculate work done:

II Identify given values: Force (F = weight) = 600 N, Distance (d = height) = 3 m.

III Formula for work: W = Fd.

IV Substitute values: W = 600 N × 3 m.

V Calculate: W = 1800 J.

VI(b) Calculate power:

VII Identify given values: Work (W) = 1800 J (from part a), Time (t) = 5 s.

VIII Formula for power: P = W/t.

9 Substitute values: P = 1800 J / 5 s.

10 Calculate: P = 360 W.

Answer

(a) The work done against gravity is 1800 J. (b) The power developed by the person is 360 W.

Remember that weight is a force, and height is a distance in the direction of that force (against gravity).

Common mistakes

✗Confusing work with effort or simply applying a force; work is only done if there is movement in the direction of the force.
✗Using distance instead of displacement in the direction of the force when calculating work (e.g., carrying a bag horizontally does no work against gravity).
✗Mixing up the units for work (joules) and power (watts).
✗Incorrectly rearranging the formulas, e.g., calculating time by dividing power by work.
✗Not converting units to SI units (e.g., cm to m, minutes to seconds) before calculation.

Exam tips

★Always write down the formula you are using before substituting values.
★Show all your steps clearly, as partial marks can be awarded for correct method.
★Include the correct SI units with your final answer.
★Read the question carefully to determine if it's asking for work, power, or another quantity that requires rearranging the formulas.

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