Work done
Work, Energy & Power - OCR A-Level Physics
Key Definition
Work done
The energy transferred when a force causes an object to move through a displacement. Measured in joules (J). 1 J = 1 N m.
The energy transferred when a force causes an object to move through a displacement. Measured in joules (J). 1 J = 1 N m.
$$W = QV$$
$$W = Fs\cos\theta$$
- When the force is in the same direction as displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). ($\theta =$ 0), W = Fs
- When the force is perpendicular to displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). ($\theta =$ 90°), W = 0. The force does no work (e.g. centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.)
- When the force opposes displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). ($\theta =$ 180°), W = -Fs. Negative work means energyThe capacity to do work. Measured in joules (J). is removed from the object
- The area under a force-displacement graph equals the work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference).
- Work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). against friction is transferred to thermal energyThe capacity to do work. Measured in joules (J). (internal energyThe capacity to do work. Measured in joules (J).The sum of the randomly distributed kinetic and potential energies of all the molecules in a system.) of the surfaces and surroundings
Common Mistake
MEDIUM
Students often: Watch out: Calculate work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). using the total force when the force is at an angle to the displacement.
Instead: Use $W = Fs \cos(\theta). Only$ the component of force parallel to the displacement does work. Always identify the angle between the force and the direction of motion.
Instead: Use $W = Fs \cos(\theta). Only$ the component of force parallel to the displacement does work. Always identify the angle between the force and the direction of motion.
Worked Example [3 marks]
A child pulls a sledge 50 m across flat ground using a rope at 30 degrees to the horizontal. The tension in the rope is 40 N. Calculate the work done by the tension.
Show Solution
1
Identify
$F = 40 \text{ N}, s = 50 \text{ m}, \theta = 30°$
[1]2
$W = Fs\cos\theta = 40 \times 50 \times \cos 30°$
[1]3
$W = 40 \times 50 \times 0.866 = 1732 \text{ J} \approx 1700 \text{ J (2 s.f.)}$
[1]Answer
1700 J