Work Done (Cambridge International IGCSE Science)

Work done & energy transfers

• Mechanical work is done when an object is moved over a distance by a force applied in the direction of its displacement

  • It is said that the force does work on the object
  • If a force is applied to an object but doesn’t result in any movement, no work is done

• When work is done, energy is transferred

• Work done and energy transferred are equivalent quantities

Work done pushing a box

Work is done when a force is used to move an object over a distance, and energy is transferred from the person to the box

Work done equation

• The formula for work done is:

$W=Fd=\Delta E$

• Where:

  • $W$ = work done, measured in newton-metres (N m)
  • $F$ = force applied, measured in newtons (N)
  • $d$ = distance in metres (m)
  • $\Delta E$ = energy transferred, measured in joules (J)

Formula triangle for work done, force and distance

To use a formula triangle, simply cover up the quantity you wish to calculate and the structure of the equation is revealed

• Using formula triangles is covered in more detail in the revision note on Speed & velocity

• Mechanical work done and electrical work done are equivalent to energy transferred

$\mathrm{work} \mathrm{done}=\mathrm{energy} \mathrm{transferred}$

• Therefore:

$1Nm=1J$

Examples of work done

• Work is done on a ball when it is lifted to a height:

  • A force is required to lift the ball
  • Work is done against the weight force to lift the ball through the gravitational field
  • Energy is transferred as work is done

The weight on the ball produced by the gravitational field does work on the ball over a distance

• Work is done when a bird flies through the air

  • A force is required to overcome the drag force
  • Work is done against the drag force as the bird flies over a distance
  • Energy is transferred as work is done

Work done by a bird

The bird does work against air resistance (drag) as it flies through the air

Worked Example A car moving at speed begins to apply the brakes. The brakes of the car apply a force of 500 N, which brings it to a stop after 23 m.

Calculate the work done by the brakes in stopping the car.

Answer:

Step 1: List the known quantities

• Distance, $d=23m$
• Force, $F=500N$

Step 2: Write out the work done equation

$W=Fd$

Step 3: Calculate the work done on the car by the brakes

$W=500\times23$

$W=11500J$

Step 4: Round to an appropriate number of significant figures

• The lowest number of significant figures in the input values is 1 s.f. (500 N)
• Therefore, the final answer must be rounded to 1 s.f.

$W=10 000 \mathrm{J} (1 \mathrm{s} . \mathrm{f} .)$

Exam Hint Remember to always convert the distance into metres and force into newtons so that the work done is in joules or newton-metres

Video of Work done