Power in practice: motors, cranes and machines

5 minAS Level5.1.6

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can solve problems that use $P = \dfrac{W}{t}$ , doing the two jobs in the right order: find the work first, then divide by the time.

Two steps, every time

Machine questions usually tell you what the machine moves, not the work it does. So the method is always the same:

Find the work done: $W = Fs$ , where $F$ is the force the machine applies along the motion.
Divide by the time: $P = \dfrac{W}{t}$ .

For a load lifted at a steady speed, the lifting force equals the weight of the load (forces balance when the velocity is constant), and the distance moved is the height lifted.

Definition

Power, work and time

$P = \dfrac{W}{t}$

Rearranged:

$W = Pt \qquad t = \dfrac{W}{P}$

Unit check: $\dfrac{\text{J}}{\text{s}} = \text{W}$ , so a power in watts is a number of joules transferred each second.

Worked example: Worked example: a crane lifting a girder

A crane lifts a girder of weight $1500\ \text{N}$ through a height of $6.0\ \text{m}$ in $10\ \text{s}$ , at a steady speed.

Calculate the useful power output of the crane.

Have a go first?

Quick check

CalculateQuestion 1 · Recall

Fill in the blanksQuestion 2 · Recall

Answer the 2 questions above to continue.