2.5 Moments, levers and gears — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

A force of 400 N acts on an area of 0.20 m². Calculate the pressure.
Change 25 cm into metres.

Answers

$p = \dfrac{F}{A} = \dfrac{400}{0.20} = 2000\,\text{Pa}$ , which is $2.0 \times 10^3\,\text{Pa}$ .
There are 100 cm in 1 m, so $25\,\text{cm} = 0.25\,\text{m}$ .

If question 2 went wrong, remember to divide by 100, not multiply.

Practise with help

1. A force of 25 N acts at a perpendicular distance of 0.40 m from a pivot. Calculate the moment of the force.

Hint

The moment uses the force and the perpendicular distance from the pivot.

Next step

Write $M = Fd$ , then multiply 25 N by 0.40 m. The distance is already in metres.

Full working

\begin{aligned} M &= F d \\ &= 25 \times 0.40 \\ &= 10\,\text{N m} \end{aligned}

2. A weight of 500 N sits 0.60 m from the pivot of a balanced beam. A second weight sits 1.5 m from the pivot on the other side. Calculate the second weight.

Hint

Balance means the clockwise moment equals the anticlockwise moment.

Next step

Work out the known moment, $500 \times 0.60$ . Then divide it by the second distance, 1.5 m.

Full working

\begin{aligned} 500 \times 0.60 &= F \times 1.5 \\ 300 &= F \times 1.5 \\ F &= \frac{300}{1.5} \\ &= 200\,\text{N} \end{aligned}

3. A lever has an effort of 120 N at 0.50 m from the pivot and a load at 0.10 m from the pivot. Calculate the force on the load.

Hint

The lever is balanced, so the two moments are equal.

Next step

Work out the effort moment, $120 \times 0.50$ . Then divide it by 0.10 m.

Full working

\begin{aligned} 120 \times 0.50 &= F \times 0.10 \\ 60 &= F \times 0.10 \\ F &= \frac{60}{0.10} \\ &= 600\,\text{N} \end{aligned}

4. A lever is used to lift a heavy stone. Explain how the lever transmits the turning effect of the force, and why it makes the job easier.

Hint

Compare the distance of the effort from the pivot with the distance of the load.

Next step

Say what happens to the moment when the same force acts further from the pivot.

Full working

A lever turns about a pivot. The effort makes a moment, $M = Fd$ , which turns the lever. The load is closer to the pivot than the effort, so the effort acts on a longer lever arm. A small effort therefore makes a moment large enough to give a large force on the load. The lever multiplies the force. This answer is a model answer for you to compare with your own wording.

5. A gear with 20 teeth drives a gear with 40 teeth. The driving gear has a moment of 12 N m. Calculate the moment of the driven gear.

Hint

The moments are in the same ratio as the numbers of teeth.

Next step

Work out the ratio $\dfrac{20}{40}$ , then multiply the driving moment by it.

Full working

The ratio of the teeth is $\dfrac{20}{40} = 0.5$ . The driven gear has a smaller moment.

M = 12 \times 0.5 = 6.0\,\text{N m}