Moments, levers and gears GCSE physics lesson: M = Fd and balancing a beam

Moments: balance the beam

Each beam is an interactive scene (a model, not a practical): the beam is light, g = 9.8 N/kg, and positions are measured from the beam's left end. Predict which way it turns, then move it until it balances.

1. The pivot is 2.0 m from the left end. Load 1 (3 kg) is 1.0 m from the left end; load 2 (2 kg) is at 2.5 m. Work out on paper where load 2 must go, then slide it there until the beam balances.They change an interactive scene (moments on a beam) until it does it.
2. Now it balances: how far is load 2 from the pivot, in metres?
3. Load 1 (6 kg) is 0.5 m from the left end; load 2 (2 kg) is at 3.7 m. Predict: should the pivot move left or right? Then move it until the beam balances.They change an interactive scene (moments on a beam) until it does it.
4. Where did the pivot end up, and why there?
   1. In the middle of the two loads: balance means the same distance each side
   2. Nearer the 2 kg load: the lighter load needs to be closer
   3. Nearer the 6 kg load: it is three times as heavy, so it needs a third of the distance
5. The pivot is 2.0 m from the left end. Load 1 (5 kg) is at 0.4 m, load 2 (2 kg) at 3.0 m and load 3 at 3.5 m. Work out on paper what mass load 3 needs, then set it so the beam balances.They change an interactive scene (moments on a beam) until it does it.
6. Load 3 is moved to the right end of the beam, 4.0 m from the left end. What mass, in kg, would it need now to balance? (Work it out; the scene stays as it is.)

Moments, levers and gears: practice

Show your working on paper. Use g = 9.8 N/kg. Give moments in N m and forces in N; turn centimetres into metres first. The stretch is optional.

Diagnostic question: choose and explain

1. A light beam 3.0 m long has its pivot 0.5 m from its left end. A 20 N weight hangs at the right end. What is the weight's moment about the pivot?
   1. 10 N m
   2. 50 N m
   3. 60 N m
   4. 8 N m

Practice questions

1. A force of 40 N pushes at right angles to a door, 0.50 m from its hinges. What is its moment, in N m?
2. A nut is stuck tight. Which push gives the biggest moment?
   1. Near the nut, at right angles to the spanner
   2. At the end of a long spanner, at right angles to it
   3. At the end of a long spanner, along the spanner towards the nut
3. A 2.5 kg mass hangs 0.40 m from a pivot. Use g = 9.8 N/kg. What is its moment, in N m?
4. A light plank 3.0 m long pivots at its middle. A 30 N weight sits 0.5 m from the left end. What is the weight's moment about the pivot, in N m?
5. A force of 12 N acts at right angles 25 cm from a pivot. What is its moment, in N m?
6. A child weighing 400 N sits 1.5 m from a see-saw's pivot. How far from the pivot, on the other side, must a child weighing 300 N sit to balance, in metres?
7. A small gear with 10 teeth turns a large gear with 30 teeth. Compared with the small gear, the large gear turns…
   1. faster, with a bigger moment
   2. more slowly, with a smaller moment
   3. more slowly, with a bigger moment
   4. at the same speed, with the same moment
8. With a long crowbar, a small push lifts a heavy stone. What is the catch?
   1. The end you push moves much further than the stone does
   2. The crowbar makes extra energy
   3. There is none: a lever gives you a bigger force for free
9. A crowbar's pivot is 0.10 m from a 600 N stone, and you push 1.2 m from the pivot on the other side. What push, in newtons, just balances the stone?
10. A light beam pivots at its middle. On the left, 20 N hangs 1.0 m from the pivot and 10 N hangs 0.5 m from it. How far to the right of the pivot must a 25 N weight hang to balance, in metres?
11. Stretch: the pivot is 2.0 m from the left end, 4 kg sits at 0.5 m and 1 kg at 3.0 m. Choose load 3's mass and place so the beam balances. Then find a second way on paper.They change an interactive scene (moments on a beam) until it does it.

Support: Draw the beam, mark the pivot, and write each distance from the pivot on the drawing before any multiplying. For balance: clockwise moments on one side of an equals sign, anticlockwise on the other.

Moments: exit

Mark the pivot on a sketch and write each distance from it first.

1. A light beam 4.0 m long pivots 1.0 m from its left end. A 600 N load hangs at the left end. What force, in newtons, at the right end balances it?
2. The load moves 0.5 m nearer the pivot. What force at the right end balances it now, in newtons?

Exit check

A balance with positions from the beam's end shows who takes distances from the pivot.

A light beam 4.0 m long pivots 1.0 m from its left end. A 600 N load hangs at the left end.

Moments, levers and gears

Use g = 9.8 N/kg. Draw a sketch for each question with the pivot marked and each distance from it written on.