Define the moment of a force.
State the unit for the moment of a force.
A force of 2.5 N acts at a perpendicular distance of 3 m from a pivot.
Calculate the moment.
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A rubbish bin on wheels is tilted at different angles to see how far it can go without toppling over.
Figure 1 shows the bin at different angles. The weight acts through point X.
Figure 1
State which of the bins will topple. Explain why.
A person applies a force of 100 N to the bin to keep it stationary.
Calculate the moment of the 100 N force. Give the unit.
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Figure 1 shows a uniform seesaw in equilibrium with a box placed on each side.
The box on the left has an anticlockwise moment of 150 N m about the pivot.
The box on the right has weight W.
Figure 1
State the clockwise moment due to the box on the right.
Show that the weight W of the box on the right side of the seesaw is 100 N.
The box on the left-hand side of the seesaw is now removed.
State and explain what happens to the seesaw.
The following passage is about gears.
Complete the sentences.
Choose answers from the box.
Each answer can be used once, more than once or not at all.
| pivot | a different | weight |
| the same |
size | centre of mass |
Gears consist of wheels with toothed edges that rotate on an axle or shaft, which acts as the ..................... .
As one gear turns, the other must also turn. Where the gears meet, the teeth will then move in .................... direction.
Although the force will be the same on both gears, the moment is not. This depends on the .................... of the gear, which changes the distance of the teeth to the axle.
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A builder uses a uniform plank to lift a concrete block.
They hold the plank horizontally.
The arrows on the diagram represent three forces on the plank.
Complete the table to identify the missing force.
| Force | Name of force |
| F | Force of the builder pushing down on the plank |
| 1200 N | Weight of the block |
| 200 N |
Calculate the clockwise moment of the block about the pivot.
Calculate the force of the builder pushing down on the plank.
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The diagram shows a gate with a lever-operated catch.
A loop on the bolt fits around the lever-arm at B.
Describe how the lever-arm is used to move the bolt.
Explain the function of the spring.
The force applied at point B is 22 N. The pivot is 110 cm from point B and 38 cm from point A.
Calculate the force exerted on the lever-arm at point A by the spring.
Explain how the force applied at point B would need to change if the distance from the pivot to point A is increased.
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A student wants to investigate the principle of moments. They connect a ruler to a stand with a pivot and hang a 2 N weight from the 60 cm mark on the ruler. They use a newtonmeter to hold the ruler horizontal.
The scale on the newtonmeter reads from 0 N to 10 N.
Describe how the student could check that the ruler is horizontal.
Calculate the moment of the 2 N weight.
State the unit.
The student holds the ruler horizontal with the newtonmeter at the 10 cm mark. They expect the reading on the forcemeter to be 12 N. The actual reading is 10 N.
Explain why the correct reading should be larger than 12 N, but the actual reading is only 10 N.
The student encounters a practice question involving two fishermen using a pole to carry some fish.
Fisherman P and fisherman Q feel different forces on their shoulders.
Use ideas about moments to explain why fisherman P feels the larger force.
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Figure 1 shows a spanner being used to tighten a nut.
Figure 1
Calculate the moment being applied to the nut in the figure.
Give your answer in newton metres (Nm).
The moment applied to the nut could be increased by exerting a greater force on the spanner.
Suggest one other change that could be made in order to increase the moment on the nut.
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Figure 2 shows a bicycle pedal at one point in time.
Figure 2
The pedal is connected to a cassette, which pulls the chain, creating tension (a force).
Calculate the moment of the force applied to the pedal.
The cassette transfers this moment to the chain, creating tension in it.
Using your answer to part (a), calculate the tension (force) in the chain.
Suggest two changes that could be made to the pedal and cassette which would increase the tension in the chain.
The chain passes around another cassette attached to the back wheel of the bicycle.
A small rear cassette allows the bike to go fast, but can make pedalling difficult.
A larger rear cassette makes pedalling much easier but results in a slower ride.
Use the idea of moments to explain why.
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Figure 3 shows a man pushing a wheelbarrow full of rubble.
Figure 3
The wheelbarrow and its contents have a combined weight of 300 N, which acts through its centre of mass.
Calculate the upward force that the man will have to apply to the handles in order to hold the wheelbarrow steady.
As the man pushes the load, the contents slide towards the front of the wheel barrow.
Explain what effect this will have on the force being applied by the man.
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Some children set up a wooden plank as a diving board over a pond, as shown in Figure 4, using a wooden crate filled with rocks to hold it in place.
Figure 4
The point where the plank overhangs the pond acts as a pivot.
By calculating the moment of the crate and the moment caused by the weight of the plank, explain why the plank is stable when nobody is standing on it.
Calculate the maximum weight that the diving board could support, placed on its right-hand edge.
A child of weight 300 N starts to walk out along the plank.
How far will they be able to get from the end of the plank before it starts to topple?
The children realise that if they move the plank to the left, it will eventually be capable of supporting the child at the very right-hand edge of the plank.
Calculate how far they will need to move the plank.
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A chest of drawers is empty, other than for some heavy items that are placed in the top drawer.
The drawer, along with its contents, has a weight of 300 N.
The rest of the chest has a combined weight of 200 N.
The centres of mass are shown in Figure 5.
Figure 5
As the drawer is pulled out from the chest it eventually reaches a point where the whole chest starts to topple, pivoting about the lower right corner.
Calculate how far the centre of mass of the drawer can be pulled from the chest, before it starts to topple.
To prevent drawers from toppling over, they are often attached to the wall using a short strap, as shown in Figure 6.
Figure 6
Calculate the force in the strap when the drawer is pulled out as shown in the above figure.
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