Pressure, Moments and Simple Machines
Pressure is the force acting on each unit of area, calculated as pressure = force divided by area and measured in pascals, where one pascal is one newton per square metre. The same force spread over a larger area gives a smaller pressure, which is why skis prevent a person sinking into snow and why a drawing pin has a sharp point. In fluids, pressure acts in all directions and increases with depth because there is a greater weight of fluid above. A moment is the turning effect of a force about a pivot, calculated as moment = force multiplied by perpendicular distance from the pivot, and measured in newton metres. When an object is balanced, the principle of moments applies: the total clockwise moment equals the total anticlockwise moment. Simple machines such as levers, gears and pulleys use this to trade force against distance. A lever lets a small effort at a large distance from the pivot balance a large load close to it, but the effort must move further than the load does.
Method
- Write down the quantities you are given with their units before touching a formula. Convert centimetres to metres and grams to kilograms first, or the answer will be out by a factor of a hundred or a thousand.
- For a pressure calculation, use pressure = force / area. If you are given a mass, find the weight first using weight = mass x 10 N/kg.
- Check the area carefully. If an object stands on four legs, the area is the area of one leg multiplied by four.
- For a moment, use moment = force x perpendicular distance from the pivot. The distance must be measured at right angles to the line of the force.
- For a balanced beam, write clockwise moment = anticlockwise moment, put the numbers you know into both sides, and solve for the missing one.
- When you have an answer, sanity check it against the physics: a larger area should give a smaller pressure, and a force further from the pivot should need to be smaller to balance.
Worked example
A see-saw is balanced on a central pivot. A child of mass 30 kg sits 1.8 m to the left of the pivot. An adult sits 1.2 m to the right. Calculate the mass of the adult. Take the gravitational field strength as 10 N/kg.
- Find the child's weight, which is the force acting downwards: weight = mass x gravitational field strength = 30 x 10 = 300 N.
- Calculate the anticlockwise moment from the child: moment = force x distance = 300 x 1.8 = 540 N m.
- Apply the principle of moments. The see-saw is balanced, so the clockwise moment from the adult must also be 540 N m.
- Rearrange to find the adult's force: force = moment / distance = 540 / 1.2 = 450 N.
- Convert the force back to a mass: mass = weight / gravitational field strength = 450 / 10 = 45 kg.
- Check it makes sense: the adult sits closer to the pivot than the child, so the adult must be heavier. 45 kg is greater than 30 kg, so the answer is reasonable.
Practice questions
Try each question, then tap to reveal the answer.
Q1State the equation for pressure and give the unit.Show answer
Answer: Pressure = force / area. The unit is the pascal (Pa), which is one newton per square metre.
Q2A box exerts a force of 240 N on the floor through a base of area 0.6 square metres. Calculate the pressure.Show answer
Answer: 240 / 0.6 = 400 Pa
Q3Explain why walking on soft snow in skis stops you sinking, even though your weight is unchanged.Show answer
Answer: Skis spread the same weight over a much larger area. Since pressure = force / area, a larger area gives a much smaller pressure on the snow, so the snow is not compressed enough for you to sink.
Q4A spanner is 0.25 m long and a force of 60 N is applied at right angles to the end. Calculate the moment about the nut.Show answer
Answer: 60 x 0.25 = 15 N m
Q5A beam balances with a 20 N force 0.9 m from the pivot on one side and a force F at 0.6 m on the other. Calculate F.Show answer
Answer: 20 x 0.9 = 18 N m, so F = 18 / 0.6 = 30 N
Q6Explain why the pressure at the bottom of a deep swimming pool is greater than just below the surface.Show answer
Answer: There is a greater depth of water above that point, so a greater weight of water is pressing down on each square metre. Pressure in a fluid increases with depth.
Q7A wheelbarrow lets one person lift a load they could not lift directly. Explain how, using moments.Show answer
Answer: The wheel acts as the pivot. The load sits close to the wheel, so its moment is force x a small distance. The person lifts at the far end of the handles, a much larger distance from the pivot, so a much smaller effort force produces an equal moment. The trade-off is that the handles have to move further than the load rises.
Exam-style questions
Written in the style of a KS3 Science exam paper, with a full mark scheme.
A rectangular concrete block has a mass of 80 kg. Its base measures 0.5 m by 0.4 m. Take the gravitational field strength as 10 N/kg. (a) Calculate the pressure the block exerts on the ground when it rests on this base. (b) The block is tipped onto a smaller face measuring 0.4 m by 0.2 m. Calculate the new pressure. (c) Explain why builders place wide steel plates under the feet of scaffolding on soft ground.
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A uniform plank 3.0 m long rests on a pivot 1.0 m from its left-hand end. A load of 180 N hangs from the left-hand end. (a) Calculate the moment of the load about the pivot. (b) A person pushes down at the right-hand end to balance the plank. Calculate the force needed. (c) Explain what happens to the force required if the pivot is moved to the middle of the plank, and why.
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Free printable worksheet
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