IGCSE Physics: forces, momentum, moments and pressure

What each board puts where

Key ideas

Force is a vector. When several forces act along one line, add those in one direction and subtract those in the other to get the resultant. A resultant force changes the speed or direction of motion; no resultant force means the object stays at rest or keeps moving in a straight line at constant speed. Mass is the quantity of matter in an object and is measured in kilograms; weight is the gravitational force on it, in newtons. On Earth g is about 9.8 N/kg, so a 50 kg student weighs about 490 N.

For a spring, extension is proportional to the load up to the limit of proportionality, which shows as the straight part of a load-extension graph. Cambridge Supplement candidates use k = F/x. The moment of a force is force x perpendicular distance from the pivot. In equilibrium there is no resultant force and no resultant moment, so clockwise moments equal anticlockwise moments about any pivot.

Momentum is mass x velocity. In a collision or explosion with no external force, total momentum before equals total momentum after. A force changes momentum: F = change in momentum / time, which is why crumple zones, airbags and seat belts reduce injury by making the stopping time longer. Pressure is force per unit area; in a liquid it increases with depth and with the density of the liquid.

Worked examples

1. Momentum (Cambridge Supplement, Edexcel Paper 2). A 1200 kg car moving at 15 m/s hits a stationary 800 kg car and the two move off together. Momentum before = 1200 x 15 + 800 x 0 = 18 000 kg m/s. After, the combined mass is 2000 kg, so 2000 x v = 18 000 and v = 9.0 m/s in the original direction.

2. Force from momentum change. A 0.060 kg ball is hit from rest to 40 m/s, with contact lasting 0.012 s. Change in momentum = 0.060 x 40 = 2.4 kg m/s. Force = 2.4 ÷ 0.012 = 200 N.

3. Moments. A 400 N child sits 1.5 m from the pivot of a seesaw. Where must a 600 N adult sit to balance it? Anticlockwise moment = 400 x 1.5 = 600 N m. Clockwise moment = 600 x d. So d = 600 ÷ 600 = 1.0 m from the pivot, on the other side.

4. Pressure in a liquid. A diver is 12 m below the surface of seawater of density 1030 kg/m^3. Pressure due to the water = 1030 x 9.8 x 12 = 121 128 Pa, about 1.2 x 10^5 Pa. Total pressure would also include atmospheric pressure, roughly another 1.0 x 10^5 Pa, if the question asks for it.

5. Spring constant (Cambridge Supplement). A 6.0 N load stretches a spring by 4.0 cm. Convert to metres first: k = 6.0 ÷ 0.040 = 150 N/m.

Common mistakes

• Giving weight in kilograms. Weight is a force, measured in newtons.
• Using the distance along a slanted beam instead of the perpendicular distance from the pivot.
• Ignoring direction in momentum questions. Choose a positive direction and give velocities the other way a minus sign.
• Leaving extension in centimetres while the spring constant is wanted in N/m.
• Calling the limit of proportionality the elastic limit. Cambridge says an understanding of the elastic limit is not required; use the term the question uses.
• Using area in cm^2 with force in N and calling the answer pascals. 1 Pa = 1 N/m^2.
• Writing that safety features "reduce the momentum". They increase the time taken to change momentum, so the force is smaller.

Exam technique and mark-scheme language

Most force questions are short calculations: write the equation, substitute with units, give the answer with its unit. In momentum questions, examiners expect the phrase "total momentum before = total momentum after" written out before the numbers. For safety features the scoring chain is: the feature increases the time of the collision, so the rate of change of momentum is smaller, so the force on the person is smaller.

For moments experiments (Cambridge Supplement 1.5.2.6), describe a metre rule balanced on a pivot with masses hung at measured distances, then show that the sum of clockwise moments equals the sum of anticlockwise moments. For the spring practical (Edexcel 1.22, Cambridge 1.5.1.2), mention measuring the extension from the original length with a ruler at eye level, adding loads in equal steps and checking that the spring returns to its original length.

How one-to-one lessons help with this topic

Forces is wide rather than deep, so gaps are easy to miss in class. A tutor works through a short diagnostic covering each sub-topic, then spends lesson time on the weak spots, usually momentum signs and multi-force moments problems. For Edexcel students the tutor makes sure the Paper 2 statements are covered, since some schools leave them until late in Year 11.

Self-check

1. Find the resultant of several forces along a line.
2. Explain the difference between mass and weight, with units.
3. Use F = ma and W = mg, rearranging for any quantity.
4. Describe a load-extension investigation and identify the limit of proportionality.
5. Use the principle of moments to find an unknown force or distance.
6. Solve a collision problem with conservation of momentum.
7. Explain how a crumple zone reduces the force on passengers.
8. Calculate pressure from force and area, and pressure at a depth in a liquid.