Forces

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

A force is a push or a pull, measured in newtons. What matters is the resultant force: add forces that act in the same direction and subtract forces that act in opposite directions. If the resultant is zero, the object stays at rest or keeps moving in a straight line at constant speed. Otherwise it accelerates: its speed or direction changes.

A falling object speeds up until the drag on it equals its weight. It then falls at terminal velocity. An object moving in a circle needs a force towards the centre.

Forces can also stretch objects and turn them. The turning effect of a force is its moment. An object is more stable with a low centre of gravity and a wide base.

Rules to remember

resultant force = mass × acceleration (F = ma), with F in N, m in kg, a in m/s²
Newton's first law: with no resultant force, an object stays at rest or moves in a straight line at constant speed
Newton's third law: if A pushes on B, B pushes on A with an equal and opposite force. The two forces are the same type and act on different objects
spring constant = force ÷ extension (k = F/x); extension = stretched length − original length
Limit of proportionality: the point beyond which extension is no longer proportional to load (the graph stops being a straight line)
moment = force × perpendicular distance from the pivot, in N m. In equilibrium: total clockwise moment = total anticlockwise moment
stopping distance = thinking distance + braking distance; thinking distance = speed × reaction time

Common mistake

Putting a single force into F = ma instead of the resultant force. Find the resultant first (for example driving force − friction), then divide by the mass.

Worked example

A car of mass 800 kg has a driving force of 2000 N. The total resistive force (friction and air resistance) is 800 N. What is the acceleration of the car?

The two forces act in opposite directions, so resultant force = 2000 − 800 = 1200 N forwards
a = F ÷ m = 1200 ÷ 800
a = 1.5 m/s²

Answer: 1.5 m/s² in the direction of the driving force.

Practice questions

Try each one, then open the answer.

1. A ball on a string moves in a horizontal circle at constant speed. The tension in the string is increased while the speed and mass of the ball stay the same. What happens to the path of the ball?

A
the radius of the circle decreases
B
the radius of the circle increases
C
the radius of the circle does not change
D
the ball flies off along a tangent

Show answer

Answer: A. A larger force towards the centre, with the same speed and mass, pulls the ball round a tighter circle, so the radius decreases. The ball would fly off along a tangent only if the force were removed.

2. Which factor increases the thinking distance of a driver but not the braking distance?

A
worn tyres
B
a wet road
C
tiredness
D
a heavier load

Show answer

Answer: C. Thinking distance depends on reaction time (tiredness, alcohol, drugs, speed). Braking distance depends on speed, road, tyres, brakes and load.

3. A force of 20 N acts at a perpendicular distance of 0.30 m from a pivot. What is the moment of the force?

A
0.015 N m
B
6.0 N m
C
20.3 N m
D
66.7 N m

Show answer

Answer: B. moment = force × perpendicular distance from the pivot = 20 × 0.30 = 6.0 N m.

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