A force is a push or a pull. Forces change the motion or shape of an object, and the study of how forces affect motion is one of the central themes of CSEC Physics. The rules that govern this were set out by Isaac Newton in his three laws of motion.
Types of force and their effects
Forces (measured in newtons, N) can be contact (friction, tension, air resistance, normal reaction) or non-contact (gravity, magnetic, electrostatic). A force can:
- start an object moving, speed it up or slow it down;
- change the direction of motion;
- change the shape of an object.
When several forces act, what matters is the resultant (net) force — the single force that has the same effect as all of them combined.
Mass, weight and gravity
- Mass (kg) is the amount of matter in an object; it is the same everywhere.
- Weight (N) is the force of gravity on the object, and it changes with location.
weight = mass × gravitational field strength W = m × g (on Earth, g ≈ 10 N/kg, or 9.8 N/kg)
A 5 kg bag therefore weighs about 50 N on Earth but less on the Moon, where g is smaller.
Newton's three laws
First law (inertia). An object stays at rest, or keeps moving at constant velocity, unless a resultant force acts on it. So if the forces are balanced (resultant = 0), the motion does not change. Inertia is the tendency of an object to resist changes in its motion; more massive objects have more inertia.
Second law. A resultant force makes an object accelerate in the direction of the force:
force = mass × acceleration F = m × a
So for a given force, a larger mass gives a smaller acceleration. This equation is used constantly — e.g. the force needed to accelerate a 1000 kg car at 2 m/s² is 1000 × 2 = 2000 N.
Third law. For every action there is an equal and opposite reaction. The two forces act on different objects (e.g. a swimmer pushes the water back, the water pushes the swimmer forward).
Friction
Friction is a force that opposes motion between surfaces in contact. It can be useful (walking, braking, grip) or a nuisance (wears parts, wastes energy as heat). It is reduced by lubrication, rollers/ball-bearings or streamlining.
Air resistance (drag) is friction with the air. A falling object speeds up until its weight is balanced by air resistance; the forces are then balanced, so it falls at a steady terminal velocity.
Momentum
Momentum measures the "quantity of motion":
momentum = mass × velocity (units kg·m/s)
In any collision or explosion, the total momentum is conserved (stays the same) provided no external force acts. This explains recoil (a gun and bullet move apart with equal and opposite momentum) and is the basis of safety features such as crumple zones, which increase the time of impact and so reduce the force.
Hooke's law
When a spring is stretched, the extension is proportional to the force applied, up to the limit of proportionality:
force = spring constant × extension (F = k e)
Beyond the limit of proportionality the spring no longer obeys this rule and may be permanently deformed.
Describing motion — distance, speed and acceleration
Forces cause changes in motion, so you must also be able to describe motion itself:
- Speed = distance ÷ time (m/s); velocity is speed in a stated direction.
- Acceleration = change in velocity ÷ time taken (m/s²); a negative acceleration (deceleration) means slowing down.
These appear in motion graphs, which are a favourite exam topic:
- On a distance–time graph, the gradient (slope) gives the speed; a horizontal line means the object is stationary.
- On a velocity–time graph, the gradient gives the acceleration, and the area under the line gives the distance travelled.
Being able to read a gradient and an area from these graphs links directly to the force equations, because a resultant force is what produces the acceleration shown on a velocity–time graph.
Worked example — combining the ideas
A 2 kg trolley is pushed with a resultant force of 6 N. By Newton's second law its acceleration is a = F ÷ m = 6 ÷ 2 = 3 m/s². If it starts from rest, after 4 seconds its velocity is v = a × t = 3 × 4 = 12 m/s, and its momentum is then p = m × v = 2 × 12 = 24 kg·m/s. A single push therefore connects force, acceleration, velocity and momentum — showing how the topic fits together. Notice that if the same 6 N acted on a heavier 6 kg trolley, the acceleration would be only 1 m/s², illustrating Newton's second law in action.
Common exam mistakes
- Confusing mass (kg) and weight (N) — weight is a force.
- Saying a moving object needs a force to keep moving — by Newton's first law, with balanced forces it keeps moving at constant velocity.
- Putting both Newton's-third-law forces on the same object; they act on different objects.
- Dropping units in F = ma or W = mg calculations.
Key terms to remember
- Force — a push or pull, measured in newtons (N).
- Resultant force — the single net force equivalent to all forces acting.
- Mass — the amount of matter (kg); the same everywhere.
- Weight — the force of gravity on an object (N); W = mg.
- Inertia — the tendency of an object to resist a change in its motion.
- Friction — a force opposing motion between surfaces in contact.
- Terminal velocity — the steady speed reached when weight is balanced by air resistance.
- Momentum — mass × velocity (kg·m/s); conserved in collisions.
- Hooke's law — extension is proportional to force, up to the limit of proportionality.
Quick recap
- A force is a push/pull (N) that changes motion or shape; the resultant force decides the effect.
- W = mg; mass is constant, weight depends on g.
- Newton: (1) balanced forces → no change in motion; (2) F = ma; (3) action and reaction are equal, opposite, on different objects.
- Friction and air resistance oppose motion; balanced forces in free fall give terminal velocity.
- Momentum = mass × velocity and is conserved in collisions; springs obey F = ke up to the limit of proportionality.