Newton's Laws and Forces

Forces

A force is a push or a pull, measured in newtons (N). Forces are vectors (they have size and direction). They can be:

• Contact forces (friction, air resistance, tension, normal contact) — objects must touch.
• Non-contact forces (gravity, magnetism, electrostatic) — act at a distance.

Resultant force

When several forces act on an object, they combine into a single resultant force. If forces are balanced (resultant = 0) the object's motion doesn't change. If unbalanced, the object accelerates.

Weight and mass

• Mass (kg) is the amount of matter — the same everywhere.
• Weight (N) is the force of gravity on a mass — it changes with gravitational field strength.

weight = mass × gravitational field strength   (W = m × g,  g ≈ 9.8 N/kg on Earth)

Newton's laws of motion

Newton's First Law

An object stays still, or keeps moving at a constant velocity, unless acted on by a resultant force. (Objects resist changes to their motion — this is inertia.)

Newton's Second Law

The acceleration of an object is proportional to the resultant force and inversely proportional to its mass:

force = mass × acceleration   (F = m × a)

A bigger force gives more acceleration; a bigger mass gives less.

Newton's Third Law

When two objects interact, they exert equal and opposite forces on each other. (E.g. you push on the ground, the ground pushes back.)

Work done

When a force moves an object, work is done (energy is transferred):

work done = force × distance   (W = F × s)   — in joules

Hooke's law (springs)

The extension of a spring is proportional to the force applied (up to the limit of proportionality):

force = spring constant × extension   (F = k × e)

Worked example

A resultant force of 20 N acts on a 4 kg trolley. Find its acceleration.

a = F ÷ m = 20 ÷ 4 = 5 m/s²

✓

Common mistakes

• Confusing mass (kg, constant) with weight (N, depends on gravity).
• Rearranging F = ma incorrectly — for acceleration, a = F ÷ m.
• Forgetting that balanced forces mean constant velocity (which includes staying still), not necessarily stationary.

Exam tips

• Learn all three of Newton's laws and be able to give an example of each.
• Know W = mg and F = ma and how to rearrange them.
• For Newton's Third Law, name both forces as equal, opposite and on different objects.

Key facts to remember

• Force (N) is a vector; resultant force determines whether motion changes.
• Weight = mass × g (g ≈ 9.8 N/kg); 1st law = inertia, 2nd law = F = ma, 3rd law = equal and opposite forces.
• Work done = force × distance (joules); Hooke's law F = k × e.