Physics · Lesson 5

Newton's three laws

JAMBWAECNECO

What the syllabus asks

JAMB: Newton's laws, linear momentum and its conservation, impulse, inertia, applications (rockets, recoil of guns)

WAEC: Newton's laws of motion, inertia, mass and weight, momentum, impulse, conservation of linear momentum, collisions (elastic and inelastic), recoil, friction, motion in a lift

NECO: Newton's laws of motion, inertia, mass and weight, momentum, impulse, conservation of linear momentum, collisions (elastic and inelastic), recoil, friction, motion in a lift

What you will learn

State and explain Newton's three laws with everyday examples.
Distinguish mass from weight and calculate W = mg.
Apply F = ma, including problems with friction and several forces.
Define momentum and impulse and use Ft = mv − mu.
State and apply the principle of conservation of linear momentum to collisions, explosions and recoil.
Distinguish elastic from inelastic collisions using kinetic energy.
Analyse apparent weight in a lift and simple connected bodies.

Key points

A force changes or tends to change motion or shape; unit N; vector.
1st law: no resultant force means no change in velocity; mass measures inertia.
W = mg; mass is constant, weight depends on g.
p = mv (kg m/s); a rebound changes momentum by m(u + v).
2nd law: F = rate of change of momentum = ma, using the RESULTANT force.
Impulse = Ft = mv − mu = area under a force–time graph; longer impact time means smaller force.
3rd law: action and reaction are equal, opposite and act on different bodies.
Conservation: total momentum before = after, with no external force; explosions and recoil start from zero.
Elastic: KE also conserved; inelastic: KE lost; perfectly inelastic: bodies stick.
Friction F = μR; lift: R = m(g ± a); free fall gives apparent weightlessness.

Start here: What is a force?

Every change in motion has a cause, and that cause is a force. When you push a stalled car, when a goalkeeper catches a penalty, when a mango drops from a tree, a force is at work. A force is simply a push or a pull.

Force: a push or pull that changes, or tends to change, the state of rest or uniform motion of a body, or its shape. The SI unit is the newton (N).

Notice the words "tends to". If you push the wall of your classroom, it does not move, but you are still applying a force. Forces can also change shape: squeezing an orange, stretching a catapult rubber.

Forces come in two families. Contact forces need touching: friction, tension in a rope, the push of your hand, the normal reaction of a table holding up a book, air resistance. Field (non-contact) forces act across space: gravitational force (weight), magnetic force and electrostatic force. A magnet picks up pins without touching them.

Force is a vector: its direction matters as much as its size. Two boys pulling a goat with 50 N each in the same direction give 100 N. If they pull in opposite directions, the resultant is zero, and the goat stays put (and complains).

When several forces act along one line, choose one direction as positive and add with signs. The resultant is the single force that would have the same effect as all of them together.

Worked example 5.1

A carton is pushed east with 45 N, while friction of 12 N and a child pulling back with 8 N act west. Find the resultant.

Take east as positive. We do this so that every force gets a sign that shows its direction.
Resultant = 45 − 12 − 8 = 25 N.
The answer is positive, so it points east.

25 N east

⚠️ Common mistake: adding the sizes of forces without considering direction. Always pick a positive direction first.

Try it yourself. Forces of 20 N north and 35 N south act on a body. Find the resultant.

Show solution

Take north positive: 20 − 35 = −15, so 15 N south.

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Practice questions

1. A 900 kg car accelerates at 2.5 m/s². Find the resultant force.

Show worked answer

900 × 2.5 = 2250 N.

2. A 0.15 kg ball moving at 30 m/s is caught and stopped in 0.1 s. Find the average force.

Show worked answer

4.5/0.1 = 45 N.

3. A 5 kg mass moving at 4 m/s collides with a 3 kg mass at rest; they stick. Find the common velocity.

Show worked answer

20/8 = 2.5 m/s.

4. A 5 kg rifle fires a 0.02 kg bullet at 450 m/s. Find the recoil velocity.

Show worked answer

9/5 = 1.8 m/s backward.

5. Find the reading of scales under a 40 kg boy in a lift accelerating downward at 3 m/s² (g = 10).

Show worked answer

40 × 7 = 280 N.

Key words

Force: A push or pull that changes, or tends to change, a body's state of rest or motion; unit newton (N).
Inertia: The reluctance of a body to change its state of rest or uniform motion.
Mass: The quantity of matter in a body and the measure of its inertia; unit kg.
Weight: The gravitational pull on a body, W = mg; unit N.
Momentum: Mass × velocity; a vector, unit kg m/s.
Impulse: Force × time for which it acts; equals change of momentum; unit N s.
Resultant (net) force: The single force with the same effect as all the forces acting together.
Equilibrium: The state in which the resultant force is zero.
Elastic collision: A collision in which both momentum and kinetic energy are conserved.
Inelastic collision: A collision in which momentum is conserved but some kinetic energy is lost.
Perfectly inelastic: Bodies stick together after colliding.
Recoil: The backward motion of a gun (or body) when it fires a bullet (or pushes something) forward.

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