Newton's laws of motion explained with examples

If the forces on an object are balanced (the resultant force is zero), a stationary object stays stationary and a moving object keeps moving at the same speed in the same direction. A car cruising at a steady 30 m/s has a driving force exactly balanced by air resistance and friction. The tendency to keep doing what it's doing is called inertia.

with resultant force in newtons (N), mass in kg and acceleration in m/s².

1. A 1,200 kg car accelerates at 2.5 m/s². $F = 1200 \times 2.5 = 3{,}000$ N.
2. A resultant force of 20 N acts on a 4 kg trolley. $a = 20 \div 4 = 5$ m/s².
3. A 50 N push and 10 N of friction act on a 10 kg box. Resultant force $= 40$ N, so $a = 4$ m/s².

Always use the resultant force, not just the biggest force.

When you push on a wall, the wall pushes back on you with an equal force in the opposite direction. The two forces:

• are equal in size and opposite in direction;
• are the same type of force;
• act on different objects, so they never cancel each other out.

A rocket pushes exhaust gases backwards; the gases push the rocket forwards.

Weight is the force of gravity on a mass: $W = m g$, with $g \approx 9.8$ N/kg on Earth. A 60 kg person weighs about 590 N.

A falling skydiver accelerates at first because weight is bigger than air resistance. As speed increases, air resistance increases until it equals the weight. The resultant force is then zero, so the skydiver falls at a steady terminal velocity (first law in action). Opening the parachute increases air resistance, they slow down, and reach a new, lower terminal velocity.

Momentum is mass × velocity ($p = m v$), in kg m/s. In a collision or explosion, total momentum is conserved. Higher-tier and Extended students also learn that force equals the rate of change of momentum, which explains why crumple zones and airbags reduce injuries: they make the change in momentum take longer, so the force is smaller.

• Using one force instead of the resultant force in $F = ma$.
• Thinking third-law pairs cancel out (they act on different objects).
• Confusing mass (kg) with weight (N).

1. A resultant force of 3 N acts on a 0.5 kg trolley. What is its acceleration?
2. A 2,000 kg lorry accelerates at 1.5 m/s². What resultant force acts on it?
3. What is the weight of a 70 kg astronaut on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg)?

Answers: 6 m/s²; 3,000 N; 686 N on Earth and 112 N on the Moon (the mass is still 70 kg).