Force and acceleration
Push a cart. Then push it twice as hard. How does its acceleration change?
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- 20 N on 2 kg gives 10 m/s².
- Double the force to 40 N. The acceleration doubles to 20 m/s².
- Keep 40 N but use 4 kg. It falls back to 10 m/s².
Twice the net force doubles the acceleration, for the same mass.
The rule
Net force equals mass times acceleration, F = ma. One newton gives 1 kg an acceleration of 1 m/s².
This is Newton's second law. Here F is net force, m is mass and a is acceleration. So a = F ÷ m.
With the same mass, double the net force and the acceleration doubles. With the same net force, double the mass and the acceleration halves.
The acceleration points the way the net force points. The unit of force is the newton, N.
Gravity pulls with F = mg. Here g is the acceleration due to gravity: 9.8 m/s² near Earth. This pull is the object's weight, in newtons. For quick calculations, take g = 10 m/s².
| Case | Working | Answer |
|---|---|---|
| 20 N on a 2 kg cart | 20 ÷ 2 | 10 m/s² |
| Net force 100 N on a 50 kg trolley | 100 ÷ 50 | 2 m/s² |
| A 1200 kg car at 2.5 m/s² | 1200 × 2.5 | 3000 N |
| Weight of a 40 kg student | 40 × 9.8 | 392 N |