Newton's Second Law
Why is a full trolley so much harder to push than an empty one?
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Explain
Big pushes make things go faster.
Heavy things are harder to get moving.
Two things decide how quickly something speeds up: how hard you push it, and how much stuff is in it.
Push harder and it speeds up faster. Double the push, and it gains speed twice as quickly.
Add more mass and it speeds up more slowly. Double the mass, and it gains speed half as quickly.
Scientists call speeding up acceleration. Try the sliders to see this for yourself.
Newton's second law: the net force on an object equals its mass multiplied by its acceleration. We write this as F = m × a, and rearrange it to a = F / m.
Acceleration is directly proportional to net force, and inversely proportional to mass. One newton is the force that gives 1 kg an acceleration of 1 m/s².
Worked example: a 50 N net force acts on a 10 kg cart. So a = 50 / 10 = 5 m/s², which means it gains 5 m/s every second.
On the graph, a steady acceleration makes a straight line. A steeper line means a larger acceleration.
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The simulation has no friction, so the force you set is also the net force. In real life, only the net force counts. Acceleration means any change in velocity, so it includes slowing down and turning as well as speeding up. F = m × a is a vector equation, so acceleration points the same way as the net force. It also needs correcting for speeds close to the speed of light, which you will meet in Einstein's big ideas.
The Formula
force = mass × acceleration
- the net force, measured in newtons (N)
- the mass being moved, measured in kilograms (kg)
- the acceleration, measured in metres per second squared (m/s²)
Try the numbers
Acceleration: 5 m/s²
Try it at home
You need a shoebox, some books, a smooth floor.
You need: a shoebox, some books, a smooth floor.
Push the empty box. Now fill it and push again.
- Give the empty box a gentle push and see how far it slides.
- Put books in the box.
- Push it just as gently, and compare.
What's happening: the bigger mass gets less acceleration from the same force. The full box also presses harder on the floor, so there is more friction to overcome.
Physics is life
Your body
Your strong legs push you to run fast.
Daily life
A big lorry needs a big engine.
Nature
A cheetah is strong and light, so it speeds up fast.
Space
Big rockets need huge pushes to fly.
Quick check
Question 1 of 3
Words to know
Mass: How much stuff is in an object. It is measured in kilograms.
- Acceleration
- How quickly the velocity of something changes.
- Mass
- How much stuff is in an object. It is measured in kilograms.
- Force
- A push or a pull on something.
- Net force
- The total force left over after adding up all the pushes and pulls.