Force, mass and acceleration

The idea

A net force accelerates an object in the direction of the net force, with acceleration proportional to the net force and inversely proportional to the object's mass: a = F/m, or F = ma.

Pushing two carts

You push a light cart and a heavy cart with the same force. You also push the light cart harder.

What do you think decides how quickly a cart speeds up?

• The force and the mass together
• Only the colour of the cart
• Nothing, they speed up equally

Change F and m

Set the values asked for and watch the acceleration.

Force over mass

The acceleration was 2 m s⁻² when 10 N acted on 5 kg. It doubled when the force doubled, and it halved when the mass doubled. The block accelerated in the direction of the net force.

A net force accelerates an object in the direction of the net force, with acceleration proportional to the net force and inversely proportional to the object's mass: a = F/m, or F = ma.

Notes

Second law: a net force gives acceleration a = F/m, in the direction of the force; F = ma.

Check yourself

A net force of 12 N acts on an object of mass 3 kg. What is its acceleration?

Answer: 4 m s⁻²

a = F/m = 12 N ÷ 3 kg = 4 m s⁻².

A net force of 20 N gives an object an acceleration of 4 m s⁻². What is its mass?

Answer: 5 kg

m = F/a = 20 N ÷ 4 m s⁻² = 5 kg.

The net force on an object is doubled and its mass stays the same. Its acceleration…

The mass of an object is doubled and the net force stays the same. Its acceleration…

• is halved. Acceleration is proportional to the net force, so doubling the force doubles the acceleration.
• is doubled — correct. Yes!
• stays the same. Acceleration is proportional to the net force, so it changes when the force changes.
• is doubled. Acceleration is inversely proportional to the mass, so doubling the mass halves it.
• stays the same. Acceleration is inversely proportional to the mass, so it changes when the mass changes.
• is halved — correct. Yes!