## Why do things with different masses fall at the same rate?

Physics Narrative for 11-14

#### A simple explanation of why all objects fall at the same rate

If one object has twice the mass of another the Earth will pull it with twice the force:

Box of mass 2 kilogram: Pull of Earth is 20 newton

Box of mass 4 kilogram: Pull of Earth is 40 newton

Since the larger box has twice the force pulling on it (and this is what you feel when you hold it in your hand), it is tempting to predict that it will fall more quickly. But, the larger box has twice as much mass to set into motion, so it will accelerate at the same rate as a lighter object.

A force of 20 newton on a 2 kilogram mass has the same effect as a force of 40 newton on a 4 kilogram mass.

In fact, we can use Newton's second law of motion (see the SPT: Forces topic) to calculate the acceleration in each of these cases.

This is quite unlike the case for horizontal motion, where you can vary the force exerted and the mass independently.

#### Using the relationship to reinforce the understanding

acceleration = forcemass

For the smaller mass, the force is 20 N and the mass is 2 kg, so:

20 N2 kg = 10 m s^{-2}

For the larger mass, the force is 40 N and the mass is 4 kg, so:

40 N4 kg = 10 m s^{-2}

Both objects fall with an acceleration of about 10 metre second^{-2}.

This is often referred to as the acceleration due to gravity and is the value obtained if the air resistance force acting on the falling object is negligible.