Mass, Weight and Free Fall: Quick Revision

A brief note on Mass, Weight and Free Fall. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Free fall: only gravity acts. Every object, heavy or light, falls with $g = 9.8\ \text{m/s}^2$ (without air).
• From rest: $v = gt$, $h = \tfrac12 gt^2$, $v^2 = 2gh$. Thrown up at $u$: it stops after $\dfrac{u}{g}$, at a height $\dfrac{u^2}{2g}$.
• Mass is the amount of matter, in kg; it is the same everywhere.
• Weight is the pull of gravity, $W = mg$, in newtons; it changes from place to place.
• On the Moon $g = 1.6\ \text{m/s}^2$, about a sixth of the Earth's, so you weigh about a sixth as much.
• Astronauts in orbit float because they and their station fall round the Earth together, not because gravity is gone.

The facts at a glance

A worked example

A stone dropped down a well hits the water $1.5\ \text{s}$ later. How deep is the water surface, and how fast is the stone then?

1. Depth. $h = \tfrac12 \times 9.8\ \text{m/s}^2 \times (1.5\ \text{s})^2 = 11.0\ \text{m}$.
2. Speed. $v = 9.8\ \text{m/s}^2 \times 1.5\ \text{s} = 14.7\ \text{m/s}$.
3. So the water is about $11.0\ \text{m}$ down, and the stone reaches it at $14.7\ \text{m/s}$, whatever its mass.

Practice with new numbers

A program to try

The program works out the well.

Mistakes to avoid

• Weight in kilograms. Kilograms are for mass; weight is a force, in newtons.
• 'A heavy stone falls faster.' Without air, all objects fall together.
• 'At the top of a throw the acceleration is zero.' The speed is zero there, but $g$ still acts.
• 'There is no gravity in a space station.' There is plenty; everything inside is falling freely.

Check yourself

1. What is the weight of a $25\ \text{kg}$ box on the Earth?

2. A feather and a hammer are dropped together on the Moon. Which lands first?

3. A ball is thrown up at $9.8\ \text{m/s}$. How long does it take to reach the top?

4. An astronaut's mass is $90\ \text{kg}$ on the Earth. What is it on the Moon?

5. A stone falls from rest for $2\ \text{s}$. How far does it fall? ($g = 9.8\ \text{m/s}^2$)