Going further: rockets and jets (optional)

How can a rocket move in empty space?

There is no air or ground to push on in space. Yet rockets speed up there. How?

The idea

The rocket pushes hot gas backward out of its nozzle. By the third law, the gas pushes the rocket forward. In momentum terms: the gas gets backward momentum each second, so the rocket gets the same forward momentum.

Why a rocket speeds up more and more

The thrust stays the same, but the rocket burns fuel and gets lighter. With the same force on less mass, the acceleration grows: $a = \dfrac{\text{thrust}}{m} - g$ near the ground.

You should find that the acceleration rises as the rocket gets lighter. If the thrust is less than the weight, $Mg$, it cannot lift off at all.

Other examples

A garden hose kicks back, a balloon let go zooms around, a jet engine throws air backward, and a squid squirts water to swim.

Watch out. A rocket does not push against the air. It pushes against its own gas, so it works best in empty space.

A worked example

A $1.5\ \text{kg}$ model rocket throws out $0.05\ \text{kg}$ of gas each second at $900\ \text{m/s}$. Find its thrust and its upward acceleration.

1. Thrust. $0.05\ \text{kg} \times 900\ \text{m/s} = 45\ \text{N}$.
2. Weight. $1.5\ \text{kg} \times 9.8\ \text{m/s}^2 = 14.7\ \text{N}$, so the net upward force is $30.3\ \text{N}$.
3. Acceleration. $\dfrac{45\ \text{N}}{1.5\ \text{kg}} - 9.8\ \text{m/s}^2 = 20.2\ \text{m/s}^2$.

Practise with new numbers

Try it in Python

The program works out the model rocket.

Remember these

• Rockets push their own gas backward; the gas pushes them forward.
• Thrust $= ru$: gas each second times its speed.
• As the rocket gets lighter, the same thrust gives more acceleration.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why can a rocket work in space where there is no air?

2. A rocket throws out $10\ \text{kg}$ of gas each second at $2000\ \text{m/s}$. What is its thrust?

3. Why does a blown-up balloon zoom off when you let go?

4. Why does a rocket's acceleration grow even though its thrust stays the same?