The Third Law and Conservation of Momentum: Quick Revision

A brief note on The Third Law and Conservation of Momentum. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Third law: when A pushes B, B pushes A with an equal force in the opposite direction.
• Pair forces act on different objects, so they never cancel.
• Conservation of momentum: with no outside force, the total momentum stays the same.
• Recoil: things that start at rest end with equal and opposite momenta.
• Rockets push their own gas backward and are pushed forward; thrust $=$ gas each second $\times$ its speed.

The facts at a glance

A worked example

A $50\ \text{kg}$ skater at rest catches a $2\ \text{kg}$ ball thrown at $10\ \text{m/s}$. How fast do they move off?

1. Before. Only the ball moves: $2\ \text{kg} \times 10\ \text{m/s} = 20\ \text{kg m/s}$.
2. After. $(50\ \text{kg} + 2\ \text{kg})\,v = 20\ \text{kg m/s}$.
3. So $v = \dfrac{20\ \text{kg m/s}}{52\ \text{kg}} = 0.385\ \text{m/s}$.

Practice with new numbers

A program to try

The program works out the catch.

Mistakes to avoid

• Cancelling a pair. A pair acts on two objects; only forces on one object can cancel.
• The weight and the floor's push as a pair. Both act on the same object: they are balanced, not a pair.
• Forgetting signs for opposite directions in momentum sums.
• 'Rockets push on the air.' They push on their own gas.

Check yourself

1. You push a wall with $30\ \text{N}$. How hard does it push you?

2. Why does a gun recoil?

3. A $4\ \text{kg}$ trolley at $3\ \text{m/s}$ sticks to a $2\ \text{kg}$ trolley at rest. How fast do they move?

4. A horse pulls a cart and the cart pulls the horse back equally. How do they move at all?

5. A rocket throws out $5\ \text{kg}$ of gas each second at $2000\ \text{m/s}$. What is its thrust?