State the law of conservation of momentum and show how it follows from Newton's second law. Use it to explain the recoil of a gun, and find the recoil velocity of a 3 kg gun that fires a 15 g bullet at 500 m s⁻¹.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the law. The total momentum of a system stays constant if no external force acts on it.
2 · Show it from the second law.
F = (p₂ − p₁)/t
With no external force, F = 0
So p₂ = p₁: momentum is conserved
3 · Apply it to a gun. Gun and bullet are at rest, so the total momentum before firing is zero. After firing, the bullet's forward momentum must be balanced by the gun's backward momentum.
4 · Draw a sketch. [Diagram: gun pointing right; bullet with an arrow v to the right; gun with an arrow V to the left]
5 · Work the numbers.
15 g = 0.015 kg
0 = MV + mv = 3 × V + 0.015 × 500 = 3V + 7.5
V = −7.5 ÷ 3 = −2.5 m s⁻¹
6 · Real-life link. A soldier presses the rifle butt firmly to the shoulder to take the recoil safely.
7 · Close in one line. So the gun recoils at 2.5 m s⁻¹, opposite to the bullet.
Scoring tip: Convert grams to kilograms first (15 g = 0.015 kg). Explain the minus sign: it means the gun moves opposite to the bullet.
