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Rockets & Staging Worksheet
By the end you will: explain thrust with Newton's third law, use thrust-to-weight ratio and the rocket equation, and see why rockets use stages.
A. Explore with the simulation
Set 300 t of fuel, a 5 t payload and 5,000 kN of thrust. Fly with 1, 2 and 3 stages.
Stages Rocket equation Δv (km/s) Top speed (km/s) 1 2 3 Keep 2 stages and lower the thrust to 2,500 kN. What happens? Why?
Why is the top speed always less than the rocket equation's Δv?
B. Calculate (then check in the simulation)
A rocket of mass 50,000 kg has 800 kN of thrust. Find its weight, its thrust-to-weight ratio and its starting acceleration (g = 9.8 m/s²).
An engine burns 200 kg of propellant a second, with exhaust at 3,000 m/s. Find the thrust.
Exhaust speed is 3 km/s and the mass ratio (full ÷ empty) is 5. Find Δv. (ln 5 ≈ 1.61)
C. Think it through
A rocket works in space where there is no air to push against. Explain with Newton's third law.
Answer key (for teachers and parents)
- 1 stage: Δv 6.65 km/s, top speed about 4.96 km/s · 2 stages: 9.86 km/s, about 7.48 km/s · 3 stages: 11.08 km/s, about 8.21 km/s. More stages, more speed from the same fuel.
- It stays on the pad. Thrust-to-weight ratio is about 0.76, less than 1, so the thrust can't even lift the rocket's weight.
- The rocket equation ignores gravity (and air). Climbing against gravity uses up part of the speed gain.
- Weight = 50,000 × 9.8 = 490 kN. TWR = 800 ÷ 490 ≈ 1.63. a = (800,000 − 490,000) ÷ 50,000 = 6.2 m/s².
- Thrust = 200 × 3,000 = 600,000 N = 600 kN.
- Δv = 3 × 1.61 ≈ 4.8 km/s.
- The rocket pushes the exhaust gas backwards; the gas pushes the rocket forwards with an equal and opposite force. It needs nothing outside to push on.
Free to print and share for teaching. Made with the interactive simulation at jugnix.com/simulations/rocket-staging.