A rocket in deep space fires its engines, ejecting hot gases backwards. Explain, using Newton's laws of motion and the concept of momentum, why the rocket accelerates forwards when the engines fire, and why the rocket continues to move at a constant velocity after the engines are switched off.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A rocket travelling through deep space is far from any significant gravitational fields. When its engines fire, hot gases are expelled backwards at high speed. The engines are then switched off and the rocket continues to travel through space.
Model answer (5 marks)
The rocket and the gases form an isolated system. Initially the total momentum is zero because the rocket is at rest. When the engines fire the gases are expelled backwards, giving them a negative momentum. By conservation of momentum the rocket must acquire an equal positive momentum, so it moves forwards.
Newton’s third law also explains the acceleration: the rocket pushes the gases backwards, and the gases push the rocket forwards with an equal and opposite force. This forward force is the resultant force on the rocket, so by Newton’s second law F = ma the rocket accelerates forwards.
After the engines are switched off there is no external force on the rocket (no gravity, no air resistance). With zero resultant force, Newton’s first law states that the rocket continues to move at a constant velocity.
Newton’s third law also explains the acceleration: the rocket pushes the gases backwards, and the gases push the rocket forwards with an equal and opposite force. This forward force is the resultant force on the rocket, so by Newton’s second law F = ma the rocket accelerates forwards.
After the engines are switched off there is no external force on the rocket (no gravity, no air resistance). With zero resultant force, Newton’s first law states that the rocket continues to move at a constant velocity.
Examiner tips
- Use the phrase "conservation of momentum" to link the gases and rocket. Show the force pair from Newton’s third law. State Newton’s second law when explaining acceleration. Mention Newton’s first law for motion after engines off.
Common mistakes
- Failing to state that the system is isolated. Confusing the direction of the gas momentum with the rocket’s. Omitting the force pair from Newton’s third law. Not linking the lack of force to Newton’s first law.
Mark scheme (5 marks)
- The total momentum of the rocket-gas system before the engines fire is zero (rocket is stationary) / momentum is conserved in the system
- The gases are given momentum in the backwards direction, so by conservation of momentum the rocket gains equal and opposite momentum forwards
- By Newton's third law, the gases exert an equal and opposite force on the rocket to the force the rocket exerts on the gases
- The resultant forward force on the rocket causes it to accelerate forwards, in accordance with Newton's second law (resultant force = mass × acceleration)
- Once the engines are off, there is no resultant force on the rocket (deep space — no air resistance or gravity), so by Newton's first law it continues at constant velocity
Key terms in this question
Related
- All OCR A-Level Physics A (H556) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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