Chapter 5, Problem 17TE

In the previous chapter, rocket propulsion was explained in terms of Newton's third law. That is, the force that propels a rocket is from the exhaust gases pushing against the rocket-the reaction to the force the rocket exerts on the exhaust gases. Explain rocket propulsion in terms of momentum conservation.

To determine

The working of rocket propulsion in terms of momentum conservation.

Answer to Problem 17TE

By conservation of momentum principle, the gases escape with velocity v in downwards direction and the rocket moves with velocity $$\left(\frac{m}{M}\right)v$$ in upwards direction

Explanation of Solution

Rocket propulsion is the best example of the principle of conservation. When fuel is burned in a rocket engine, the hot gases expand quickly and escape from the nozzle at very high velocities. The rocket and gases both combine formed a system on which no external force is acting. Applying the principle of conservation of momentum, the net momentum of the system must remain constant.

Suppose the gases escape from the nozzle with some velocity after the combustion of fuel.

Write the expression for the conservation of momentum.

mv + MV = 0

Here,

m is the mass of the gas

M is the mass of the rocket

v is the velocity of the gas

V is the velocity of the rocket

Write the velocity of the rocket in terms of velocity of the gas.

$$V=-\left(\frac{m}{M}\right)v$$

From the above relation, it is clear that the gases escape with velocity v in downwards direction and the rocket moves with velocity $$\left(\frac{m}{M}\right)v$$ in upwards direction.

Conclusion:

Therefore, by conservation of momentum principle, the gases escape with velocity v in downwards direction and the rocket moves with velocity $$\left(\frac{m}{M}\right)v$$ in upwards direction.