Question

If a rocket is propelled while in space, is the momentum of the rocket itself (not including the exhaust products) conserved?

Answer 1

No, the momentum is not conserved.

This is because the law of conservation of momentum applies to a system. Because the rocket is an object within the system, and not the entire system, which would include the exhaust products, the momentum of the rocket will not be conserved. However, if the complete system was taken into consideration, it would be observed that momentum is in fact conserved.

Answer 2

No, momentum of the rocket itself will not be conserved as the net external force on the rocket itself is not zero.

Further explanation

When a rocket leaves the ground they need a huge amount of thrust to lift off from the ground. This is not an easy task to lift off from the ground due to the heavy weight of the rocket. Generally Liquid fuels are used as a propellant in the rocket.

Given:

A rocket is propelled in the space.

Concept:

The logic behind the momentum conservation is Newton’s third law.

A force is defined as the rate of change of momentum with respect to time.

Mathematically,

$\boxed{\vec F = \dfrac{{d\vec p}}{{dt}}}$

If net external force on a particle is zero, the rate of change of momentum will be zero so momentum will be constant.

$\vec p = {\text{constant}}$

Thus, we can say momentum will be conserved. One point should be noticed that momentum is a vector quantity so vector sum is used while summing together momentum of two or more bodies.

Now for an isolated system, net external force on an isolated system is zero; therefore momentum is conserved for an isolated system.

When exhaust gases leaves the engine downward with a very high velocity, it exerts a reaction force on the rocket in upward direction. The action and reactions are equal in magnitude but the direction is opposite to each other. So if we consider rocket and exhaust gases as a system net force on the system will be zero and momentum will be conserved for (rocket+exhaust) system.

But if rocket itself is taken as a system, a reaction force (say N) acts on the rocket in upward direction which is responsible for lift off the rocket, therefore momentum cannot be conserved.

Thus, the momentum of the rocket itself will not be conserved as the net external force on the rocket itself is not zero.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Laws of motion

Keywords:

Rocket, propelled, space, momentum, not, conserved, reaction, upward, direction, balanced, force on rocket, launch, exhaust gas, rocket propulsion, momentum conservation.