Rocket Propulsion Principle: Newton's Laws and Conservation of Momentum | 10th Science

Rocket Propulsion

ROCKET PROPULSION

Propulsion of rockets is based on the law of conservation of linear momentum as well as Newton’s III law of motion. Rockets are filled with a fuel (either liquid or solid) in the propellant tank. When the rocket is fired, this fuel is burnt and a hot gas is ejected with a high speed from the nozzle of the rocket, producing a huge momentum. To balance this momentum, an equal and opposite reaction force is produced in the combustion chamber, which makes the rocket project forward.

While in motion, the mass of the rocket gradually decreases, until the fuel is completely burnt out. Since, there is no net external force acting on it, the linear momentum of the system is conserved. The mass of the rocket decreases with altitude, which results in the gradual increase in velocity of the rocket. At one stage, it reaches a velocity, which is sufficient to just escape from the gravitational pull of the Earth. This velocity is called escape velocity. (This topic will be discussed in detail in higher classes).

Understanding the Principle of Conservation of Linear Momentum

Principle of Conservation of Linear Momentum

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.

Let us prove the law of conservation of linear momentum with the following illustration:

Figure 1.7 Conservation of linear momentum

Proof:

Let two bodies A and B having masses m₁ and m₂ move with initial velocity u₁ and u₂ in a straight line. Let the velocity of the first body be higher than that of the second body. i.e., u₁>u₂ . During an interval of time t second, they tend to have a collision. After the impact, both of them move along the same straight line with a velocity v₁ and v₂ respectively.

Force on body B due to A,

F_B= m₂ (v₂–u₂)/t

Force on body A due to B,

F_A = m₁ (v₁–u₁)/t

By Newton’s III law of motion,

Action force = Reaction force

F_A    =         –F_B

m₁ (v₁-u₁)/t  =       –m₂ (v₂-u₂)/t

m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂ ------ (1.9)

The above equation confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.

Hence the law of conservation linear momentum is proved.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail. 10th Science : Chapter 1 : Laws of Motion : Principle of Conservation of Linear Momentum.