Practical Applications of Conservation of Linear Momentum

1. When a bullet is fired from a gun, the gun recoils or give a force in backward direction.

Let M be the mass of gun and m the mass of bullet. Initially, both the gun and the bullet are at rest. On firing the gun, suppose that the bullet moves with a velocity $ \displaystyle \overrightarrow{v}\text{ }$ and the gun moves with velocity $ \displaystyle \overrightarrow{V}$.

According to the principle of conservation of the momentum,

total momentum of gun and bullet before firing = total momentum of gun and bullet after firing

$ \displaystyle {\text{i}\text{.e}\text{. }0=M\vec{V}+m\vec{v}}$

$ \displaystyle {\Rightarrow \vec{V}=-\frac{m}{M}\vec{v}}$

The negative signs shows that $ \displaystyle \overrightarrow{v}\text{ and }\overrightarrow{V}$ foreign opposite direction i.e. as the bullet moves forward, the gun will move in backward direction. The backward motion of the gun is called recoil of the gun.

2. While firing a bullet, the gun must be held tight to the shoulder

Otherwise because of recoil velocity of the gun, the shoulder may get hurt. If the gun is held tight to the shoulder, then the body of the man firing the gun recoils along with the gun. As the total mass is quite large, the recoil velocity will be very small and the shoulder of the man will not get hurt.

3. When a man jumps from a boat to the shore, the both slightly moved away from the shore.

Initially, the total momentum of the boat and the man is zero. When the man jumps from the boat to the shore, total momentum of man and the boat will be zero only if the boat moves in opposite direction.

4. Rocket works on the principle of conservation of momentum.

As the fuel in the rocket undergoes combustion, the burnt gases leave the body of the rocket with the large velocity in downward direction and thus provide upward thrust to the rocket. If you assume that the fuel is burnt at a constant rate, then rate of change of momentum of the rocket will be constant. As more and more fuel gets burnt, the mass of the rocket goes on decreasing and it leads to increase of the velocity of the rocket more and more rapidly.

It may be pointed out that rocket propulsion is an application of the principal of conservation of momentum to a situation, in which the mass of the system goes on changing.

5. If an astronaut in open space, away from space safe wants to return to his spaceship, he can do so by throwing something in a direction opposite to that in which the spaceship is moving

When the is not throw some object away from the spaceship, he himself will recoil i.e. will move in opposite direction. Due to this, the astronaut will move towards the spaceship.

6. If someone left on a frictionless floor desire to get out of it, he can do so by blowing air out of his mouth.

For the reason explained above, he will move in a direction opposite to in which air is blown out by him. However, in this case the required velocity will be small and it may take him a long time to get out. If it throws away some heavy object, he can acquire comparatively large recall velocity and can get out soon.