LAW OF CONSERVATION OF LINEAR MOMENTUM

“When no external force acts on a system of several interacting particles, the total linear momentum of the system remains conserved”

Practical applications of the law of conservation of linear momentum

(i) Recoil of a gun. Let M be the mass of the gun and m be the mass of the bullet. Before firing, both the gun and the bullet are at rest. After firing, the bullet moves with the velocity v and the gun moves with the velocity V. As no external force acts on the system, linear momentum is conserved.

Total momentum before firing = Total momentum after firing

0 = mv+ MV

Or V = - mv/M

The negative sign shows that V and v are in opposite directions.

 (ii) When a man jumps out of a boat to the shore, the boat slightly moves away from the shore. Initially, the total momentum of the boat and the man is zero. As the man jumps from the boat to the shore, he gains a momentum in the forward direction. To conserve momentum, the boat also gains an equal momentum in the opposite direction.

Q1. A shell of mass 0.02 kg is fired by a gun of mass 100 kg. If the muzzle speed of the gun is 80 m/s, what is the recoil speed of the gun?

Ans. m = 0.02 kg, M = 100 kg, v = 80 m/s

Let V be the recoil speed of the gun

According to the law of conservation of momentum,

Initial momentum = Final momentum

0 = mv + MV

V = - mv/M = - 0.02 x 80/100 = - 0.016 m/s

*Negative sign indicates that the gun moves backward as the bullet moves forward.

Q2. Can a sailboat be propelled by air blown at the sails from a fan attached to the boat?

Ans. No. When the fan pushes the sail by blowing air, the air also pushes the fan in opposite direction. As the fan is a part of the boat, the vector sum of the momenta of the fan and the boat is zero. The boat will only move if some external agency applies force on it.

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