State and Prove the law of conservation of linear momentum for the system of two
bodies.
Answers
Explanation:
The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.
Linear momentum is mathematically expressed as:
p→ = mv→ p→ is the linear momentum.
v→ is the linear velocity.
m is the mass of the body.
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Conservation Of Linear Momentum Equation
The law of conservation of momentum can be explained from the second law of motion. Newton’s second law of motion says that the rate of change of linear momentum of a body is equal to the net external force applied to it.
Mathematically it is expressed as:
dPdt=(mv)dt=mdvdt=ma=Fnet
If the net external force acting on a body is zero, then the rate of change of momentum is also zero, which means that there is no change in momentum.
Two bodies of mass M and m are moving in opposite directions with the velocities v. If they collide and move together after the collision, we have to find the velocity of the system.
Since there is no external force acting on the system of two bodies, momentum will be conserved.
Initial momentum = Final momentum
(Mv – mv) = (M+m)VFinal
From this equation, we can easily find the final velocity of the system.
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The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.