Conservation of momentum
The law of conservation of momentum has been deduced from large number of observations and experiments. This law was formulated nearly three centuries ago. It is interesting to note that not a single situation has been realised so far, which contradicts this law. Several experiences of every-day life can be explained on the basis of the law of conservation of momentum.
Law of conservation of momentum:
In the absence of any external force on the system, its total momentum is conserved.
Proof: From Newton’s second law, F = Change in momentum / time taken
F = (final momentum – initial momentum) / time taken (t)
F = (mv-mu) / t
IF external force applied on the system is zero (F = 0).
0 = (mv-mu) / t ⇒ 0 = (mv-mu)
mv = mu
Final momentum – Initial momentum, indicating that momentum is conserved or constant.
For constant mass system, ⇒ mv = mu
v = u
The body maintains its state or its velocity is constant.
Derivation of law of conservation of momentum:
Consider two bodies of mass m1 and m2 moving in the same direction along a straight line with velocities u1 and u2 (u1 > u2), respectively. There are no other unbalanced external forces acting on them. Since u1 is more than u2 so both body collide and comes in contact with each other for short interval of time t. During collision, the body 1 exerts a force F12 on body 2 and the body 2 exerts a force F21 on body 1. After the collision, both bodies get separated and move with velocities v1 and v2 respectively.
QUIZ-1 Force and Laws of Motion 🖱️👉 START
Conservation of momentum: Important Questions
Question 1:
Why does a gun required on firing a bullet?
Ans: The bullet and gun are both at rest, and their initial momentum is zero. After firing the bullet, the bullet gains significant momentum in a forward direction, and the gun must have equal momentum in the opposite direction to conserve momentum, so the gun must recoil backward with the same magnitude of momentum. That’s why it is advisable to hold a gun tight to one shoulder when it is being fired.