Question

what is conservation of momentum? derive its expression

Answer 1

Momentum of a body is the quantity of motion contained in the body. It is measured as the product of mass and velocity of a body.

It is represented by P.

P = mv

Conservation of Momentum :-

The total momentum of an isolated system of constant mass remains constant or conserved and does not change with time.

If the momentum of two particles system of masses M and m are P and p respectively, then the net momentum of the whole system is given by :-

${P}_{net}$ = P + p = constant

Now,

Derivation of Law of Conservation of Momentum :-

Force applied on particle A by particle B = F and force applied on particle B by particle A = f

F = dP/dt

f = dp/dt

From 3rd Law of Newton,

F = -f

dP/dt = -dp/dt

dP/dt + dp/dt = 0

d(P+p)/dt = 0

P + p = Constant...

Now, Conservation of Momentum for the collision of two bodies :-

Two bodies of mass M and m collide on frictionless surface in the same direction with respective velocities U and u. After collision their velocities becomes V and v respectively.

Initial Momentum of body before collision.

P = MU

p = mu

Final Momentum of body after collision.

P' = MV

p = mv

During collision force applied on particle A exerts force f on particle B and particle B exerts force F on particle A.

From 3rd Law of Sir Newton,

F = - f

M(V-U)/t = -m(v-u)/t

MV - MU = -mv + mu

MV + mv = MU + mu