Question

derive equation for linear momentum. i.e (m1u1+m2u2) = (m1v1+m2v2)

Answer 1

This cant be fully derived but a part of it can be.

In an elastic collision kinetic energy is conserved, so

1/2*m1*u1^2 + 1/2*m2*u2^2 = 1/2*m1*v1^2 + 1/2*m2*v2^2

m1*u1^2 + *m2*u2^2 = *m1*v1^2 + *m2*v2^2

m1*u1^2 - *m2*v1^2 = *m2*v2^2 - *m2*u2^2

m1(u1+v1)(u1-v1)=m2(v2+u2)(v2-u2) ---------- equation 1

NOW,

Accordinbg to conservation of linear momentum,

m1u1 + m2u2 = m1v1 + m2v2

m1(u1-v1) = m2(v2-u2) ---------- equation 2

dividing equation 1 by 2 we get ,

u1 + v1 = u2 + v2

u1-u2 = v2-v1

v2-v1/u1-u2 = 1

THUS , WE GET A EQUATION WHICH IS THE COEFFICINT OF RESTITUTION EQUALS TO 1.

THIS PROVES THAT IF COLLISION IS ELASTIC THIS WILL BE EQUAL TO 1.

MOREOVER,OF IT APPROACHES 1 BOTH THE EQUATIONS WILL BE SATISFIED APPROXIMATELY ,

WHICH WILL CONTRIBUTE TO THE FACT THAT KINETIC ENERGY IS CONSERVED WHICH IN TURN

WILL INCREASE THE FACT THAT COLLISION HAPPENS IN A ELASTIC PLANE.

THUS ITS A MEASURE OF ELASTIC COLLSION,

Answer 2

Explanation:

this is the derivation of conservation of momentum

and it hopes help u