Question

In conservation of linear momentum m1u1+m2u2 =m1v1+much if the initial velocity is zero that is m1u1 +m2u2 = 0 that means m1v1+m2v2 = 0 that means body should not have any acceleration but in the case of horse and cart horse moves why

Answer 1

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Applying the law of conservation of momentum,

Total momentum before collision = total momentum after collision

m1v1i + m2v2i = m1v1f + m2v2f (in magnitude)

or m1 (v1i - v1f) = m2 (v2f - v2i) --------------- (i)

Since the collision is elastic, the kinetic energy will be conserved.

Kinetic energy before collision = Kinetic energy after collision

Dividing (ii) by (i), we get

v1i + v1f = v2f + v2i

or v1i - v2i = v2f - v1f ------------ (iii)

(v1i - v2i) is the magnitude of the relative velocity of A w.r.t B.

(v2f - v1f) is the magnitude of the relative velocity of B w.r.t A.

It may be noted that the direction of relative velocity is reversed after the collision.

From equation (iii)

v2f = v1i - v2i + v1f

From equation (i)

m1 (v1i - v1f) = m2 (v1i - v2i + v1f - v2i)

or m1v1i - m1v1f = m2v1i - 2m2v2i + m2v1f

or -m1v1f - m2v1f = -m1v1i + m2v1i - 2m2v2i

or (m1 + m2) v1f = (m1 - m2) v1i + 2m2v2i

Again, from equation (iii),

v1f = v2f - v1i + v2i

Substituting this value in equation (i) and simplifying, we get