Question

Deduce the relation for the velocity of masses after collision if the velocity in straight line before collision is u1 and u2

Answer 1

2 answers · Physics

Best Answer

Since u2>u1, and both are moving in the same straight line,

We find the relative velocity of m2 assuming m1 to be at rest.

Hence the new velocity of m2 is U2 = (u1+u2) and that of m1 is ZERO.

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Total momentum before collision

[m2uU2 + 0]

After collision

m1v1 + m2v2

m1v1 + m2v2 = m2*U2

m1v1 = m2 (U2-v2) -------------1

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In elastic collision K.E is also conserved.

m2U2^2 = m1v1^2 + m2v2^2

m2 [U2^2 – v2^2] = m1v1^2

Substituting for m1v1 from 1

m2 [U2^2 – v2^2] = m2 (U2-v2)*v1

[U2+v2] = v1 Since [U2^2 – v2^2] = [U2+v2]* [U2-v2]

Multiplying by m1 on both sides and replacing m1v1 by m2 (U2-v2)

m1 [U2+v2] = m2 (U2-v2)

(m1+m2) v2 = (m2 –m1) U2

Final velocity of m2 is

v2 =[ (m2 –m1) / (m1+m2)]*U2 where U2 = (u1+u2)

From m1v1 = m2 (U2-v2)

Final velocity of m1 is

v1 = (m2/m1) (U2-v2)

Substituting for v2

v1 = 2m2U2/( m1+m2) where U2 = (u1+u2)