Question:
A body of mass m1, moving with velocity u1, collides head on with another body of mass m2 at rest (i.e. u2 = 0 ) .The system remains isolated from the surroundings.
(a) Derive an expression for the velocities with m1 and m2 will move after the collision,if the collision is perfectly elastic.
(b) Obtain an expression for the final kinetic energy of the system when the collision is perfectly inelastic.
Answer:
Before collision:
Consider body A of mass m1 and velocity u1 collides with another body of mass m2 and velocity u2 = 0
After collision:
The body moves with a velocity V
Case 1: Collision is elastic
In elastic collision, kinetic energy is conserved
½ m1v12 + ½ m2v22 = ½ m1u12 + 0
m1v12 + m2v22 = m1u12
Case 2: Collision is inelastic
In elastic collision, momentum is conserved
m1u1+ 0= m1v1 + m2v2
m1u1+ 0= (m1+m2)V where V is the velocity after collision
V = m1u1/ (m1+m2)
Kinetic energy after collision = ½ MV2 = ½ (m1+m2)V2 = ½ (m1+m2) * m1u1/ (m1+m2) * m1u1/ (m1+m2)
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