Question

Block B is initially at rest. Then block A slides on the smooth surface to the right and collides with block B with a velocity vAvA. Consider three following collision cases where: i) elastic impact; ii ) perfectly plastic impact; iii ) e = 0.5. Just after the collision, rank these three cases where the relative velocitiy of B with respect to A is from largest to smallest magnitude.

Answer 1

Coefficient of restituiton, e=relative velocity of seperation/relative velocty of approach.

   where e ranges between 0 to 1. Here are velocities of B and A after collision respectively. are velocities of B and A before collision respectively.

Given =vA.

i) For perfectly elastic collision: e=1

So e=1= and =vA-0=vA.

Therefore Relative velocity of B wrt A is = vA.

ii) For perfectly plastic collision, e=0

So e=0= and hence =0

Therefore Relative velocity of B wrt A is = 0.

iii) Now for e=0.5,

So e=0.5= and hence =0.5vA.

Therefore Relative velocity of B wrt A is = 0.5vA.

Hence rank of relative velocity is

Rank-1:elastic impact

Rank-2:e=0.5 case

Rank-3:perfectly plastic.