Two blocks A and B of mass m and 2m respectively are moving towards a massive ("mass" gt gt 2m) cliff with velocities 2v and v respectively. The cliff moves with a velocity v. If the coefficient of restitution of collision at the surface of the cliff is e = 1//2, find the: a. velocity of the block B just after colliding with the cliff. b. work done by the cliff during collision. c. maximum compression of the spring of stiffness k which is fitted with the block B.

Two blocks A and B of mass m and 2m respectively are moving towards a

1.	Two blocks A and B of mass m and 2m respectively are moving towards a massive ("mass" gt gt 2m) cliff with velocities 2v and v respectively. The cliff moves with a velocity v. If the coefficient of restitution of collision at the surface of the cliff is e = 1//2, find the: a. velocity of the block B just after colliding with the cliff. b. work done by the cliff during collision. c. maximum compression of the spring of stiffness k which is fitted with the block B.
Answer» Solution :As the cliff is very heafy so its velocity ALMOST remains same after collision. Let velocilty of BLOCK `B` just after Collision be `v_(1)` `v_(2)-v_(1)=E[u_(1)u_(2)]` `impliesv-v_(1)=1/2[2-v]impliesv_(1)=v/2` b. work DONE by clif =change in `KE` of `m` `1/2m[(v/2)^(2)-(2)^(2)]a=-15/8mv^(2)` c. Just after collision with cliff At maximum compression `COLM: 2mv_(0)+mv_(0)=2mv+(mv)/2impliesv_(0)=5/6v` COME:` 1/2kx_(m)^(2)+1/2(3m)v_(0)^(2)=1/2(2m)v^(2)+1/2m(v/2)^(2)` `implies x_(m)=(sqrt(m/(6k)))v`