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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» <html><body><p><br/></p>Solution :As the cliff is very heafy so its velocity <a href="https://interviewquestions.tuteehub.com/tag/almost-373246" style="font-weight:bold;" target="_blank" title="Click to know more about ALMOST">ALMOST</a> remains same after collision. <br/> Let velocilty of <a href="https://interviewquestions.tuteehub.com/tag/block-18865" style="font-weight:bold;" target="_blank" title="Click to know more about BLOCK">BLOCK</a> `B` just after Collision be `v_(1)` <br/> `v_(2)-v_(1)=<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>[u_(1)u_(2)]` <br/> `impliesv-v_(1)=1/2[2-v]impliesv_(1)=v/2` b. work <a href="https://interviewquestions.tuteehub.com/tag/done-2591742" style="font-weight:bold;" target="_blank" title="Click to know more about DONE">DONE</a> by clif =change in `<a href="https://interviewquestions.tuteehub.com/tag/ke-527890" style="font-weight:bold;" target="_blank" title="Click to know more about KE">KE</a>` of `m` <br/> `1/2m[(v/2)^(2)-(2)^(2)]a=-15/8mv^(2)` <br/> c. Just after collision with cliff <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/BMS_VOL2_C01_E01_085_S01.png" width="80%"/> <br/> At maximum compression <br/> `COLM: 2mv_(0)+mv_(0)=2mv+(mv)/2impliesv_(0)=5/6v` <br/> COME:` 1/2kx_(m)^(2)+1/2(3m)v_(0)^(2)=1/2(2m)v^(2)+1/2m(v/2)^(2)` <br/> `implies x_(m)=(sqrt(m/(6k)))v`</body></html>


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