Question

204. In a game of billiards, ball A approaches to the black ball with an initial velocity of V, and continues with vi' after impact. The black ball is at rest in the beginning and can end in the hole as shown with a velocity of vz' after the collision. Determine final velocities of both balls in terms of V1 and find out the percentage of kinetic energy loss during impact. The coefficient of restitution is 0.9. P 45°

Answer 1

given data cocfficient of restitution, e=0.9 have Same mass Both Ball solution Before impact After impact и 8 1415 Visin45 visino Vz Tvis VICOS450 vi lose of according to conservation mommentum, Ca-direction) momentum Linear momentum Linear before b. impact (& Direction after impact Ca direction) 1 mv, cosagot nco) mv Coso +0. Vi Cosas = mvil cose vi coso coefficient of restitution, e- Vi COS45 -0 1 - Vi' cose 0.qx vi VICOS 45 - ri coso 0.63639 V along y-düection mv, sin 45 0 mui'sino + mva? vi sino + V2' Vi Sin45 V2 - visino CS Scanned with CamScanner Visina50

0.9 X Vi Sini = Vz - vi sino 0.63639 V1 = va'- visine @ Add equation and O. TOTI V 11 ve't visine 0.63639 V - ve' visino 1.34349 Vi 2 V2' V2' = 0.6717 V Put value in ean 0.63639 vi 0.6717 Vi - Vi Sino -risino visine = 0.03535 Vi egin vi sino 0.03535 vi egn 1 يوم 0.707 Y tano = 0.0 499 0 - 2.862 Loss of kinetic energy Along x-direction kinetic energy = m vicosas)' + o Initial KEI - 0.25m vi? 1 mcvicose)? +0 kinetic energy = FINAL (-0.63639 v)? 2 2 KE2 = 0.202 MV KE - KEZ 0.25 mv ²-0.202 mu? energy KEI 0.25mvi? Fraction Loss of kinetic Result] Cipraction of Scanneet Heinetic enery loss -0.192 Q: 2.862 canne!
so the percentage of kinetic energy loss would be 0.192×100=19.2%