Dynamics_Part41

Dynamics_Part41 -

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Unformatted text preview: Problem 5: Problem 4. Problem: In a game of billiards, a player hits the cue ball at speed V parallel to the left cushion as shown. After the impact, the eight ball moves at an angle to the left cushion and, after impacting the cushion, goes into the upper-right corner pocket. Both balls have mass m and the coefficient of restitution for the billiard balls is e. (a) Determine the velocity of the cue ball after the impact, V . Express your answer in terms of the indicated x and y axes. (b) Assuming = 50o and that the angle at which the cue ball moves after the impact is 35o , determine the coefficient of restitution, e. y vV V . ........................ ...... .................................................................................................................................................................................... ...................................................................................................................................................................................... ........................................................................................................................................................................................ ........ .. ............ .. ............ ............... ... .................. .. ............ .......... . . .............................................................................................................................................................. 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...................................................................................................................................................................................... ...................................................................................................................................................................................... ...................................................................................................................................................................................... ...................................................................................................................................................................................... f v x So ut on: Our approach o h s prob em s o f rs do a br ef k nema cs compu a on Th s w fac a e re a ng quan es n he xy coord na e sys em o hose n he nt coord na e sys em needed o ana yze he mpac be ween he cue ba and he e gh ba Then we use he Pr nc p e of Momen um and Impu se o de erm ne he cue ba 's ve oc y af er he mpac F na y we compu e he coeff c en of res u on for = 50o and = 35o (a) The ne of mpac s para e o he e gh -ba 's ve oc y as moves oward he cush on on he ef s de of he ab e A gn ng he n ax s w h he e gh -ba 's ve oc y un vec ors n and t n he n and t d rec ons respec ve y are re a ed o un vec ors and j n he x and y d rec ons respec ve y as fo ows n = - s n + cos j = - s n n + cos t n and and t = cos + s n j j = cos n + s n t k ~ n ~ ...
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