Please show me the steps to solve the following problem: Collisions in One Dimen

Question

Please show me the steps to solve the following problem:

Collisions in One Dimension Part A On a frictionless horizontal air table, puck A (with mass 0.255 kg) is moving toward puck B (with mass 0.375 kg), which is initially at rest. After the collision, puck A has velocity 0.125 m/s to the left, and puck B has velocity 0.651 m/s to the right What was the speed vAi of puck A before the collision? Hints UAi = 0.832 m/s Submit My Answers Give Up Correct If you are required to use the answer obtained for a subsequent hint or part, use your unrounded/full precision answer. Part B Calculate K the change in the total kinetic energy of the system that occurs during the collision Hints A2cp Submit My Answers Give Up Incorrect; Try Again; 4 attempts remaining

Explanation / Answer

given, on a frictionless air track

Ma = 0.255 kg

initial speed = Ua

final speed, Va = -0.125 m/s ( to the left)

Mb = 0.375 kg

initial speed, Ub = 0

final speed Vb = 0.651 m/s ( to the right)

a. hence form conservation of momemtnum

MaUa + MbUb = MaVa + MbVb

0.255*Ua = 0.255*(-0.125) + 0.375*0.651

Ua = 0.832352 m/s to the right

hence Ua = Vai = 0.8323529 m/s

b. initial KE of the system = 0.5(MaUa^2 + MbUb^2)

KEi = 0.5*0.255*0.83235^2 = 0.0883334 J

final KE of the system = 0.5(MaVa^2 + MbVb^2)

KEf = 0.5*0.255*0.125^2 + 0.5*0.375*0.651^2 = 0.081454875 J

so change in KE = KEi - KEf = 0.006878525 J

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