The drawing shows a collision between two pucks on an air-hockey table. Puck A h

Question

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0240 kg and is moving along the x axis with a velocity of +4.08 m/s. It makes a collision with puck B, which has a mass of 0.0480 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B.

Multiple-Concept Example 9 reviews the concepts that play roles in this problem. The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0240 kg and is moving along the x axis with a velocity of +4.08 m/s. It makes a collision with puck B, which has a mass of 0.0480 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B.

Explanation / Answer

First , let us conserve momentum in the vertical direction ( y -direction i.e., perpendicular to line of collision )

mavaSin650 - mbvbSin370 = 0 . Since before collsion , there was no momentum in this direction . Substituting given values we get ,

0.024*va*0.906 = 0.048*vb*0.6

implies , Va= 1.506 Vb ------- (1)

Now , lets conserve momentun in the direction of collision ,

intial momemntum = mavai = 0.024*4.08 = 0.0979 kgm/s.

final momentum = mavaCos650 + mbvbCos370 = 0.01va + 0.0383vb .

Equating we get , 0.0979? = 0.01va + 0.0383vb ; -------- (2) .

Solving equations (1) and (2) , we get ,

va = 2.763 m/s and vb = 1.835 m/s .

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