The drawing shows a collision between two pucks on an air-hockey table. Puck A h
ID: 2141906 • Letter: T
Question
The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.028 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.058 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 final speed of puck B.
Explanation / Answer
Use conservation of momentum
let U = initial speed and V = final speed
the initial momentum (pi) = MaUa + 0 = 0.023(5.5) = 0.1265 kg*m/s (right)
not that pi in the x direction is 0.1265 and pi in the y-direction is 0. By conservation of momentum, pf(x) = pi(x) and pf(y) = pi(y)
MaVa(x) + MbVb(x) = 0.1265 MaVa(y) - MbVb(y) = 0
0.023Va(cos65) + 0.058Vb(cos37) = 0.1265 and 0.023Va(sin65) - 0.058Vb(sin37) = 0
from the equation on the right, 0.058Vb = 0.023Va(sin65)/(sin37) ****
substituting into the equation on the left:
0.023Va(cos65) + 0.023Va(sin65)/(sin37) = 0.1265
Va = 0.1265 / (0.023cos65 + 0.023sin65/sin37)
Va = 2.9 m/s
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