Question

Croquet ball A moving at 8.9 m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 5.0 m/s .

What fraction of the initial kinetic energy is lost in the collision?

Answer #1

_{A}) = m

Mass of ball B (m_{B}) = m

Initial velocity of ball A (u_{A}) = 8.9 m/s

Initial velocity of ball B (u_{B}) = 0 m/s

Now the initial momentum of the system = m_{A}u_{A}
= 8.9m ------------(1)

Final velocity of the ball A = V_{A}

Final velocity of the ball B (V_{B}) = 5 m/s

Final momentum of the system = m_{A}V_{A} +
m_{B}V_{B} = mV_{A} + 5m
----------(2)

Applying conservation of momentum

mV_{A} + 5m= 8.9 m

V_{A} = 3.9 m/s

Now initial kinetic energy(K_{i}) =
(1/2)mu_{A}^{2} = (1/2)m*8.9^{2}
= 39.605m --------(1)

Final kinetic energy (K_{f})=
(1/2)mV_{A}^{2} + (1/2)mV_{B}^{2} =
(1/2)m*(3.9^{2}) +(1/2)*(m*5^{2}) = 20.105m
------------(2)

Now the

K_{f} /K_{i} = 20.105/39.605 = 0.51

Therefore lost kinetic energy = 1-0.51 = 0.49

hence 0.49 fraction of initial kinetic energy is lost.

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