Two carts undergo an inelastic collision where they stick together. Cart A has an initial velocity v0, and the second cart B is initially at rest. After the collision, it is observed that the ratio of the final kinetic energy system to its initial kinetic energy is KfK0= 1/6. Determine the ratio of the carts' masses, mBmA. (Assume the track is frictionless.)

Explanation:

Initial kinetic energy of the system = 1/2 mA v0²

If Vf be the final velocity of both the carts

applying conservation of momentum

final velocity

Vf = mAvo / ( mA +mB)

kinetic energy ( final ) =  1/2 (mA +mB)mA²vo² /  ( mA +mB)²

= mA²vo²  / 2( mA +mB)

Given 1/2 mA v0²  / mA²vo²  / 2( mA +mB) = 6

mA v0² x ( mA +mB) / mA²vo² = 6

( mA +mB) / mA = 6

mA + mB = 6 mA

5 mA = mB

mB / mA = 5 .

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