Momentum with accelerating ball

Classical Mechanics Level 3

Two balls of masses 1 k g 1kg and 2 k g 2kg are 20 m 20m apart (when t = 0 ) t=0) . If the 1 k g 1kg ball rolls to the right at 2 m / s 2m/s , and the 2 k g 2kg ball rolls towards the left at ( t + 1 ) m / s (t+1)m/s . If the collision is perfectly elastic, and the 1 k g 1kg ball rolls to the left at 4 m / s 4m/s after the collision, what velocity is the 2 k g 2kg ball travelling at the instant after the collision? If this is v 2 f v_{2f} , find ∣ v 2 f ∣ \left |v_{2f}\right| .

Details and Assumptions: - Ignore energy loss due to friction.


The answer is 2.

Charley Shi by Charley Shi , 19, New Zealand

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1 solution

Only momentum conservation suffices to solve the problem. Acceleration of the 2kg. mass is 1m/sec/sec. Distance traveled by it in t seconds is t+(t^2/2), while that by 1kg. mass is 2t. Therefore 2t+t+(t^2/2)=20. Solving this we get t=4sec. Therefore the speed of the 2kg. mass at that instant is 5m/s. Applying momentum conservation law, we get the magnitude of the final velocity of this mass as 2m/s towards left.

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