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The question is :

Heavier object A, initially at rest, is struck by lighter object B. Is it possible for object A to have a larger final momentum than the initial momentum of object B?

The answers is yes and the argument as follows: Suppose a pingpong bouncing back upon hitting a stationary truck. The change in momentum of the ball is $ 2mv$. Conservation of momentum then requires the more massive object to have a momentum $2mv $ in the opposite direction.

But how is it possible? After the collision the ball retains same kinetic energy while granting some of it to the truck? Isn't it violation of the law of conservation of energy?

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    $\begingroup$ Calculate the kinetic energy before and after the collision and see for yourself. $\endgroup$
    – CuriousOne
    May 27, 2015 at 7:19

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The ping pong ball would lose a tiny amount of kinetic energy to the truck. The truck ends up with a momentum of just under twice what the ping pong ball had. However, energy is 1/2 m*v^2 = 1/2(m*v)^2/m. Since the truck is much more massive than the ping pong ball, it carries much less energy for a given momentum. The end result is that the small amount of energy lost in the ping pong ball due to the momentum given to the truck is equal to the extra energy given to the truck (ignoring losses due to imperfect elasticity).

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  • $\begingroup$ So the maximum speed to which the truck can be accelerated by pingpong ball is up to $ 2p_{ball}/m_{ball} $ ? And if the kinetic energy of the ball is absorbed by the truck then the maximum possible speed to which truck can be accelerated is $ p_{ball}/m_{ball} ? $ Maan, I'm so disoriented. $\endgroup$
    – wuschi
    Jun 7, 2015 at 9:28
  • $\begingroup$ Isn't $p_{ball}/m_{ball}$ just $v_{ball}$? If the mass of the truck is negligible compared to the mass of the ping pong ball, it will be accelerated by $2v_{ball}$, since it's just this experiment in reverse. That last part isn't right though. How did you calculate it? $\endgroup$
    – DanielLC
    Jun 9, 2015 at 8:23
  • $\begingroup$ The ball lost all its incident momentum but didn't bounced back so in order the momentum to be conserved, the truck should be accelerated by the ball's lost momentum. But this does not make intuitively sense since the ball lost all of this energy. I'm most probably misunderstanding the whole thing. $\endgroup$
    – wuschi
    Jun 17, 2015 at 16:17
  • $\begingroup$ I'm confused as to what's going on here. Is this an inelastic collision? Does the ball end up going the speed of the truck? $\endgroup$
    – DanielLC
    Jun 17, 2015 at 21:12

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