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I Variation of mass in a system and acceleration

  1. Apr 14, 2016 #1
    Is it really possible for a system to decrease its velocity with no forces acting on it, just because the mass in it is "varying"?

    Consider for example a freight car and a hooper from which sand is released in to the car. The freight car will decrease its initial velocity if there is no force supplied, but that's not because its mass is increasing, but because the sand that comes in to the freight car produces friction with it (equivalently "tries" to be accelerated) and the friction force is the one that makes the velocity of the freight car decrease.

    So actually there is a force, which cause the acceleration (deceleration). Is this correct? Or it is really just the increasing of mass that change the velocity of the freight car?
  2. jcsd
  3. Apr 14, 2016 #2
    I know a physical explanation would be more affective, but mathematically, conservation of linear momentum would cause the velocity to decrease even if mass just appeared in the freight car.
  4. Apr 14, 2016 #3


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    Here are two physical explanations. Pick one that feels right.

    Draw the boundary for the system containing the freight car between the sand that is still falling and the sand which has just hit the pile and has not yet finished sliding to rest. The freight car loses velocity because the average velocity of its contents is decreased by the addition of the new zero-velocity sand. The force of friction does not enter in because it is an internal force.

    Draw the boundary for the system containing the freight car between the sand which is sliding to rest and the sand that has finished settling. The freight car loses velocity from friction. Under this description, the friction is an external force. The averaging effect does not enter in because the sand that moves from outside the system to inside is at zero velocity relative to the car.
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