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Conservation of momentum

  1. Mar 3, 2014 #1
    Hi -

    When an engine uses chemical energy to move a vehicle, the fuel loses mass in the conversion, so that momentum (mv) stays the same before and after the acceleration? If this is true, then we convert mass to velocity all the time, while keeping mv constant, right? Where does velocity become mass? Or is all mass becoming velocity, and everything eventually ends up with a lot of velocity and no mass?

    You can see where I need clarification I'm sure. Thank you for your time.
  2. jcsd
  3. Mar 3, 2014 #2


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    Although the fuel technically loses mass when it loses chemical energy, this is an unbelievably small amount compared to the masses of the molecules themselves, and can easily be neglected (unless of course you have a nuclear powered car , and even then, the difference is still rather small).

    The momentum of a car does not stay the same before and after its acceleration; if its final velocity is different than its initial velocity, and its mass doesn't change appreciably, its momentum must have changed.
  4. Mar 3, 2014 #3
    The mass does not convert to velocity. First off, if the engine is running, it is accelerating the vehicle, so momentum is not conserved. ##\frac{d}{dt}(mv)=F## applies. But since ##m## is a function of ##t##, this is a more complicated problem than normally. We find ##m'(t)v(t)+m(t)a(t)=F## if there is a constant force. ##m'(t)## will be negative since the mass is decreasing as fuel is burned. Beyond this, specific problems might be easier to follow.

    Edit: jfizzix is correct for vehicles like cars. ##m'(t)## is so small it doesn't matter. This becomes important with rockets and other vehicles that burn fuel very quickly
  5. Mar 3, 2014 #4
    I thought momentum was always conserved, all the momentum in the universe. Where does the momentum for the car come from, and where does it go?

  6. Mar 3, 2014 #5
    It comes from the ground since the ground is acting a force on the car (friction) that makes the car accelerate. The momentum of the car isn't conserved because momentum is being transferred to it by the action of an external force.
  7. Mar 3, 2014 #6


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    The momentum of the universe is always conserved. The momentum of the car plus the rest of the earth (and the rest of the Universe) is a constant. This means that when the car is moving, the Earth is not spinning at the same rate it would if the car were at rest. Of course, this difference is so very tiny because the Earth is much more massive than the car. This effect is more dramatic in say, the Hubble telescope, where they actually spin heavy wheels to maintain the orientation of the telescope without rockets.

    The thing about the conservation of momentum is that, while the total is constant, the momentum of the parts can all change, so long as that total remains constant. The car gets its momentum from pushing against the earth, which also gets a corresponding change in its momentum. The car loses momentum due to the air needing to be pushed out of the way of the car as it moves (among other forces). This imparts momentum to the atmosphere, but the total momentum of the universe remains constant.
  8. Mar 3, 2014 #7
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