Conservation of momentum and loss of energy in inelastic collisions

  1. I just learned that, in elastic collisions, the total momentum in the system is preserved while a certain amount of kinetic energy is lost.
    I know that kinetic is energy may be lost in the form of heat or sound. Isn't the same energy responsible for keeping the two objects in motion and preserving their momentum? How then does the momentum remain the same when the amount of energy in the system decreases?
     
  2. jcsd
  3. ZapperZ

    ZapperZ 29,765
    Staff Emeritus
    Science Advisor
    Gold Member

    You need to read again where you learn all this.

    In elastic collision, BOTH momentum and KE are conserved.

    Zz.
     
  4. Opps. My mistake. I made a small typing error. What I meant was "inelastic".
     
  5. atyy

    atyy 9,941
    Science Advisor

    Momentum is a vector. Energy is a scalar. Say you have 2 vectors of equal magnitude pointing in opposite directions = 0. Now subtract lots of little vectors representing the energy loss as heat in all directions (ie. non-directionally). Now the vector sum is still 0.
     
  6. umm...
    So what you are saying is that the loss of heat energy in all directions adds up to zero. Therefore it can make no change to momentum?
     
  7. You seem to believe that energy causes momentum. It doesn't.

    Consider a motionless boulder poised at the top of a cliff. It has a lot of energy but no momentum.

    And conversely, an object doesn't consume energy to keep it moving. Such would be an Aristotelian, rather than a Newtonian, model of the world.
     
  8. "You seem to believe that energy causes momentum."
    That's exactly what I was thinking.
    Since it is true that an object with momentum has kinetic energy, I assumed that a loss of energy would be accompanied by a loss of momentum.
    But I still don't understand why a loss of energy has no effect on momentum.
     
  9. Doc Al

    Staff: Mentor

    An object with momentum has macroscopic kinetic energy (associated with its center of mass movement). But it also has plenty of random kinetic energy (internal, thermal energy).
    Sure, if a single object loses macroscopic kinetic energy (due to some force acting on it) it also loses momentum. But in an inelastic collision between two objects, the net momentum of the system remains unchanged. But the momentum of each object changes, and thus the macroscopic kinetic energy of each object changes. When all is said and done, in an inelastic collision the momentum of the system remains the same while the total macroscopic kinetic energy is lower. (That "lost" energy becomes random thermal energy.)
     
  10. Yes, a single object that has momentum also has kinetic energy. If you slow it down, then both the momentum and kinetic energy decrease. But a system of objects can have kinetic energy, but no momentum. Recall atyy's observation that one is a scalar and the other is a vector.

    Imagine two balls of putty speeding towards each other. The total momentum is zero, even though the total kinetic energy is not. When they collide, the kinetic energy converts into heat. But remember the momentum is already zero. How could it lessen?
     
  11. First of all, thanks for your replies.
    I understood the puttyball example but I didn't understand the how force being a scalar quantity and momentum being a vector quantity could explain the conservation of momentum
     
  12. Doc Al

    Staff: Mentor

    Both force and momentum are vector quantities. Kinetic energy is a scalar.
     
  13. Oh. After a little thinking I understand what's happening,. Thanks for all your replies.
     
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