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Homework Help: Momentum and Mechanical Energy.

  1. Jan 31, 2014 #1
    Is momentum conserved when it is said that the mechanical energy is? My teacher says no, but I cannot think of any example. Looking at the formulas, it seems as though constant mechanical energy will always conserve momentum...
  2. jcsd
  3. Jan 31, 2014 #2
    Mechanical energy can either be potential or kinetic. Throw a ball up and at it's apex its momentum = 0 because v = 0, but its energy is constant.
  4. Jan 31, 2014 #3


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    I can't think of a practical situation where that would happen, off the top of my head. But I can think of some impractical situations (perhaps some might call them silly, or maybe trivial).

    Momentum is always conserved for closed system (one in which there are no external forces and no external torques involved). Always.

    So if momentum is not conserved, there is the implication that an external force (or external torque for the angular version) is present.

    So imagine an inelastic collision between two clay balls. After the collision, the two clay balls stick together. So far, momentum is conserved, but not mechanical energy. But now imagine that an external force is applied, after the fact, such that by coincidence it brings the final mechanical energy back up to the original value before the collision. Now the initial and final mechanical energies are equal but the momentum has changed.

    Silly, "stupid" example? Perhaps. But silly things like that are all I can think of at the moment.

    Maybe a more graceful example can be found by considering objects in an accelerating frame of reference. But I can't think of anything off the top of my head.
  5. Jan 31, 2014 #4


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    There's a more graceful situation! Very nice. :smile:

    It's not possible to violate conservation of momentum without external forces/torques or accelerating/rotating frames of reference though, which is my original point.

    If you take the ball example, but include the momentum of the Earth into the equation, you find that the momentum of the Earth plus the momentum of the ball is conserved. It's only when you take the Earth out of the picture and treat the gravitational force as external where momentum is not conserved.
  6. Feb 1, 2014 #5
    ;) :) ;) :) :-))
    Last edited: Feb 1, 2014
  7. Feb 1, 2014 #6
    :) :)
    Last edited: Feb 1, 2014
  8. Feb 1, 2014 #7

    In an Inenelastic collision momentum is conserved but mechanical energy is not conserved.consider a body having mass m1 fallen verticall downwards from some hight (h) then the ball is unable to rise completely to its original height after collision with the ground and attains a hight (h') {h>h'}, thus the decrease in hight is due to the lost of energy in the form of heat energy, sound energy.
    since movementum is conserved as;
    when body colloids with ground the mutual impulsive forces acting over the collision time t2-t1 cause a change in their respective momenta :
    Change in P1=F12*(t2-t1)
    Change in P2=F21*(t1-t2)
    where F12 is force exerted on the body(1) by the ground(2) and F21 is force exerted on the ground(2) by the body(1).
    from Sir Newton's third law;
    F12=F21 this implies
    Change in P1 Change in P2 = 0
    where P1 and P2 are momentums of body(1) and ground(2) respectively.
    But the potential energy of the body at hight h and h' are as;
    mgh>mgh' as {h>h'}
    Thus mechanical energy is not conserved.
    It happens also in streaching of spring.
    This type of collitio is called #inelastic collisions.
  9. Feb 1, 2014 #8


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    All true, but not the point of the question. The OP is asking about the converse: can mechanical work be conserved when momentum is not.
    e^(i Pi)+1=0's example answers it, though may be a little unsatisfactory in that the mechanical energy has to be allowed to convert between kinetic and potential. For an example which is purely kinetic, consider a mass on a string suspended from a vertical rod, spinning about the rod in a horizontal plane. The linear momentum of the mass is constantly changing (not in magnitude, but as a vector).
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