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Can we imagine that momentum is the total energy stored in the body at

  1. Jun 5, 2010 #1
    can we imagine that momentum is the total energy stored in the body at a particular velocity?if not then why?
     
  2. jcsd
  3. Jun 5, 2010 #2

    CompuChip

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    Re: momentum

    Not really, although they are related. The definition of momentum is
    p = m v
    while the kinetic energy of a body is
    E = (1/2) m v2.

    You may notice, if you know calculus, that p = dE/dv.
    The second law of Newton is actually
    F = dp/dt,
    i.e. the force is the (instantaneous) change in momentum in time. When the mass of an object is constant, this reduces to F = ma.

    Basically it expresses the ancient experimental fact that to move an object, not only the force that you extert determines the velocity it will get, but also the mass matters. In Egyptian terms, kicking a cat is easier than moving a pyramid :)
     
  4. Jun 5, 2010 #3
    Re: momentum

    Momentum as far as I've read is best defined as the property of a body of mass M to move at a speed V given a certain impetus P. So the momentum stored in a body gives it the ability to move at a certain velocity. Kinetic Energy can be defined as the rate of translation of momentum or the measure of the amount of "activity" in a body due to its motion.
     
  5. Jun 6, 2010 #4
    Re: momentum

    Momentum is related to the integral of a force over a time integral dt:

    ∫F dt = mv

    Total energy is related to the integral of a force over a displacement dx:

    ∫F dx = ½mv2

    Bob S
     
  6. Jun 13, 2010 #5
    Re: momentum

    i could not understand your last sentence if i have commit any mistake theni am sorry for that.
     
  7. Jun 13, 2010 #6
    Re: momentum

    What is possible is to derive conservation of momentum using only conservation of energy without invoking forces. Suppose we have in one frame of reference:

    1/2 m1 v1^2 + 1/2 m2 v2^2 = 1/2 m1 v1'^2 + 1/2 m2 v2'^2

    Here the velocities are vectors, square means inner product of the vector with itself. In another frame of reference moving with velocity U the conservation of energy equation reads:

    1/2 m1 (v1-U)^2 + 1/2 m2 (v2-U)^2 =

    1/2 m1 (v1'-U)^2 + 1/2 m2 (v2'-U)^2

    f you expand out the squares, use conservaton of energy in the original frame and conservation of mass, you are left with the double inner product terms. Then noting that U is arbitrary, you are led to the conclusion that momentum is conserved.
     
  8. Jun 13, 2010 #7
    Re: momentum

    You do not necessarily have to expend energy to bring a travelling body to a complete halt.

    Nevertheless you have to apply effort to do this.

    Momentum can be thought of as a measure the the amount of 'effort' required.
     
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