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Momentum p=mv

  1. Nov 3, 2005 #1
    Hello I'm stuck on two momentum concept problems and can't figure them out, I was hoping someone could provide help.


    1.A small truck and a large truck have the same kinetic energies, which truck has the greater momentum? Justify your answer.

    Well i know Ek=.5mv^2 and that momentum p=mv Ive tried rearranging these into eachother and can't find a clear answer. I think it is the large truck but at the same time the small one will have a greater velocity so I dont know what one will have more momentum.


    2. Can an object have kinetic energy but not momentum? Can an object have momentum but no kinetic energy? explain.

    I said no to both because if you have kinetic energy you have a velocity, and if you have momentum then you have a veolocity therefore kinetic energy. I want to make sure I'm right here though.
     
  2. jcsd
  3. Nov 3, 2005 #2

    Fermat

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    For 1), if they have the same KE then what is the ratio of their velocities ?
    Use that ratio to compare their momenta.

    Part 2) is correct.
     
  4. Nov 3, 2005 #3

    Galileo

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    1. Strictly speaking, size isn't the relevant quantity but mass is. It's ofcourse meant that the larger truck has a greater mass.
    Since you know [itex]E=\frac{1}{2}mv^2[/itex] and [itex]p=mv[/itex] the idea is to write the energy in terms of the momentum and mass, since those are the quantities that are 'given'. Write the kinetic energy by eliminating the velocity v in favor of the momentum p. Now what does it tell you?

    2. That's correct.
     
  5. Nov 3, 2005 #4
    Ok Im trying to figure out what you mean by writing the equations in terms of m and v. After playing around with the algebra for a while i got that P1=(P2V2)/V1 But i cant figure out what use this is. (2 is the larger truck 1 is the smaller one, I assume when it says smaller it references mass). I know since the kinetic energies are the same that V1 must be greater then V2. but in this equation i have 3 unknows so I dont know where to go.

    Another thing I tried is E=.5PV so P=2E/V. I THINK this is what im supposed to find. So this means that the smaller truck will have less momentum since it has a greater velocity. Am i correct?
     
    Last edited: Nov 3, 2005
  6. Nov 3, 2005 #5

    Fermat

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    You have a big truck and a small truck. So m2 > m1, say.

    KE1 = KE2
    ========
    (1/2)m1.v1² = (1/2)m2.v2²
    m2/m1 = (v1/v2)²
    =============

    Momentum
    ========
    P1 = m1.v1
    P2 = m2.v2

    P1/P2 = ????

    Can you finish it off now ?
     
  7. Nov 3, 2005 #6
    k... So my other one was wrong then. I did this and got (p1/p2)=v2/v1 and since v2 will be less then v1 this means that p2 is larger right? Bah im getting so confused by such a small question, I did fine with all the ones with actual data but this one is confusing me.
     
  8. Nov 4, 2005 #7

    Galileo

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    I said writing the kinetic energy in terms of the momentum p by eliminating v. You 'll get [itex]\frac{1}{2}mv^2=p^2/2m[/itex].
    Let's call the mass of the small truck m and the mass of the big truck M. Since you know the energies are equal, you know that:
    [tex]\frac{p_s^2}{2m}=\frac{p_l^2}{2M}[/tex]
    the subscript s and l stand for small and large respectively. Now what does it tell you?
     
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