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Effect on velocity if force stays constant and mass is changed

  1. May 30, 2009 #1
    (solved) Effect on velocity if force stays constant and mass is changed

    1. The problem statement, all variables and given/known data
    A cannon exerts a constant force on an object. If the mass of the object is doubled, how is the velocity changed


    2. Relevant equations
    Fnet = ma; v = v + at


    3. The attempt at a solution
    i solved for a, so a = Fnet/m
    so v = fnet/m * t

    so the new velocity is v/2?

    but the answer says it is v/square root 2
     
    Last edited: May 30, 2009
  2. jcsd
  3. May 30, 2009 #2

    jgens

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    The best way to think of this problem is probably in terms of energy. We know that the work done on the ball in both instances is going to be W = F*s since the force is constant and the length of the cannon does not change. Now, where does this energy go and can you write an equation for it?

    Edit: Hootenanny beat me to it.
     
  4. May 30, 2009 #3

    Hootenanny

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    Expanding on jgens' post, whilst the question states that the force exerted on the ball remains constant, it make no mention of the time. Therefore, we cannot assume that it remains constant. This is why your method fails.
     
  5. May 30, 2009 #4
    ok thanks. I think got it.

    Work = change in energy => kinetic energy = 1/2mv^2
    v = sq.rt(2w/m)
     
  6. May 30, 2009 #5

    jgens

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    Well, I'm not sure I would do it that way. Since the work done in each instance is the same, you can write your energy equation as follows:

    KE1 = KE2

    Using that equation, solve for your desired velocity.
     
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