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Homework Help: Force problem

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    A .8kg cannon ball is shot out of a cannon with force 2000-100,000t. When the ball leaves the cannon, the force is zero. What is the velocity of the ball as it leaves the cannon.

    Although the problem doesn't specify, I assume there is no gravity or any other external forces since there is no angle of the force or cannon given.

    2. Relevant equations
    Unfortunately, I have not learned how to solve equations dealing with varying acceleration, so I don't really know what to do...

    3. The attempt at a solution
    I found that the cannon ball leaves the cannon at t=.02, but I don't know what to do once I have that to find the final velocity...
  2. jcsd
  3. Nov 23, 2009 #2


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    Hi Cherrybawls, welcome to PF!

    The easiest way to do it is to integrate the a(t) function (acceleration as a function of time) in order to get the final velocity:

    [tex] v(0.02) - v(0) = \int_0^{0.02} a(t)\, dt [/tex]​

    If you haven't done any calculus, then the above will probably not mean much to you. However, another method, which is *entirely equivalent* is to compute the area underneath the a vs. t graph, over that time interval. That will give you the change in velocity over that time interval. In this case, I think we can assume that the initial velocity, v(0), is 0, so that the change in velocity is just equal to the final velocity achieved.
  4. Nov 23, 2009 #3
    Well, I am learning calculus now, but we have not yet gotten to integrals so I will go ahead and try the second method you mentioned, thank you so much
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