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Is this an ok way to solve this word problem?

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data
    You are in charge of a cannon that exerts a
    force 19000 N on a cannon ball while the ball
    is in the barrel of the cannon. The length of
    the cannon barrel is 1.92 m and the cannon is
    aimed at a 37° angle from the ground.

    The acceleration of gravity is 9.8 m/s^2.

    If you want the ball to leave the cannon
    with speed v0 = 79.3 m/s, what mass cannon
    ball must you use?


    2. Relevant equations

    W=∫C F•dx

    3. The attempt at a solution

    I already have done the problem, the answer is 11.56kg. My question is if the way I solved this problem was ok. i got several points docked for the way I answered it.

    I wanted to make sure I understood the concept well enough to apply it to more complex problems, such as ones where the path taken by an object was not a straight line and the force varied with position, so I made the path taken into a vector valued function r(t) where 0≤t≤1 (t is arbitrary since I'm calculating work right?) and then combined the force of gravity with the force exerted by the cannon into a force field existing along the path taken by the cannonball. I calculated dr from the vector-valued function, and solved the line integral. Of course the whole thing only turned out to be the force dotted into the path taken by the cannonball anyways, but I was just trying to make sure I understood the concept.

    So my question is this: is there something wrong with the way I solved the problem?

    Edit: I meant "work problem" not word problem, my apologies.
     
    Last edited: Oct 8, 2012
  2. jcsd
  3. Oct 8, 2012 #2
    You got the right answer, that is good. Sounds like you made the problem more complicated then it needed to be. Time is money, keep it simple.
     
  4. Oct 8, 2012 #3
    I'm aware of that. Like I said I just wanted to make sure I understood how I could solve more complicated versions of the problem. thanks.
     
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