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Toy Cannon

  1. Nov 4, 2006 #1
    A toy cannon uses a spring to project a 5.30g soft rubber ball. Spring is compressed 5.00 cm, k=8.00 N/m. Barrel is horizontal.

    The ball moves 15.0 cm through the barrel, with friction force of 0.0320 N between thebarrel and the ball. With what speed does the projectile leave the barrel of the cannon?

    I thought this problem was simple, but the answer 'in the back' is different from what I am getting, so I thought I would ask for some help.

    I use

    mv^2/2 = kx^2/2 - fk(x+d)

    x = compression of spring, d = distance along the barrel, so

    m = 5.32 * 10^-3 m,
    k = 8 N/m
    x = 0.05 m
    k = 8 N/m
    fk = 0.032 N
    d = 0.15 m

    With these figures, I get v = 1.17 m/s.

    The answer in the back is 1.40 m/s.

    Can anyone see where I am going wrong?

    Dorothy
     
  2. jcsd
  3. Nov 4, 2006 #2
    Are you sure you are supposed to use ... - fk(x+d)?
    if you use mv^2/2 = kx^2/2 - fk(x) instead, it will give a v of 1.40 m/s
    I think the problem was trying to help you-it gave you the TOTAL distance the projectile has to travel in the barrel. I tried to make a diagram below, I'm not sure it worked.

    Oh, and you meant m=5.30 x 10-3 kg right?

    /\/\/ is the compressed spring
    X is the projectile


    ......|-0.15m-|
    -------------
    /\/\-X---->
    -------------
     
    Last edited: Nov 4, 2006
  4. Nov 4, 2006 #3
    That makes sense. Thanks. Yes, I used 5.30E-3.

    Thanks again,
    Dorothy
     
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