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Work Problem

  1. Oct 10, 2007 #1
    1. The problem statement, all variables and given/known data
    A ballista is essentially a very large bow and arrow, except that it fires 3-m long, 2-kg arrows. The arrows are propelled by the stretched bowstring and bow, which behave as if they are two nonlinear springs that each behave according to the equation
    F = -kx^1.5, where the force constant k = 500 N·m-1.5 and equilibrium length l = 0.5 m. The ballista is cocked, so that the distances x and y are 1.0 m and 1.3 m, respectively. A constant 10-N frictional force opposes all motion of the arrow. The arrow is shot straight upwards.

    How much work was required to attach the bowstring to the bow?

    How much work was required to cock the ballista?

    2. Relevant equations
    dW = F dx

    3. The attempt at a solution
    I just used the equation above, set F to -kx^1.5 and integrated from x=0 to x=0.5.

    I did the same thing for the second question, except that I integrated from x=0 to x=0.8. I'm not sure what exactly I did wrong...
  2. jcsd
  3. Oct 10, 2007 #2


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    Homework Helper

    Hmmm... do they give a picture? I'm finding it hard to understand the problem exactly. What do the x and y distances mean? "x and y are 1.0 m and 1.3 m"
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