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Finding Work from the Derivative of Power

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data

    A machine delivers power at a decreasing rate P = P(o)*t(o)^2 / (t + t(o))^2 , where P(o) and t(o) are constants. The machine starts at t = 0 and runs forever.

    Find the amount of total work.

    2. Relevant equations

    P = w / t
    W = f * d

    P = P(o)*t(o)^2 / (t + t(o))^2

    3. The attempt at a solution

    I'm not really sure what to do here. My guess is that it is an improper (infinite) integral problem, but I'm just not sure how to really start. I tried to separate P(o) and t(o) from the equation since they are constants, but I couldn't get it work out.

    Can anyone point me in the right direction?
     
  2. jcsd
  3. Oct 6, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    If you integrate power (Watts = Joules/sec) over time you will get Joules, which equates to the energy delivered. i.e., work. So do the integration :wink:
     
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