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Constant power question

  1. May 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Object A of mass m is pushed with a constant force, another object B of the same mass is pushed with a force that does work at constant rate. Velocity of both objects increase from v to 2v and they move a distance of s. Find the ratio of the time taken by objects A and B to move the distance s


    2. Relevant equations



    3. The attempt at a solution
    Firstly, for object A
    s = 1/2(v + 2v)t
    t = 2s/3v

    Object B has constant power, thus
    F1v = F2(2v)
    But I don't know how to find an expression for the time taken by object B in term of v and s
     
  2. jcsd
  3. May 6, 2010 #2
    Use energy considerations.

    First: What is the total change in energy?

    Second: Find the velocity as a function of P and t and integrate this to obtain the position as a function of time.

    Now you can use these to equations to eliminate P.

    Good luck :)

    Edit: For more info on motion with constant power, see https://kb.osu.edu/dspace/bitstream/1811/2458/1/V30N04_218.pdf
     
  4. May 7, 2010 #3
    change in energy = work done = 3/2 mv2
    3/2 mv2 = Pt
    v = (2Pt/3m)1/2
    integrating this term, i get
    s = 1/3 (8Pt3/9m)1/2

    But how do i eliminate m and p?
     
  5. May 9, 2010 #4
    Indeed.

    Try looking at the first equation again. Can't you use that to eliminate the ratio P/m?
     
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