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Mechanical energy of frictionless pulley

  1. Mar 16, 2015 #1
    1. The problem statement, all variables and given/known data
    In the system shown, the block M (mass of 15.65 kg) is initially moving to the left with a speed of 3.4 m/s The mass of m is 8.26 kg and the coefficients of friction are μs=0.411 and μk=0.304. The string is massless and the pulley is massless and frictionless. How fast will M be traveling when m has fallen through a height h=2.47 meters?

    diagram: http://is.byu.edu/courses/univ/694820121008/media/8_problem_blockmass.jpg

    2. Relevant equations
    Ef - Ei = Kf - Ki + Uf - Ui = -fkd + ∑ W_otherforces

    K = 1/2mv^2
    U=mgy

    3. The attempt at a solution

    Since M does not have any change in potential energy, but it is acted on by a tension force, I got

    Ef - Ei = 1/2mvf2 - 1/2mvi2 = -fkd + T
    where fkd = μkMgd and T = (( μk+1)Mg)/(1+M/m)

    I solve for vf but keep getting the wrong answer. The answer should be about 4.32 m/s
    What am I doing wrong?
     
  2. jcsd
  3. Mar 16, 2015 #2

    BvU

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    Gold Member

    Hello DNS, welcome to PF :smile: !

    I looks like you are adding an energy (fkd) to a force (T) That can't be !

    It also looks like your change in kinetic energy doesn't depend on M, which is very strange.

    Finally, your energy balance should also have a term Uf - Ui which I miss in your solution attempt.

    If you show your work, step by step, I may be able to answer your question. With the information you provide now it's impossible.

    (And I do get 4.31 m/s if I use g = 9.81 m/s2 )
     
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