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Pulley Mass System, unknown mass(1/2M and M) and acceleration, known coefficent of friction

  1. Nov 2, 2014 #1

    brb

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    1. The problem statement, all variables and given/known data
    A large weight hangs over the side of a building from a cable. The cable goes over a pulley to a horizontal roof and is attached to a small weight of half the mass. The coefficient of sliding friction between roof and the small weight is 0.5. What is the approximate acceleration of the mass?

    Answer: 5

    Not sure how they got this answer.

    2. Relevant equations
    T - (1/2M)g(friction coefficient) = (1/2M)a
    Mg - T = Ma

    (g(M-(1/2M)(friction coefficient)))/(M + (1/2)M) = a


    3. The attempt at a solution
    T - (1/2M)g(friction coefficient) = (1/2M)a
    Mg - T = Ma

    Adding the equations to remove tension gives us the equation of (g(M-(1/2M)(friction coefficient)))/(M + (1/2)M) = a or (9.8(M-(1/2M)(.5)))/(M + (1/2)M)

    Where i'm stuck is we still don't know M so how will we get acceleration? What is the other equation in the systems of equation to solve this?
     
  2. jcsd
  3. Nov 2, 2014 #2

    BvU

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    Gold Member

    Hello brb, welcome to PF :)

    No reason for despair: you have two equations with three unknowns (M, a and T). Eliminate T (add the equations) and discover that M can be divided out !
     
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