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

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1. Nov 2, 2014

### brb

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?

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. Nov 2, 2014

### BvU

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 !