Solving a Physics Problem: Large Weight Over a Building

[brb]

Homework Statement

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.

Homework Equations

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

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

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?

 

[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 !