Physics: Find the mass of the pulley?

Question

By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows, with m1 = 10.3 kg and m2 = 43.4 kg. The pulley can be treated as a uniform, solid, cylindrical disk. The downward acceleration of the 43.4 kg block is observed to be exactly one-half the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.
______kg

http://www.webassign.net/CJ/p9-42alt.gif

Answer 1

For a massless pulley

F=(m2-m1)g=(m1+m2)a

The tension on the rope must be t=m1g

With a pulley of mass m3 we have to be a bit more careful

Force F3 equal to torque T applied divided by radius R
F3=T/R
T=IA where
I - moment of inertia
A - angular acceleration

A=a/R so if there is no slip acceleration of the system = a

T=Ia/R
F3= Ia/R^2 I=(1/2)mR^2
F3= (1/2) m3R^2 a /R^2=m3a/2

Now
F= W2-W1= F1+F2+F3
F= (m2-m1)g = m1a + m2a +m3a/2

m3= 2[(m2-m1)g -(m1+ m2)a ]/a
since a=1/2g

m3= 4[(m2-m1)g -(m1+ m2)g/2 ]/g
m3= 4[m2- m1-m1/2 - m2/2]
m3=2[m2 - 3m1 ]
m3=2[43.4 - 3 x 10.3]=25 kg

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