Acceleration of a block on a massive pulley

[EchoTheCat]

Homework Statement

A block of mass MB = 0.7 kg hangs from a string wrapped around a hoop that can rotate around its center. The hoop has a mass of MH = 1.3 kg and a radius of R = 0.4 m. The block descends under the influence of gravity. What is the magnitude of the acceleration of the mass in m/s2?

Homework Equations

a = -g(m1-m2)/(m1+m2+.5mp)
where, m1 and m1 = masses of the blocks and mp = mass of the pulley

The Attempt at a Solution

a = -9.8*(0.7)/(.7+.5*1.3) = -5.081 m/s/s

 

[jbriggs444]

Homework Statement

A block of mass MB = 0.7 kg hangs from a string wrapped around a hoop that can rotate around its center. The hoop has a mass of MH = 1.3 kg and a radius of R = 0.4 m. The block descends under the influence of gravity. What is the magnitude of the acceleration of the mass in m/s2?

Homework Equations

a = -g(m1-m2)/(m1+m2+.5mp)
where, m1 and m1 = masses of the blocks and mp = mass of the pulley

The equation you quote appears to assume a pulley which is a solid disk or cylinder with two masses hanging, one from either side. That's not the problem at hand. This pulley is hollow. There is a mass hanging from only one side.