(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

A 26.3 kg block (m1) is on a horizontal surface, connected to a 7.10 kg block (m2) by a massless string as shown in the figure below. The frictionless pulley has a radius R = 0.060 m and a moment of inertia I=0.090 kgm2. A force F = 220.1 N acts on m1 at an angle theta = 29.5°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

Image attached.

The attempt at a solution

I'm got myself into a bit of circular thinking here.

T2 = m2a = m2(g + a)

a = alpha/r

alpha = τ/I

τ = T1rsinθ

T1 = Fparallel - m1a

I'm looking for the linear acceleration of the system, so I tried

T2 + T1 + m1a = Fpara

m2a + Ia + m1a = Fpara

a(m2 + I + m1a) = Fpara

a = Fpara / (m2 + I + m1)

a = 191.6 / (7.1 + .09 + 26.3)

a = 5.59 m/s

This isn't right. I'm not confident in the entire process - radius should be important and the way I have it, it isn't being taken into account. Problem is, I don't know how to work it in. I really need some guidance. Any help is appreciated!

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# Homework Help: Upward Acceleration of a Hanging Mass Connected to Another By a Pulley

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