8. The figure below shows two masses connected by a cord passing over a massive

Question

8. The figure below shows two masses connected by a cord passing over a massive pulley of radius R0. Mass MA slides on a frictionless surface, and MB hangs freely. Both block move with acceleration a. The acceleration due to gravity is g. (a) Determine the tension TA in the part of the string connected to mass MA, and the tension TB in the part of the string connected to mass MB. Express your answers in terms of the given quantities. (b) Find tau net, the magnitude of the net torque acting on the pulley. Then find I, the pulleys moment of inertia. Express your answers in terms of the given quantities.

Explanation / Answer

Part A)

From the sum of forces on MA

TA = MAa

From the sum of forces on MB

TB = MBg - MBa = MB(g-a)

Part B)

Torque is from the difference in the tensions...

Torque = Fr = (TB - TA)Ro

That is torque = (MBg - MBa - MAa)Ro

Also torque = I(alpha) and alpha = a/r

Ia/Ro = (MBg - MBa - MAa)Ro

I = [(MBg - MBa - MAa)Ro2]/a

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