Two blocks are connected by a light string passing over a pulley of radius 0.40

Question

Two blocks are connected by a light string passing over a pulley of radius 0.40 m and moment of inertia I. The blocks move (towards the right) with an acceleration of 1.10 m/s2 along their frictionless inclines (see the figure).

(a) Draw free-body diagrams for each of the two blocks and the pulley. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Determine FTA and FTB, the tensions in the two parts of the string.

(c) Find the net torque (magnitude only) acting on the pulley, and determine its moment of inertia, I.

Explanation / Answer

(b)
For the left block:

Fnet1 = (m1)a
or:
FT1 - m1*g*sin(30) = (m1)a

For the right block:

Fnet2 = (m2)a
or:
m2*g*sin(60) - FT2 = (m2)a

So you now have these two equations:

FT1 - m1*g*sin(30) = (m1)a
m2*g*sin(60) - FT2 = (m2)a

You already know the values of m1(=8.0kg); m2(=10.0kg); g(=9.8 meters/s

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