As shown in the figure below, two blocks are connected by a string of negligible

Question

As shown in the figure below, two blocks are connected by a string of negligible mass passing over a pulley of radius 0.360 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 1.50 m/s2. (Let m1 = 13.5 kg, m2 = 20.0 kg, and = 37.0°.) From this information, we wish to find the moment of inertia of the pulley.

(a) What analysis model is appropriate for the blocks?

particle in equilibriumparticle under constant acceleration    particle under constant speedparticle under constant angular accelerationparticle in simple harmonic motion

(b) What analysis model is appropriate for the pulley?

particle in equilibriumparticle under constant acceleration    particle under constant speedparticle under constant angular accelerationparticle in simple harmonic motion

(c) From the analysis model in part (a), find the tension T1.
N

(d) From the analysis model in part (a), find the tension T2.
N

(e) From the analysis model in part (b), find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T1 and T2, the pulley radius r, and the acceleration a.
I =  

(f) Find the numerical value of the moment of inertia of the pulley.
kg · m2

Explanation / Answer

A) particle under constant acceleration

B) particle under constant angular acceleration

C) T1-m1*g*sin(theta) = m1*a

T1 = m1(a+g*sin(theta)) = 13.5*(1.5+9.81*sin(37)) = 99.95 N

D) m2g-T2 = m2*a

T2 = m2(g-a) = 20*(9.81-1.5) = 166.2 N

E) (-T1*r) + T2*r = I*(a/r)

I =[( T2-T1)*r^2]/a

F) I = [(166.2-99.95)*0.36*0.36]/1.5 = 5.724 kg*m^2

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