Question

As shown in the figure below, two blocks are connected by a string of negligible mass passing over a pulley of radius 0.270 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 1.20 m/s2. (Let m1 = 15.5 kg, m2 = 22.0 kg, and θ = 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 equilibrium

particle under constant acceleration   

particle under constant speed

particle under constant angular acceleration

particle in simple harmonic motion

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

particle in equilibrium

particle under constant acceleration    

particle under constant speed

particle under constant angular acceleration

particle 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

Answer 1

a) Particle under constant acceleration

b) Particle under constant angular acceleration

c) T1 - m1g sinθ = m1*a --->> T1 = m1 * (a + g sinθ) = 110.11 N

d) m2g - T2 = m2*a --->> T2 = m2 * (g-a) = 189.42 N

e) a = 1.2 m/s2 ; r = 0.27 m so, α = a/r = 1.2/.27 = 40/9 rad/s2

(T2 - T1)*r = I α

I = (T2 - T1)*r/α = 4.818 kg.m2