A green drum with a moment of inertia of 11.93kgm and radius 0.68m rotates freel

Question

A green drum with a moment of inertia of 11.93kgm and radius 0.68m rotates freely about a vertical axis. A rope is wound around it and strung over a red wheel with a moment of inertia of 14.25kgm2 and radius 0.52m that rotates freely about a horizontal axis. The rope is then attached to a cube dangling below with a mass of 15.18kg. The cube falls 2.21m from rest. Take the acceleration of gravity to be 9.81 Assume that the rope does not slip and has negligible mass. What is its velocity at that point? Tn m. 8 what is the acceleration? 7m 8 what is the tension in the string right above the cube?

Explanation / Answer

Applying energy conservation,

Work done = change in KE

(15.18 x 9.8 x 2.21) = (15.18)(v^2 /2) + (14.25(v/0.52)^2 / 2) + (11.93 (v/0.68)^2 / 2)

v = 2.65 m/s ......Ans

Applying vf^2 - vi^2 = 2 a d

2.65^2 - 0^2 -= 2(a)(2.21)

a = 1.59 m/s^2 ......Ans

m g - T = m a

T = 15.18 (9.81 - 1.59)

T = 124.8 N ......Ans

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