A green drum with a moment of inertia of 10.55kgm2and radius 0.77m rotates freel

Question

A green drum with a moment of inertia of 10.55kgm2and radius 0.77m rotates freely about a vertical axis.

A green drum with a moment of inertia of 10.55kgm^2 and radius 0.77m rotates freely about a vertical axis. A rope is wound around it and strung over a red wheel with a moment of inertia of 10.27kgm^2 and radius 0.79m that rotates freely about a horizontal axis. The rope is then attached to a cube dangling below with a mass of 13.57kg. The cube falls 1.76m from rest. Take the acceleration of gravity to be 9.81 m/s^2. Assume that the rope does not slip and has negligible mass. What is its velocity at that point? What is the acceleration? What is the tension in the string right above the cube?

Explanation / Answer

We know

Torque=I*angular accleration

Let tension in rope is T and accleration is a

Angular accleration=a/R=a/0.77=1.3a

For drum

T=I*1.3a=13.7a

For block

mg-T=ma

132.986-13.7a=13.57a

So we got

a=4.9 m/s2

Given distance =1.76m

Using newton equation

We got v=4.2 m/s

T=13.7a=67.13 N

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