Question

A 2.28 kg bucket is attached to a disk-shaped pulley of radius 0.104 m and mass 0.712 kg.

If the bucket is allowed to fall, calculate the tension in the rope.

Answer 1

M = 2.28kg
r = 0.104m
m = 0.712kg
T = ?

Torque = -Tr
Tension = - Iα / r = -1/2M(ay)

Fy: T - mg = may
T = may + mg
(m + M / 2)ay = -mg
ay = - g / (1 + m / 2M)
ay = -9.8 / [(1 + 0.712 / (2 * 2.28)]
ay = -8.48m/s²

T = M(g - a)
T = 2.28kg(9.8m/s² - 8.48m/s²)
T = 3.01N <-- Answer