# Physic

A massless rope is wrapped around a hollow cylinder of radius 23 cm whose central axis is fixed in a horizontal position. A mass of 3.8 kg hangs from the rope and, starting from rest, moves 137 cm in 2.2 s. What is the mass of the cylinder? (Answer: 62kg)

Answer is provided above. Please show all work on how to get the answer.

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1. r = 0.23m
m = 3.8kg
d = 1.37m
t = 2.2s

y = -Vot + 1/2at^2
1.37m = 0 + 1/2a(2.2s)^2
a = 1.37m / 2.42s^2
a = 0.57m/s^2

T = -(3.8kg)(0.57m/s^2) + (3.8kg * 9.8m/s^2)
T = -2.17N + 37.24N
T = 35.07N

Fy: Py - T = m1α
T = Iα
rT = cmr^2α
(0.23m)(35.07N) = m2(0.23m)^2 * (0.57m/s^2 / 0.23m)
8.07Nm = m2(0.1311)
m2 = 61.56 -> 62kg

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