Asked by Anonymous
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.
Answer is provided above. Please show all work on how to get the answer.
Answers
Answered by
Anonymous
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
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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