A uniform disk with a mass of 170 kg and a radius of 1.1 m rotates initially wit
ID: 1539512 • Letter: A
Question
A uniform disk with a mass of 170 kg and a radius of 1.1 m rotates initially with an angular speed of 900 rev/min. A constant tangential force is applied at a radial distance of 0.8 m.
a. How much work must this force do to stop the wheel? Answer in units of kJ.
b. If the wheel is brought to rest in 2.5 min, what torque does the force produce? Answer in units of N · m.
c. What is the magnitude of the force? Answer in units of N.
d. How many revolutions does the wheel make in these 2.5 min? Answer in units of rev.
Explanation / Answer
Answer A)
intital KE of the disc
KE = .5Iw^2
I for a disk is .5mr^2 = (.5)(170)(1.1)^2 = 102.85 kgm^2
w = 900 rev/ min ===> 94.25 rad/s
KE = (.5)(102.85)(94.25)^2
KE = 456811.4891 J
work is required to stop it
W = 456811.4891 J
Answer B)
Apply torque = I(alpha)
to find alpha, wf = wo + (alpha)t)
0 = 94.25 + (alpha)(2.5)(60)
alpha = - 0.6284 rad/s^2
Torque = (102.85)(0.6284) = 64.63 Nm
Answer C)
Torque = Fr
64.63 = F(0.8)
F = 80.79 N
Answer D)
wf^2 = wo^2 + 2(alpha)(theta)
0 = 94.25^2 + 2(-0.6284)(Theta)
Theta = 7068 rad
Divide that by 2pi for the number of revolutions
7068 / 2*3.14 = 1125.48 revolution
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