Asked by Anonymous
How much tangential force must be exerted to stop a rotating solid disk (radius = 1.50 feet) weighing 480 lbs in 12.0 seconds? The disk is initially rotating at 600 RPM.
Answers
Answered by
Damon
aarrgh, English units
torque = F * .75 ft = .75 F foot pounds
mass = 480/32.2 = 14.9 slugs
I = (1/2) m r^2 = .5 (14.9)(.5625)
= 4.19 slug ft^2
kinetic energy = (1/2) I w^2
find w in radians/sec
w = omega = 600 rev/60 s * 2 pi rad/rev = 62.8 rad/s
so
ke = (1/2)(4.19)(62.8)^2 = 8271 slug ft^2/s^2
work done by force = torque * total angle in radians to stop
= .75 F (theta)
theta is average speed in rad/s times time to stop
average speed = 62.8/2 = 31.4 rad/s
so
theta = 31.4 rad/s * 12 s
= 377 radians to stop
so
work to stop = .75 F (377)
= 283 F ft pounds
so
283 F = 8271
F = 29.2 pounds
torque = F * .75 ft = .75 F foot pounds
mass = 480/32.2 = 14.9 slugs
I = (1/2) m r^2 = .5 (14.9)(.5625)
= 4.19 slug ft^2
kinetic energy = (1/2) I w^2
find w in radians/sec
w = omega = 600 rev/60 s * 2 pi rad/rev = 62.8 rad/s
so
ke = (1/2)(4.19)(62.8)^2 = 8271 slug ft^2/s^2
work done by force = torque * total angle in radians to stop
= .75 F (theta)
theta is average speed in rad/s times time to stop
average speed = 62.8/2 = 31.4 rad/s
so
theta = 31.4 rad/s * 12 s
= 377 radians to stop
so
work to stop = .75 F (377)
= 283 F ft pounds
so
283 F = 8271
F = 29.2 pounds
Answered by
Damon
I used radius = .75, should be 1.5
Answered by
Damon
aarrgh, English units
torque = F * 1.5 ft = 1.5 F foot pounds
mass = 480/32.2 = 14.9 slugs
I = (1/2) m r^2 = .5 (14.9)(2.25)
= 16.8 slug ft^2
kinetic energy = (1/2) I w^2
find w in radians/sec
w = omega = 600 rev/60 s * 2 pi rad/rev = 62.8 rad/s
so
ke = (1/2)(16.8)(62.8)^2 = 33,054 slug ft^2/s^2
work done by force = torque * total angle in radians to stop
= 1.5 F (theta)
theta is average speed in rad/s times time to stop
average speed = 62.8/2 = 31.4 rad/s
so
theta = 31.4 rad/s * 12 s
= 377 radians to stop
so
work to stop = 1.5 F (377)
= 566 F ft pounds
so
566 F = 33,054
F = 58.5 pounds
torque = F * 1.5 ft = 1.5 F foot pounds
mass = 480/32.2 = 14.9 slugs
I = (1/2) m r^2 = .5 (14.9)(2.25)
= 16.8 slug ft^2
kinetic energy = (1/2) I w^2
find w in radians/sec
w = omega = 600 rev/60 s * 2 pi rad/rev = 62.8 rad/s
so
ke = (1/2)(16.8)(62.8)^2 = 33,054 slug ft^2/s^2
work done by force = torque * total angle in radians to stop
= 1.5 F (theta)
theta is average speed in rad/s times time to stop
average speed = 62.8/2 = 31.4 rad/s
so
theta = 31.4 rad/s * 12 s
= 377 radians to stop
so
work to stop = 1.5 F (377)
= 566 F ft pounds
so
566 F = 33,054
F = 58.5 pounds
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