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stopyoukid
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I have two problems, they are labeled in the attached picture.
http://img99.imageshack.us/my.php?image=questions9tw.jpg
Here is the first question: A rope is fastened to the ceiling and passes under a wheel and then back up again. If the mass of the wheel is 2 kg, its moment of inertia is .04 kg m^2 and the radius of the wheel is .3m, find the upward acceleration if a force of 50N is applied to the rope. (ANS 33 m/sec^2)
Here is what I have.
Since the pulley is supported by the ceiling, this means that half of the weight is supported by the upward force. So I subtract half of the weight from the total force
F = 50 N - .5(2)(9.8) = 40.2 N
I then figure out the torque caused by the moment of inertia and the rotational acceleration.
Torque = I alpha
a = F / m, a = 40.2 / 2, a = 20.1
alpha = a / r, alpha = 20.1 / .3m, alpha = 67
Torque(wheel) = .04 * 67 = 2.68
T = rF
Torque (caused by force) = .3 * 40.2 = 12.06
Torque (net) = 12.06 - 2.68 = 9.38
9.38 = .3 F, F = 31.27,
F = ma, a = 31.27 / 2 = 15.63
Obviously Incorrect
Here is the second question:
Find the rotational acceleration of the pulley. (ANS 88.35 rad / sec^2)
So I start by figuring out the moment of inertia of the pulley, since this is a combination pulley, the moment of inertia is the sum of the individual pulleys.
SO,
(Inertia of a disk, I = 1/2MR^2)
I = 1/2(1)(.02m)^2 + 1/2(4)(.06)^2 = .0002 + .0072 = .0074
T1 =3 * 9.8 * .02 = .588
T2 = 5 * 9.8 * .06 = 2.94
T(net) = 2.94 - .588 = 2.352
2.352 = .0074 (alpha)
alpha = 317.83
Which isn't correct either.
Thanks,
Any help would be appreciated.
http://img99.imageshack.us/my.php?image=questions9tw.jpg
Here is the first question: A rope is fastened to the ceiling and passes under a wheel and then back up again. If the mass of the wheel is 2 kg, its moment of inertia is .04 kg m^2 and the radius of the wheel is .3m, find the upward acceleration if a force of 50N is applied to the rope. (ANS 33 m/sec^2)
Here is what I have.
Since the pulley is supported by the ceiling, this means that half of the weight is supported by the upward force. So I subtract half of the weight from the total force
F = 50 N - .5(2)(9.8) = 40.2 N
I then figure out the torque caused by the moment of inertia and the rotational acceleration.
Torque = I alpha
a = F / m, a = 40.2 / 2, a = 20.1
alpha = a / r, alpha = 20.1 / .3m, alpha = 67
Torque(wheel) = .04 * 67 = 2.68
T = rF
Torque (caused by force) = .3 * 40.2 = 12.06
Torque (net) = 12.06 - 2.68 = 9.38
9.38 = .3 F, F = 31.27,
F = ma, a = 31.27 / 2 = 15.63
Obviously Incorrect
Here is the second question:
Find the rotational acceleration of the pulley. (ANS 88.35 rad / sec^2)
So I start by figuring out the moment of inertia of the pulley, since this is a combination pulley, the moment of inertia is the sum of the individual pulleys.
SO,
(Inertia of a disk, I = 1/2MR^2)
I = 1/2(1)(.02m)^2 + 1/2(4)(.06)^2 = .0002 + .0072 = .0074
T1 =3 * 9.8 * .02 = .588
T2 = 5 * 9.8 * .06 = 2.94
T(net) = 2.94 - .588 = 2.352
2.352 = .0074 (alpha)
alpha = 317.83
Which isn't correct either.
Thanks,
Any help would be appreciated.