I have two problems, they are labeled in the attached picture.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: (2) Pulley Problems (Acceleration)

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