Rate of revolution for a dryer?

[pcandrepair]

Rate of revolution for a dryer?!?

Homework Statement

In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis as shown in the figure below. So that the clothes will dry uniformly, they are made to tumble. The rate of rotation of the smooth-walled tub is chosen so that a small piece of cloth will lose contact with the tub when the cloth is at an angle of 62.5° above the horizontal. If the radius of the tub is 0.385 m, what rate of revolution is needed? (revs/min)



2. The attempt at a solution

First I found the velocity of the dryer tub:

Cos(62.5) = (v^2)/gR
Cos(62.5) = (v^2)/9.8(.385)
v = 1.32m/s

Then I used that velocity to find the rate of revolution:

(v/2(pi)(.385)) * 60sec = 32.74 Revolutions/min

I submitted this answer and it said it was wrong. I can't seem to see what I did wrong. Any help or suggestions would be appreciated. Thanks.

 

[Doc Al]

Cos(62.5) = (v^2)/gR

Where does the Cos(62.5) come from?

 

[pcandrepair]

mgCos(62.5) = m(v^2)/R
mgCos(angle) is the horizontal component of mg

The masses would cancel and divide g by both sides to get:

Cos(62.5) = (v^2)/gR

 

[Doc Al]

Since mg acts downward, it has no horizontal component. Find the component of the weight in the radial direction--that's where the centripetal acceleration points.

 

[pcandrepair]

Cos(62.5) = (v^2)/gR
That was the equation that our professor lead us up to in class to find velocity. Wouldn't the component of the weight in the radial direction just equal mgCos(62.5)?

 

[Doc Al]

I believe your professor made an error. 62.5 degrees is the angle between the radial and the horizontal, not between the radial and the weight.

 

[pcandrepair]

so to find the velocity i would take the square root of g*R?

v = sqrt(9.8*.385)
v = 1.9424 m/s

then,
(v/(2pi*R)) * 60 = revs/min

(1.9424/(2pi*.385))*60 = 48.178 revs/min

 

[Doc Al]

so to find the velocity i would take the square root of g*R?

No. Follow my advice in post #4.

 

[pcandrepair]

sin(angle) = v^2 / gR ?

 

[Doc Al]

sin(angle) = v^2 / gR ?

Yes.

 

[pcandrepair]

Ok. The answer was correct. Thanks Doc Al!

 

[Doc Al]

Good! (Mark this problem "solved".)

 

[pcandrepair]

There is no option in my "thread tools" to mark problems as solved. That's where the option should be right...?

 

[Doc Al]

There is no option in my "thread tools" to mark problems as solved. That's where the option should be right...?

Yes, that's where it should be. You are not the first to state that can't find that option. (Question: Was this thread moved from another forum into this one? That might explain it.)