Finding belt tension ratio with friction coefficient 0.4 and angle 7π/6

[bnosam]

Homework Statement

http://oi59.tinypic.com/2lacy0o.jpg

Homework Equations

P = ?
T2/T1 = e^(u)(θ)
M = 150 N*m

The Attempt at a Solution

[/B]
T2/T1 = e(.4)(7π/6)

T2/T1 = 5.466

I don't even think I'm on the right track.

 

[Chestermiller]

You're on the right track.

Chet

 

[bnosam]

You're on the right track.

Chet

Nice avatar lol.

I'm not quite sure where to go from here.

 

[Chestermiller]

Nice avatar lol.

I'm not quite sure where to go from here.

Thanks. The avatar is a Mentors' April Fools joke. Hopefully, tomorrow it changes back.

Call T1 = T, and you know T2 in terms of T. So you can now do a moment balance on the flywheel to find T. Then you can do a moment balance of the lever arm to get P.

Chet

 

[bnosam]

T = T2/(5.466)

So if I get what you mean moment about O:

75 * T1 + 450 * P = 150

 

[Chestermiller]

T = T2/(5.466)

So if I get what you mean moment about O:

75 * T1 + 450 * P = 150

No. Please first show how you get T.

 

[bnosam]

T1 = T

T2/T = 5.466
T = T2/5.466
I'm lost after this.

 

[Chestermiller]

$$(T_2-T_1)0.15=150$$

Chet

 

[bnosam]

Where did .15 come from?

 

[Chestermiller]

Where did .15 come from?

The radius of the wheel. We're taking moments around the axis.

Chet

 

[bnosam]

I'm not sure why it's the axis and not O. Is it because we're trying to stop the rotation?

 

[Chestermiller]

I'm not sure why it's the axis and not O. Is it because we're trying to stop the rotation?

We're going to use both. First this.

 

[bnosam]

(T2 - T2/5.466)*.15 = 150
T2 = 1223.914 N

If I'm understanding correctly.

 

[Chestermiller]

Yes. Now, what is T1?

After that, you can do a moment balance around O to get the value of P. Don't forget to include both T1 and T2, and don't forget to use the correct moment arm on T1.

Chet