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Suspension cable statics calculus problem

by Femme_physics
Tags: cable, calculus, statics, suspension
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Femme_physics
#1
Mar31-12, 12:37 AM
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1. The problem statement, all variables and given/known data




2. Relevant equations



3. The attempt at a solution

I find myself with 2 unknowns, 1 equation.

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#2
Mar31-12, 08:45 AM
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You're on the right track. :)

You have 1 equation for point A.
Can you make another equation for point B?
Femme_physics
#3
Mar31-12, 03:51 PM
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You're on the right track. :)
I like you saying this lately :)

You have 1 equation for point A.
Can you make another equation for point B?
Oohhh....

Am I still on the right track?


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#4
Mar31-12, 05:04 PM
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Suspension cable statics calculus problem

Quote Quote by Femme_physics View Post
I like you saying this lately :)


Oohhh....

Am I still on the right track?

I'm afraid that in the 2nd line you lost ##F_H##.

And btw, you're using 15000 [lb] for ##w_0##, but ##w_0## is given to be 600 [lb/ft].
Femme_physics
#5
Apr2-12, 02:34 AM
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Quote Quote by I like Serena View Post

I'm afraid that in the 2nd line you lost ##F_H##.
You mean purely because of math?

And btw, you're using 15000 [lb] for ##w_0##, but ##w_0## is given to be 600 [lb/ft].
I see what you mean, since I don't know the length in each sectioning I can't use it like that. I'll jus use 600, with the units lb/ft. Yes?
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Apr2-12, 05:38 AM
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Quote Quote by Femme_physics View Post
You mean purely because of math?
Yes.

I see what you mean, since I don't know the length in each sectioning I can't use it like that. I'll jus use 600, with the units lb/ft. Yes?
Yes.
Femme_physics
#7
Apr5-12, 01:09 PM
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I got it. My friend helped me with the math (the one who's registered as "niece of MD") :)






We use X2 since the length can't be more than 25. Therefor we use FH2 as well..

But my big problem is relating the distance, w0 and FH, to A and B.

I end up with this diagram...

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Apr5-12, 03:36 PM
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Quote Quote by Femme_physics View Post
I got it. My friend helped me with the math (the one who's registered as "niece of MD") :)

We use X2 since the length can't be more than 25. Therefor we use FH2 as well.
Aha! So she does still do something every now and then! :)


If you're interested, I have a shorter version:
##20 x^2 = 30 (25 - x)^2##
##2 x^2 = 3 (25 - x)^2##

Since x and (25 - x) are both positive distances, we can take the square root and keep the positive versions:
##x \sqrt 2 = (25 - x) \sqrt 3##
##x \sqrt 2 = 25 \sqrt 3 - x \sqrt 3##
##x (\sqrt 2 + \sqrt 3) = 25 \sqrt 3##
##x = \frac {25 \sqrt 3} {\sqrt 2 + \sqrt 3} \approx 13.76##


But my big problem is relating the distance, w0 and FH, to A and B.

I end up with this diagram...

Looks good.
But consider that the tensional force is not pointing down, but along the rope.

Since they ask for the tension in the rope in A and in B, you need that
##F_V = {dy \over dx} \cdot F_H##
Femme_physics
#9
Apr8-12, 11:36 AM
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I think I got it, but I don't know what to make out of Fv as far as each of the reaction forces at A and B.

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Apr8-12, 02:02 PM
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Quote Quote by Femme_physics View Post
I think I got it, but I don't know what to make out of Fv as far as each of the reaction forces at A and B.

You have the result Fv for point B here.
Good.
Oh, but the unit is lb, and not l/ft.

On support B you have the horizontal force Fh and this vertical force Fv.
So what's the total force?
Femme_physics
#11
Apr9-12, 12:26 PM
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Ahh....

Each has their own force.

So,



Badabing badaboom?
OldEngr63
#12
Apr9-12, 01:14 PM
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Don't you need to add those vectorially? (or did I miss something as I skimmed down through the solution?)

BTW, how did your gripper project turn out?
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#13
Apr9-12, 02:18 PM
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Ya know wee go n bada bing, bada boom n we ah atta thereah....day won't know that OldEngr63 hit um!

(You're not supposed to simply add up forces that are perpendicular to each other. ;)
Femme_physics
#14
Apr10-12, 04:35 AM
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Ohhhhhhh Ok gotcha, now it makes perfect sense :)

I need to find the resultant vector for each! *smacks forehead*

So

(CALCULATION ATTACHED)

Rb = 9086 lb

Ra = 7735 lb

BADABING BADABOOM I said! :)



BTW, how did your gripper project turn out?
Very, very, SLOWwwww... because of the teacher, not us. We're on our passover holiday right now. And I did eventually use a gripper's PDF guide to get ideas, and basically our main idea is a double-threaded spindle. But, right now, we're still awaiting orders and formulas.
Attached Thumbnails
raandrb.jpg  
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#15
Apr10-12, 08:23 AM
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From wikipedia: http://en.wikipedia.org/wiki/Bada_Bing

OldEngr63
#16
Apr10-12, 10:06 AM
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Thank you.
Femme_physics
#17
Apr11-12, 02:40 AM
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No, thank YOU! a lot. :)


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