Catwalk attached to a wall by a hinged held up by a cord

[XxseanxX_22@h]

Homework Statement

A folding catwalk of uniform density and length 3r is attached to a wall by a hinge. At the other end it is supported by a cable which makes an angle of θ above the horizontal. If a person of mass m stands a distance r from the wall what is the tension, T, in the support cable? The gravitational field is a constant g and the mass of the catwalk itself is 2m.

The Attempt at a Solution

i got (3mg/sintheta) but i don't think this is correct

 

[tiny-tim]

Welcome to PF!

Hi XxseanxX_22@h! Welcome to PF!

A folding catwalk of uniform density and length 3r is attached to a wall by a hinge. At the other end it is supported by a cable which makes an angle of θ above the horizontal. If a person of mass m stands a distance r from the wall what is the tension, T, in the support cable? The gravitational field is a constant g and the mass of the catwalk itself is 2m.
…
i got (3mg/sintheta) but i don't think this is correct

hmm … you took vertical components, but you left out the force at the hinge.

Hint: when you've an unknown force like the reaction at the hinge, take moments about some point.

 

[XxseanxX_22@h]

thanks i figured it out

 

[Shambles]

I thought that the net moment at a hinge was 0 as the distance from rotation is 0. Is this wrong?

 

[tiny-tim]

I thought that the net moment at a hinge was 0 as the distance from rotation is 0. Is this wrong?

Hi Shambles!

No, you're absolutely right …

and that's why we take moments about the hinge …

the force there is unknown, and the question doesn't ask for it …

if we took moments about anywhere else, the force at the hinge would come in, and we'd have to use another equation to eliminate it …

by taking moments about the hinge, we reduce the number of equations we need by one!

 

[SeannyBoi71]

I know this post is very old, but I have the identical question on my physics assignment. I found out that the forces in the situation equal 3mg=Ty (Ty being the y-component of the tension in the wire) and for the net moment I have sintheta=4mg/3. Are these right, and if so how can I combine them to find T?

 

[tiny-tim]

Hi SeannyBoi71!

(have a theta: θ )

… for the net moment I have sintheta=4mg/3

hmm … that's almost right …

show us how you got that, so we can see what went wrong

 

[SeannyBoi71]

I have moment is N=rF. so moment acting clockwise as 2mg3/2r+mgr, and the opposite 3rsinθ. so simplifying, 4mg=3sinθ, and then 4mg/3=sinθ.
I used 3/2r because the weight of the beam has a uniform density and so the moment acts right in the middle of the beam, did I do that right?

 

[tiny-tim]

I have moment is N=rF. so moment acting clockwise as 2mg3/2r+mgr, and the opposite 3rsinθ. so simplifying, 4mg=3sinθ, and then 4mg/3=sinθ.
I used 3/2r because the weight of the beam has a uniform density and so the moment acts right in the middle of the beam, did I do that right?

Yes, I thought you'd done that, and I hoped you'd see what you'd left out once you typed it out …

where's the tension?? ​

 

[SeannyBoi71]

I found T= T_y/sinθ, but I don't know how to incorporate that with the rest of the information I found!

 

[tiny-tim]

Hi SeannyBoi71!

(just got up :zzz: …)

I found T= T_y/sinθ, but I don't know how to incorporate that with the rest of the information I found!

ok, when you take https://www.physicsforums.com/library.php?do=view_item&itemid=64" , as you know, every moment has to be a force times a distance, so make sure that that's what your equation has!

in this case, you multiplied your 3r/2 and r by the appropriate force (the weights), but you didn't multiply your 3rsinθ by its force, which is T …

that should give you the equation for T that you're looking for! ​

(btw, you'll never need T_y, or any other component, for moments … for moments, you always use the whole force)

 

[SeannyBoi71]

in this case, you multiplied your 3r/2 and r by the appropriate force (the weights), but you didn't multiply your 3rsinθ by its force, which is T …

that should give you the equation for T that you're looking for! ​

(btw, you'll never need T_y, or any other component, for moments … for moments, you always use the whole force)

Ok, but if I'm always using the whole force, why would I even need sinθ? Isn't that one of the component parts of the Tension that is at an angle??

As you can see I get very confused with moments and equilibrium and stuff.. it's very hard for me to grasp the concept! But thank you very much for your help so far!

 

[tiny-tim]

Ok, but if I'm always using the whole force, why would I even need sinθ? Isn't that one of the component parts of the Tension that is at an angle??

ah, now I see what you're doing!

let's go back to your …

I found out that the forces in the situation equal 3mg=Ty (Ty being the y-component of the tension in the wire) and for the net moment I have sintheta=4mg/3. Are these right, and if so how can I combine them to find T?

I found T= T_y/sinθ, but I don't know how to incorporate that with the rest of the information I found!

… you thought you could find T by finding T_y first.

Unfortunately, that doesn't help in this case because
i] you don't have any equation for T_x, to finish the job!
ii] your 3mg = T_y was wrong anyway, because you left out the y-component of the https://www.physicsforums.com/library.php?do=view_item&itemid=73" at the hinge

Instead, your only useful equation will be the moments equation (about the hinge), which you did use in your next post …

I have moment is N=rF. so moment acting clockwise as 2mg3/2r+mgr, and the opposite 3rsinθ. so simplifying, 4mg=3sinθ, and then 4mg/3=sinθ.

… and for some reason you got the correct distance 3rsinθ, but you didn't mutliply it by the force, T: that would have given you the equation 4mg=3Tsinθ.

The sinθ doesn't come from "T_y = Tsinθ", it comes from the distance 3rsinθ (which you yourself got ), so you must multiply it by the whole of T.

(You can split T into T_x and T_y, and then use a distance of 3r instead of 3rsinθ, but that isn't the way you actually did it, and although it works I don't recommend it since I think it's a bit confusing and might lead to mistakes.)

ok, sorry if that's a bit confusing : write it all out and see if you get the correct answer, and if you're still worried about anything, come back and ask

 

[SeannyBoi71]

Thank you so much! I finally got the answer. It definitely makes sense now. Thanks again :)