Circular Plate Tension Question

[jedisoccer]

URGENT QUIZ TOMMOROW - Circular Plate Tension Question

Homework Statement

Weight is 600N, and they form 30 degree angles with the vertical

Homework Equations

determine the tension in each wire

The Attempt at a Solution

I realize the two wires on the side are both 100 degrees apart from the DB, so they must be the same tension, I've tried a few methods but really haven't gotten anywhere, not sure what is the right order to start this

 

[jedisoccer]

i also tried splitting it into components along the x and y axes, but it didnt end up helping me get different answers for the tensions

 

[jedisoccer]

can i do this? 600=(T1+T2+T3)cos30
and assume all the tensions are the same?

then 600/3cos30=T
then, T= 230.94 N? or 173.205N?

 

[jedisoccer]

im really hoping someone can reply tonight if possible, I've been working on this but nowhere...any help?

 

[dynamicsolo]

can i do this? 600=(T1+T2+T3)cos30
and assume all the tensions are the same?

That won't necessarily be true: the tension in the middle cord is likely different. You can say that the tensions in the two end cords are equal.

I'd suggest ignoring the x-y axes given and use the equal 50º angles you described. But, you need to consider the forces in three dimensions, since they must balance in the plane of the disc and in the vertical direction. What would the force components in each dimension look like?

Have you dealt with torques yet in your course? I ask because they may turn out to be of concern here...

 

[jedisoccer]

Well the 600n is simply F(DO)=600k, but I am having troubles breaking up the chords into its components

and yes, we've just begun on Moments/torques as well.

the reason i first assumed they were equal is due to the 100 degree spacing from the centre chord, I am just having trouble relating it to the entire circle

 

[learningphysics]

The way I'm seeing for this problem is... 3 equations, 3 unknowns... 1 equation per axis...

suppose the three tensions are T1, T2 and T3. What is the component of T1 along the z-axis? What is the component of T1 along the x-axis? What is the component of T1 along the y-axis?

 

[jedisoccer]

so Tdc along z-axis would be DCcos30, then along y-axis, (CDsin30)(cos120), and x-axis (CDsin30)(sin60) ?
Tdc=CD(0.433i-0.25j+0.866k)?

 

[learningphysics]

The z-components are all T1cos30, T2cos30, T3cos30...

For the T1 component... first divide it into two components... one along the z-axis (T1cos30), and one in the x-y plane... so the magnitude in the xy plane is T1sin30.

Draw in that vector that has the magnitude T1sin30... it lies along that line which is 50 degrees from the x-axis... What is the component of the T1sin30 along the x-axis... along the y-axis? use trig.

 

[learningphysics]

so Tdc along z-axis would be DCcos30, then along y-axis, (CDsin30)(cos120), and x-axis (CDsin30)(sin60) ?

yes, exactly right.

Tdc=CD(0.866i-0.25j+0.433k)?

The numbers aren't right... take i to be for the x-axis, j to be for y-axis, k to be for the z-axis...

 

[jedisoccer]

Tdc=CD(0.433i-0.25j+0.866k)
Tdb=DB(-0.32i-0.383j+0.866k)
Tda=DA(-0.32i+0383j+0.866k)

so are those all correct?

 

[learningphysics]

Tdc=CD(0.433i-0.25j+0.866k)
Tdb=DB(-0.32i-0.383j+0.866k)
Tda=DA(-0.32i+0383j+0.866k)

so are those all correct?

yup. they look right to me.

 

[jedisoccer]

i thought Da and Dc were suppose to be the same so I am confused on how to move on from this stage

 

[learningphysics]

i thought Da and Dc were suppose to be the same so I am confused on how to move on from this stage

why do you say Da and Dc are the same?

Tdc=CD(0.433i-0.25j+0.866k)
Tdb=DB(-0.32i-0.383j+0.866k)
Tda=DA(-0.32i+0383j+0.866k)

Sum of the forces in the x - direction = max = 0

CD(0.433) + DB(-0.32) + DA(-0.32) = 0 (1)

Sum of the forces in the y - direction = may = 0

CD(-0.25) + DB(-0.383) + DA(0.383) = 0 (2)

Sum of the forces in the z - direction = maz = 0

CD(0.866) + DB(0.866) + DA(0.866) - 600 = 0 (3)

solve (1),(2) and (3).

 

[dynamicsolo]

i thought Da and Dc were suppose to be the same so I am confused on how to move on from this stage

You aren't up to calculating the actual force magnitudes yet. (You haven't dealt with the weight of the disc yet.) You are just finding the directions of the vectors AD, BD, and CD, in which case AD and BD will have components symmetrical about the x-axis (and the vectors are pointing toward D, since the x-components of AD and BD are negative).

 

[dynamicsolo]

why do you say Da and Dc are the same?

This is in reference to an early post: the magnitudes of the tensions in cords A and C ought to be equal by symmetry. But their direction vectors in the x-y coordinate frame won't be equal (natch)...

 

[jedisoccer]

im a little rusty at this but i got Db=452.4N and I am pretty sure that isn't right, can you lead me in the right direction solving for 3 variables

 

[learningphysics]

Oh I see. Yes, you're right jedisoccer... sorry about that. the magnitudes of DA and DC are the same by symmetry.

The first two equations:

CD(0.433) + DB(-0.32) + DA(-0.32) = 0 (1)

CD(-0.25) + DB(-0.383) + DA(0.383) = 0 (2)

will also actually give you that CD and DA are equal...

you can simplify the problem by just using the first and third equations, and using the fact that AD = DC:

DA(0.433) + DB(-0.32) + DA(-0.32) = 0 (1)

DA(0.866) + DB(0.866) + DA(0.866) - 600 = 0 (3)

two equations. two unknowns.

 

[learningphysics]

im a little rusty at this but i got Db=452.4N and I am pretty sure that isn't right, can you lead me in the right direction solving for 3 variables

Yeah, i don't think that's right. have a look at my last post... use the two equations with 2 unknowns.

 

[jedisoccer]

took me forever but DB is 103.97N and DA=DC=294.4N

finally! thanks a lot, took 5 hours but i got it

 

[learningphysics]

took me forever but DB is 103.97N and DA=DC=294.4N

finally! thanks a lot, took 5 hours but i got it

No prob. It was a tough problem. Good job!