Find Largest Safe Mass for 3D Force Equilibrium

[Melawrghk]

Homework Statement

Each of the three cables can safely carry a maximum tension force of 7.2kN. Based on this criterion, what is the largest safe mass of the suspended ceiling?

Homework Equations

Sum of forces=0
Sum of moments=0

The Attempt at a Solution

I drew this for the FBD:

I then tried to solve this by just summing all forces in the y-direction to get 'mg':
7.2kN*3-mg=0
m=2201.83kg, which isn't right.

So then I tried doing it by finding the moment about some arbitrary point (O):
$$\sum$$M₀=-14*7.2i+5*7.2k+12*7.2k-7.2*7i-4Wk+8Wi=0
From which:
-14(7.2)-7.2(7)+8W=0 W=18.9kN
and from 5*7.2+12*7.2+4W=0 W=30.6

So those don't even give me the same value... What am I doing wrong? Wrong assumption about all tensions being 7.2kN?

 

[tiny-tim]

Hi Melawrghk!

Each of the three cables can safely carry a maximum tension force of 7.2kN. Based on this criterion, what is the largest safe mass of the suspended ceiling?
...
What am I doing wrong? Wrong assumption about all tensions being 7.2kN?

Yup!

The tensions will be different … the suspended ceiling will stay safe only if the greatest tension is ≤ 7.2kN

 

[Oblivion77]

I am also doing this same question, and I tried to method you did as well. So instead of assuming the tensions in the cable are 7.2. Is it best do to the sum of the forces in
y= 3T-mg then take the moment at some point?

 

[Melawrghk]

Well, actually I figured it out. You've got to determine which cable has the greatest tension (I picked a random value of mg and calculated all tensions), which happens to be A. Then you express A in terms of W and that's how you figure out the mg, thus m.

This is the approach for hidious question 10 as well.

 

[Oblivion77]

Well, actually I figured it out. You've got to determine which cable has the greatest tension (I picked a random value of mg and calculated all tensions), which happens to be A. Then you express A in terms of W and that's how you figure out the mg, thus m.

This is the approach for hidious question 10 as well.

Hmm, interesting method. I was hoping to solve this problem using the "standard method". Did you use the sum of the forces in y to figure that out or moments?

 

[Melawrghk]

Moments. The standard method doesn't always work though.. Gotta use your imagination :P

 

[Oblivion77]

Moments. The standard method doesn't always work though.. Gotta use your imagination :P

Ah, I have a textbook that has the same problem in it. It is under the section of "3D Equilibrium" so I assumed the "standard method" taught in that section would work.

 

[Melawrghk]

You have the same book as I do, however that problem in the book doesn't have answers, which makes it challenging to make sure you're doing right. Thus I'm checking it with my homework. And this is the approach that worked.

By the way, are you in ENGG 205?

 

[Oblivion77]

You have the same book as I do, however that problem in the book doesn't have answers, which makes it challenging to make sure you're doing right. Thus I'm checking it with my homework. And this is the approach that worked.

By the way, are you in ENGG 205?

Yep ENGG 205. Damn odd numbered problems.

 

[Melawrghk]

Hahaha I know. I always forget about them not having solutions and do them and get all disappointed after. And then some problems on the midterms are similar to those odd-numbered ones. Ugggh. 205 is eviiil.

 

[Oblivion77]

Hahaha I know. I always forget about them not having solutions and do them and get all disappointed after. And then some problems on the midterms are similar to those odd-numbered ones. Ugggh. 205 is eviiil.

How much of the assignment have you done? Did you get number 9? Did you use method of sections or joints?

 

[Melawrghk]

I got it all done. I used joints, because when I did the question, the prof still hadn't taught us method of sections. Using the latter would probably save you a LOT of time though.