How Do I Solve a Translational Equilibrium Problem in Aerospace Engineering?

[rc flyer uk]

I started my aerospace enginnering degree this year but have missed the first 7 weeks of lectures due to being in hospital, i was sent all lecture notes but am strugling with my mech module. I have my first assignment questions due in this week and am having dificulty thought you guys might be able to give me some guidance! Thanks

Question?

Two cables AC and BC are tied together and loaded at C as shown. The maximum allowable tension in each cable is 800N.

Find the magnitude of the largest force P Which could be applied at C.

Also find the corresponding value of the angle α

I have attached a word document of the diagram!

My workings so far have been something like this:

I have drawn a free body diagram to help make things more simple!

I have resolved the forces and renamed bc to T1 and ac T2

Apply the equilibrium conditions-

ΣFx=0= T1cos50- T2cos35 (+Pα) unsure if (+Pcosα) is nessacery as i have never completed an angular question like this!

ΣFy=0= T1sin50 + T2sin35 - Psinα

Next i am gusing as i am teaching myself from a book! i use these to equations as simultaneous equations and solve them. I was wondering if i should use the value of 800N for T1 and T2 as this is there max allowable tension but i am not sure!

Please can some one point me in the right direction, thanks a lot your help is much apreciated.

Rob

 

[berkeman]

I don't know what "Attachment Pending Approval" means, but I'm not able to open your attachment. Hopefully it will get approved before your HW is due...

 

[FredGarvin]

You are on the right track. You will have two equations and two unknowns, P and $$\alpha$$. Here is a hint: When you have your two equations, you will be able to rearrange the terms to get $$tan \alpha =$$...

Make sure you are consistent with which is the +x and +y directions in your equations. It looks like you have set up to the right being +x and up as being +y. If you stick with that through the whole problem you'll be fine.

 

[Astronuc]

Just adding to what Fred mentioned

ΣFx = 0 = T1 cos50 - T2 cos35+Pcos α by the convention that forces to the right are + and forces to the left are - (convention in Cartesian coordinates).

ΣFy = 0 = T1sin50 + T2sin35 - Psinα is correct.

 

[rc flyer uk]

Thanks a lot guys managed to complete the question and got it handed in on time!
Much apreciated!

Rob