• Support PF! Buy your school textbooks, materials and every day products Here!

Coplanar force systems

  • Thread starter Robb
  • Start date
  • #1
225
8

Homework Statement


Hibbeler14.ch3.p30.jpg


Determine the maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 350 N

Homework Equations



upload_2016-9-27_8-19-15.png

The Attempt at a Solution



F(x)=0; F(ED)cos30 - F(CD)= 0
F(y)=0; F(ED)sin30 - W

F(ED)= 2W
F(CD)= 1.73205W

F(X)=0; 1.73205W - F(AC)(3/5) - F(CD)cos45 = 0
F(y)=0; F(AC)(4/5) - F(BC)sin45 = 0

F(AC)= F(BC).88388

This is where I start getting confused. With all the substitutions.
 

Answers and Replies

  • #2
F(X)=0; 1.73205W - F(AC)(3/5) - F(CD)cos45 = 0
This is incorrect. Check your FBD and make sure you're writing out your equation with the correct subscripts.
 
  • #3
225
8
From the lower fbd:
F(x)= 0; 1.73205W - F(AC)(3/5) - F(BC)cos45
 
  • #4
From the lower fbd:
F(x)= 0; 1.73205W - F(AC)(3/5) - F(BC)cos45
Alright, so substitute in for F(AC) in this equation. Use this to write F(BC) in terms of W. Afterwards you can then write F(AC) in terms of W. You will then have expressions for all the forces of tension in the ropes in terms of W. Comparing all of these you should be able to determine which rope develops the maximum tension in this system.
 
  • #5
Also, as a quick alternative to going through all the math: Examine each FBD carefully. Assuming static equilibrium of the ring at point D, it can be said that F(DE) must be larger in magnitude than F(CD) since only one component of F(DE) balances the force F(CD). A slightly more careful consideration of how this strategy applies to the FBD of point C should lead you to find which rope is under the maximum tension. As you can see, most of the trouble in this problem is finding that particular rope.
 
  • #6
225
8
So, F(AC) = .88388F(BC)
1.73205W - F(BC).53033 - F(BC).7071 = 0
-1.23743F(BC) + 1.73205W
F(BC) = 1.39971W

F(AC) = 1.23718W

W = 150

The answer is 17.8? Not sure how to get there.
 
  • #7
225
8
Also, as a quick alternative to going through all the math: Examine each FBD carefully. Assuming static equilibrium of the ring at point D, it can be said that F(DE) must be larger in magnitude than F(CD) since only one component of F(DE) balances the force F(CD). A slightly more careful consideration of how this strategy applies to the FBD of point C should lead you to find which rope is under the maximum tension. As you can see, most of the trouble in this problem is finding that particular rope.
I like the insight. Now that you mention it it looks obvious.
 
  • #8
225
8
So, F(AC) = .88388F(BC)
1.73205W - F(BC).53033 - F(BC).7071 = 0
-1.23743F(BC) + 1.73205W
F(BC) = 1.39971W

F(AC) = 1.23718W

W = 150

The answer is 17.8? Not sure how to get there.

See edit to W.
 
  • #9
225
8
Ok. I got it. Sorry. Thanks for your help!
 
  • #10
W = 150
Ok. I got it. Sorry. Thanks for your help!
No problem. Just one last thing.
Not sure if your edit on your post for the value of W worked. Just to clarify it should be 175 N. Although I will assume that you must have gotten that result if you calculated 17.8 kg as the mass.
 

Related Threads for: Coplanar force systems

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
10
Views
818
  • Last Post
Replies
6
Views
12K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
5K
Replies
7
Views
757
Replies
1
Views
1K
Replies
3
Views
8K
Top