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

Ridid body equilibrium, tension in hanging wires

  • Thread starter clope023
  • Start date
987
123
[SOLVED] ridid body equilibrium, tension in hanging wires

1. Homework Statement

A 60.0cm, uniform, 49.0N shelf is supported horizontally by two vertical wires attached to the sloping ceiling. A very small 25.0N tool is placed on the shelf midway between the points where the wires are attached to it.

YF-11-23.jpg


a) find the tension in the left wire
b) find the tension in the right wire

2. Homework Equations

[tex]\Sigma[/tex]Fx = 0 (condition for equilibrium)

[tex]\Sigma[/tex]Fy = 0 (condition for equilibirum)

[tex]\Sigma[/tex][tex]\tau[/tex]z = 0 (condition for equilibirum)

3. The Attempt at a Solution

[tex]\Sigma[/tex]Fy = 0 = TL(.25m) + TR(.75m) - (25+49) = 0

[tex]\Sigma[/tex]Fx = 0

tension in the left wire (torque measured from right wire)

[tex]\Sigma[/tex][tex]\tau[/tex]z = 0 =TR(0) + TL(.6) + 25(.2) + 49(.3)

TL = 33N

tension in the right wire (torque measured from left wire)

[tex]\Sigma[/tex][tex]\tau[/tex]z = 0 =TL(0) + TR(.2) + 25(.4) + 49(.3)

TR = 124N

checking with the FY equation I don't think I got the correct tensions, any help is greatly appreciated.
 

Answers and Replies

Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
Check your units on the [itex]\Sigma F_Y=0[/itex] equation; you are mixing N-m and N. Why?
 
Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
EDIT: Also, some of your distances look off. The moment around a point is the force multiplied by the lever arm (the perpendicular distance to the line of force).
 
987
123
Check your units on the [itex]\Sigma F_Y=0[/itex] equation; you are mixing N-m and N. Why?
I see that now, I wasn't exactly sure what the vertical distances for the wire pertained to (or if they pertained to anything at all).

is it that the entire distance of the rod doesn't come to play, and it's only a distance of .4m (between the 2 wires) that's being examined?
 
Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
It should help to draw a free-body diagram of the bar to make it clear what forces are applied.
 
987
123
It should help to draw a free-body diagram of the bar to make it clear what forces are applied.
I'm aware of what forces are applied, the left tension, the right right tension, the weight of the tool and the rod; I'm pretty sure the two wires have normal forces with the ceiling (but wasn't sure if they apply here), but really it doesn't seem that the extra .20m to the right of the .75m long wire is relevant, to the problem.
 
987
123
I got it.

I used TR(.4) + 49(.3) + 25(.2) = 0

TR = 49N


used TL(.4) + 49(.3) - 25(.2) = 0

TL = 25N

TR+TL = 74

74 = 74
.
 
Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
Looks good. I assume you meant TL(.4) - 49(.1) - 25(.2) = 0 on the second equation.
 

Related Threads for: Ridid body equilibrium, tension in hanging wires

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
5
Views
8K
Replies
3
Views
8K
Replies
1
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
5
Views
4K
Top