Find the Tensions in the Cables

  • #1
249
1

Homework Statement



Determine the tensions in cables AB, AC, and AD.


Homework Equations





The Attempt at a Solution


I mad point A (0,0,0)
B = (2.6, -4.2, 4.4)
C = (-2.6, -1.6, 4.4)
D = (0, 2.5, 4.4)
Firstly I found the unit vectos of AB, AC and AD, which are as follows

[itex]\hat{}n[/itex]AB = <2.6, - 4.2, 4.4>/ 6.615134

[itex]\hat{}n[/itex]AB = <0.393041i - 0.634908j + 0.665141k

[itex]\hat{}n[/itex]AC = <-2.6, -1.6, 4.4>/5.35537

[itex]\hat{}n[/itex]AC = <-0.48549i -0.29876j +0.821605k>

[itex]\hat{}n[/itex]AD = <0i +2.5j + 4.4k>/5.06063
[itex]\hat{}n[/itex]AD = oi + 0.494009j + 0.86945k

Then I took each unit vector and multiplied it by the force, 113 lb

TAB = TAB[itex]\hat{}n[/itex]AB[/SUB = TAB(0.39394i - 0.634908j + 0.665141k)

TAC = TAC[itex]\hat{}n[/itex]AC = TAC(-0.48549i -0.29876j + 0.821605k)

TAD = TAD[itex]\hat{}n[/itex]AD =TAD(0i + 0.494009j +0.86956k)

i: 0.39304*TAB - 0.48549TAC + 0TAD

j: -0.634908TAB - 0.29876TAC + 0.494009TAD

k: 0.665141TAB + 0.821605TAC + 0.86945TAD

I then put this into a matrix and then used my calculator to solve for TAB, TAC and TAD

I got:

TAB = 39.3261
TAC = 31.9374
TAD = 69.7967

But it says my answer is wrong and I don't know where I'm going wrong. Help would be appreciated
 

Answers and Replies

  • #2
249
1
Just found my mistake. I defined the location of B incorrectly. B = (2.6, -1.6, 4.4). Using these values I get

TAB = 41.9316
TAC = 41.9316
TAD = 50.7184
 

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