1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 3D Force systems

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data
    A system of cables supports a bucket. The dimensions in the figure are as follows: x_1 = 4.80 ft, x_2 = 1.70 ft, y_1 = 1.10 ft, y_2 = 3.30 ft, z_1 = 2.55 ft, and z_2 = 3.10 ft. If the bucket and its contents have a combined weight of W_1 = 17.5 lb, determine F_A, F_B, and F_C, the tensions in cable segments DA, DB, and DC, respectively.


    2. Relevant equations
    vec_F = F(unit vector)
    unit vector = vec_r / |r|
    [tex]\Sigma[/tex]F = 0
    F_DA + F_DB + F_DC + W = 0

    3. The attempt at a solution
    coordinates: A(4.8,0,2.55) B(1.7,0,0) C(0,3.3,3.10) D(1.7,1.1,0)

    r_DA = [(4.8-1.7)i +(0-1.1)j + (2.55-0)k] / [tex]\sqrt{(3.1^2+1.1^2+2.55^2)}[/tex]
    vec_F_DA = F_DA [0.74483i -0.2643j + 0.61269k]

    r_DB = [(1.7-1.7)i +(0-1.1)j + (0-0)k] / [tex]\sqrt{(1.1^2)}[/tex]
    vec_F_DB = F_DB [-1j]

    r_DC = [(0-1.7)i +(3.33-1.1)j + (3.1-0)k] / [tex]\sqrt{(1.7^2+2.2^2+3.1^2)}[/tex]
    vec_F_DC = F_DC [-0.40826i + 0.52834j +0.74448k]

    In the end... my 3 equations with the Foces unknown:
    1.) 0.74483F_DA - 0.4826F_DC = 0
    2.) -0.2643F_DA - F_DB +0.52834F_DC = 0
    3.) 0.61269F_DA + 0.74448F_DC - 17.5 = 0

    I solved for F_DA in 1.) and substituted F_DC in 3.) and using back substitution in 2.) I got:
    F_DA = 44.1 lb
    F_DB = 28.6 lb
    F_DC = 15.7 lb

    but it was wrong. What am I doing wrong???
     

    Attached Files:

    Last edited: Sep 13, 2010
  2. jcsd
  3. Sep 14, 2010 #2

    collinsmark

    User Avatar
    Homework Helper
    Gold Member

    Hello Sami23,
    Check the number above in red. It's a 'typo' of some sort.
    But in both cases, with or without the typo, I'm not coming up with same solution as you. Show us your work on how you found the tensions.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook