(adsbygoogle = window.adsbygoogle || []).push({}); 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???

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# Homework Help: 3D Force systems

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