(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"A derrick boom is guyed by cables AC and AD. A worker is lifting a 20kg block by pulling on a rope that passes through the pulley at A. Knowing that the boom AB exerts a force A that is directed from B to A, determine this force and the force in each of the two cables."

http://img213.imageshack.us/img213/4463/2673dsc0036ep9.jpg [Broken]

ANSWER: (From back of Textbook)

F(AB) = 1742N

T(AC) = 1517N

T(AD) = 403N

2. Relevant equations

F(net) in every direction = 0 (Hence statics)

F(AB) = (TensionAB)(Unit Vector Lambda)

Lamda = AB(position vector from A to B)

----

|AB|(Magnitude of AB)

3. The attempt at a solution

Coordinates:

A = 0x + 6y + 0z

B = -6x + 0y -3z

C = -10.5x + 0y -8z

D = -6x + 0y -7z

E = +6x +1.5y +0z

All forces of all the ropes and the weight force must be equal to the one supporting object: the boom(Tab).

I drew a triangle with AE as the hypotenuse.

Tan(theta) = (opp/adj) = [(6-1.5)/6]

(theta) = arctan(4.5/6)

(theta) = 36.87degrees

[(4.5^2) + (6^2)]^(1/2) = Hyp

Hyp = 7.5

W = (m)(g) = 196N = Tae

.: (196N/7.5m) = (Taex/6m) = (Taey/4.5m)

Taex = (6m)(196/7.5m) = 156.8N

Taey = (4.5m)(196/7.5m) = 117.60N

Sum Fx = 0 = Tab(6/9) - Tac(10.5/14.5) - Tad(6/11) - 156.8N

Sum Fy = 0 = Tab(6/9) - Tac(6/14.5) - Tad(6/11) -(9.8*20kg) - 117.60N

Sum Fz = 0 = Tab(3/9) - Tac(8/14.5) - Tad(7/11)

From here I used simple substitution and elimination to solve for the variable Tab, Tac and Tad; but I keep getting numbers that are off by around 150N for each value. I have tried this problem so many times, can somebody check to see if my equations above are correct? I am assuming my problem lies there and not in my simultaneous equation solving skills.

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# Homework Help: STATICS: Chapter 2, net force of lifting a given mass.

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