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

[SnickerGTI]

Homework Statement

"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

ANSWER: (From back of Textbook)
F(AB) = 1742N
T(AC) = 1517N
T(AD) = 403N

Homework 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)

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.

 

[stewartcs]

Homework Statement

"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

ANSWER: (From back of Textbook)
F(AB) = 1742N
T(AC) = 1517N
T(AD) = 403N

Homework 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)

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.

How about a drawing, I can't visualize what you are describing.

CS

 

[SnickerGTI]

A drawing of what?

 

[SnickerGTI]

Anybody have a clue?

 

[stewartcs]

A drawing of what?

A drawing of the problem. If you have inserted one already, I'm not able to see it for some reason (most likely my company is blocking the link behind the scenes).

CS

 

[nvn]

SnickerGTI: Nice work. You just made a couple of sign errors. Notice the fourth term in your summation(Fx) equation should be 156.9, not -156.8 N. (Also, generally always carry four or five significant digits for all quantities throughout your calculations, then round the final answer to three, or maybe four, significant digits.) Secondly, the third term in your summation(Fz) equation should be Tad*(7/11), not -Tad*(7/11). Give it one more try.