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

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Discussion Overview

The discussion revolves around a statics problem involving a derrick boom, where participants are attempting to determine the forces acting on the boom and the tensions in the supporting cables while lifting a 20kg block. The scope includes mathematical reasoning and technical explanations related to equilibrium in statics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Participants present a problem statement involving a derrick boom and the forces acting on it, including the weight of the block and tensions in cables AC and AD.
  • One participant outlines their approach, including calculations for angles, forces, and equilibrium conditions, but expresses uncertainty about the correctness of their equations.
  • Another participant requests a drawing to better visualize the problem, indicating a need for clarity in understanding the setup.
  • A later reply suggests that there are sign errors in the participant's equations and provides specific corrections for the summation equations, emphasizing the importance of significant figures in calculations.

Areas of Agreement / Disagreement

There is no consensus on the correctness of the initial calculations, as one participant points out potential errors in the equations. The discussion remains unresolved regarding the accuracy of the proposed solutions and the approach taken.

Contextual Notes

Participants express uncertainty about their calculations and the need for visual aids to clarify the problem setup. There are indications of missing assumptions or details that could affect the interpretation of the problem.

Who May Find This Useful

Students or individuals studying statics, particularly those working on problems involving forces in structures and equilibrium conditions.

SnickerGTI
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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.
 
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SnickerGTI said:

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
 
Last edited by a moderator:
A drawing of what?
 
Anybody have a clue?
 
SnickerGTI said:
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
 
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.