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Three Dimensional Force Systems

by theskyiscrape
Tags: dimensional, force, systems
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Oct11-10, 06:05 PM
P: 7
1. The problem statement, all variables and given/known data

A heavy ring with mass, m and radius, r is held in place by three cables and rests in the x-z plane. the ring being lifted is a distance h below the small ring affixed to the ceiling to which all three cables are attached. the small ring at A to which the cables all attach is directly over the center of the large ring that it supports. the cables attach to points B,C,D along the outer edge of the large ring. the magnitude of the angles locating points B,C,D in the x-z plane are given below and the direction of each angle from the nearest axis is shown in the diagram.
θb = 31 m = 480 kg
θc = 26 h = 3.9 m
θd = 17 r = 1.28 m

draw fully labelled FBD for each object used in your solution, give the coordinate system.

solve for the tensions in all three cables supporting the hanging weight

2. Relevant equations

Equilibreum Equations

Dot product / cross product?

3. The attempt at a solution

W = 480 x 9.81 = 4708.8N
Theta = Tan-1 (3.9/1.28) = 71.83

Do I assume that because the the distance and the angle between each cable and the y axis are the same that the tension on all cables will be equal?

if so...

T(AB) = T(AC) = T(AD) = T
T(AB)cos theta + T(AC)cos theta + T(AD)cos theta - 4708.8 = 0
3Tcos 71.83 = 4708.8
T= (4708.8/3cos71.83)
T = 5033.39
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Oct11-10, 06:05 PM
P: 7

link to diagram
Oct11-10, 10:20 PM
Sci Advisor
HW Helper
P: 2,124
Your current solution is incorrect. Start writing and using equilibrium equations, to solve for the cable tensile forces.

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