# Three Dimensional Force Systems

• theskyiscrape
In summary, the conversation discusses a problem involving a heavy ring with mass and radius being held in place by three cables attached to a small ring affixed to the ceiling. The angles and distances of the cables are given, and the goal is to solve for the tension in each cable. The attempt at a solution involves using the equilibrium equations and solving for the tension in each cable. However, the current solution is incorrect and the process of using equilibrium equations should be followed to obtain the correct tensions.
theskyiscrape

## Homework Statement

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

## Homework Equations

Equilibreum Equations

Dot product / cross product?

## 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

Last edited by a moderator:

Last edited by a moderator:
Your current solution is incorrect. Start writing and using equilibrium equations, to solve for the cable tensile forces.

## What is a three dimensional force system?

A three dimensional force system refers to a set of forces acting on a body in three dimensions, typically represented by vectors with magnitude and direction.

## How do you find the resultant force in a three dimensional force system?

To find the resultant force, you can use vector addition by adding all of the individual forces together. This will give you a resultant force vector with magnitude and direction.

## What is the difference between a coplanar and non-coplanar force system?

A coplanar force system refers to forces that all lie in the same plane, while a non-coplanar force system refers to forces that act in different planes. In a three dimensional force system, there may be both coplanar and non-coplanar forces present.

## How are three dimensional force systems used in real-world applications?

Three dimensional force systems are used in various fields, such as engineering and physics, to analyze the forces acting on structures or objects. This information can then be used to design and optimize structures, predict motion, and solve problems in mechanics.

## What are some common examples of three dimensional force systems?

Some common examples of three dimensional force systems include a car driving up a hill, a plane flying through the air, and a building supporting its own weight. These systems involve multiple forces acting in different directions and can be analyzed using principles of three dimensional force analysis.

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