Calculate Tensions in a 3D Force System with Given Dimensions and Weights

[sami23]

1. Homework Statement
A system of cables suspends a crate weighing W = 420 lb. The dimensions in the figure are as follows: h = 20.9 ft, l = 5.70 ft, x = 7.05 ft, theta = 36.0 , and phi = 20.0. Determine T_A, T_D, and T_E, the tensions in cable segments CA, CD, and CE, respectively.


2. Homework Equations
vector F = (magnitude F)(unit vector)
sum F = 0
F_CA + F_CB + F_CD + F_CE + F_CF + W = 0

3. The Attempt at a Solution
How do I start by finding the coordinates:
C(0,0,0), D(x,0,h), A(?) E(?)

I can't see how to find the correct coordinates A,B,C,D,E,F

 

[mark726]

.

your first step would be to carefully analyze the given information and identify all the variables and equations that are relevant to solving the problem. In this case, the given information includes the weight of the crate (W), the dimensions of the system (h, l, x, theta, phi), and the unknown tensions in the cables (TA, TD, TE).

The equations that are relevant to solving this problem are the equations for vector forces and the equation for the sum of forces being equal to zero. These equations can be used to find the tensions in the cables by setting up a system of equations and solving for the unknown variables.

To start, you can assume that point C is the origin (0,0,0) since it is the point of suspension and does not have any coordinates given. From there, you can use the given dimensions and angles to find the coordinates of points A, B, D, E, and F.

For example, to find the coordinates of point A, you can use the given dimensions l and theta to find the horizontal and vertical components of the cable segment CA. Then, using basic trigonometry, you can find the coordinates of point A in relation to point C.

You can repeat this process for points B, D, E, and F. Once you have the coordinates of all the points, you can use the equations for vector forces and the sum of forces to set up a system of equations and solve for the unknown tensions TA, TD, and TE.

Remember to always double check your work and units to ensure that your final answer makes sense in the context of the problem.