Statics Problem, Moment About an Axis

[yaro99]

Homework Statement

Problem 3.60:

Homework Equations

[itex]M_{AD}= \begin{vmatrix}
\lambda_x & \lambda_y & \lambda_z \\
x_{B/A} & y_{B/A} & z_{B/A} \\
F_x & F_y & F_z &
\end{vmatrix}
[/itex]

The Attempt at a Solution

Looking at the figure, these are the unit vector components for line AD:

[itex]\lambda_x=1 \ m
\\ \lambda_y= 0 \ m
\\ \lambda_z = -0.75 \ m
[/itex]

And these are the coordinates for point B where the force is applied:

[itex]x_{B/A}=0.5 \ m
\\ y_{B/A}= 0 \ m
\\ z_{B/A} = 0 \ m
[/itex]

The force vector for the tension in BG:
[itex]\mathbf{T_{BG}}= 450*(\frac{-0.5\hat{i}+0.925\hat{j}-0.4\hat{k}}{1.125})= -200\hat{i}+370\hat{j}-160\hat{k} \ N[/itex]

Plugging these values into the matrix above, I get -138.75 N*m, but the answer is supposed to be -111.0 N*m

Edit: Changed the mistake I made in the second row. Still getting the wrong answer.

 

[SteamKing]

Shouldn't λx^2+λy^2+λz^2 = 1 if these are the components of a unit vector?

 

[yaro99]

Shouldn't λx^2+λy^2+λz^2 = 1 if these are the components of a unit vector?

Yes, I actually just figured it out. I had messed up when I took the unit vector components and didn't divide by the magnitude.
Is there a way I can close this thread?

 

[berkeman]

We don't delete threads that have responses. Glad that you figured it out.

 

[Nickie]

I would suggest double-checking your calculations and equations to ensure they are accurate. It is possible that there may be a mistake in your calculations or in the given values. Additionally, I would recommend seeking help from a peer or instructor to review your work and provide feedback. It is important to always double-check your work and seek assistance when needed to ensure accurate results.