How Do You Convert Forces into a Wrench in Vector Mechanics?

[Saladsamurai]

[SOLVED] Reduction to a Wrench

So far I have moved the forces to point O where $\sum F=F_r=-10.0\hat{j}$ I have also re-written each force in Cartesian-vector form where

$F_1=10[\frac{6i-6j}{\sqrt{72}}=7.071i-7.071j$ $F_2=-10j$ and $F_3=-F_1=-7.071i+7.071j$.

I am told to decompose each force into its components and then use scalar method to find the sum (which I did above) and to find the sum of the moments about each of the x,y,z axes. Then move the forces to get a wrench.

I have found each of the moments as follows:
$$\sum M_x=2(10)-2(7.071)=5.858$$
$$\sum M_y=-6(7.071)=-42.426$$
$$\sum M_z=6(7.071)-6(7.071)= 0$$

Now I am a little confused. I am just not sure where to go from here. I know I need to find M-perp and M-parellel which looks to be what I have just found.

Are my moments correct? I think they are. And where do I go from here?

 

[Saladsamurai]

I GOT IT! Amidst all my typing I noticed that my moment about y-axis is incorrect.

M_x=5.86=M_perp--->distance from z =5.86/10=.586 ft.
M_y=-14.1=M_parellel

YAY!

 

[ogb p]

As a scientist, my response would be to first clarify the problem and its context. What is the purpose of finding the sum of moments and decomposing the forces? Is this a real-world problem or a theoretical exercise? Once the purpose is clear, I would suggest considering alternative methods or approaches to solving the problem. For example, instead of using the scalar method, perhaps vector analysis or the use of a free body diagram could provide a more efficient solution. Additionally, I would recommend double-checking the calculations and ensuring that all units are accounted for. It may also be helpful to seek assistance from a colleague or professor for further guidance and clarification.