Statics problem, finding the moment (torque) about a straight line

[TPMF]

1. Determine the magnitude and direction of the moment of the vertical 800 lb force about the straight line through points C and D. (See attachment for diagram)



2. I believe that the equation i need is (Moment vector)=(unit vector)*((position vector)X(Force Vector))



3. I feel that I working myself into a dead end. But, I think that The unit vector is 0.164i+0.986j+0k and the force vector is 0i-800j+0k
I am having trouble finding what the position vector needs to be, though as I said earlier, I think i am going about this the wrong way.

 

[SteamKing]

You might review how to calculate a moment about an arbitrary axis:

http://classes.uleth.ca/200803/engg2000a/Fri%20Oct%203.pdf

 

[voko]

Your unit vector is wrong. The CD line is in the XZ plane, so its unit vector cannot have a component in the Y direction (j).

As for the position vector, recall that it is a vector form any point on the axis to any point on the line of force.

 

[TPMF]

Thank you SteamKing and voko.
I did not realize that the position vector could be any two points, as long as they are along the line of force and the CD line. Also, thank you for pointing out my error with the unit vector, I switched the y and z values since i am use to a different orientation of the z axis.

What i ended up getting was:
u= <0.164, 0, 0.986>
r= <1.5, -3, -1>
F <0, 800, 0>

M = u*(r×F)
M = 0.164(800)-0(0)+0.986(1200)
M = 1314.4 lb-ft

I think that is correct, but do let me know if you see a mistake.
And, thank you both again.

 

[rezeew]

I would recommend approaching this problem using the right-hand rule for moments. First, we need to determine the perpendicular distance from the line through points C and D to the line of action of the 800 lb force. This distance can be found by drawing a line from the point of intersection of the two lines to the line of action of the force.

Next, we can use the right-hand rule to determine the direction of the moment. Place your right hand on the line through points C and D with your fingers pointing in the direction of the perpendicular distance we just found. Then, curl your fingers towards the direction of the force vector. Your thumb will point in the direction of the moment vector.

Finally, we can calculate the magnitude of the moment using the equation you mentioned: Moment = (position vector) x (force vector). The position vector will be the vector from the point of intersection of the two lines to the point where the force vector intersects the line through points C and D. This can be found by subtracting the coordinates of these two points.

Overall, it is important to approach statics problems systematically and to use the appropriate equations and methods to find the solution. It may also be helpful to draw a free body diagram to visualize the forces and their directions. Keep practicing and don't be afraid to ask for help if you get stuck.