Find Moment Around A with 3D Vectors: B & C

[LeftBrain]

Homework Statement

A (0,0,0)
B(5,6,1)
C(3,0,4)

|F|= 1919N

Homework Equations

The Attempt at a Solution

Cartesian:
B= {5i + 6j + 1k}
C= {3i + 4k}

r_CB ={2i + 6j - 3k}

|r_CB| = sqrt(2² + 6² + 3²) = 7

Unit vector = r_CB / |r_CB| = {2/7i + 6/7j - 3/7k}

F = |F| * Unit vector = 1919 {2/7i + 6/7j - 3/7k} = 548.29i + 1644.86j - 822.43k

Now firstly, I'm not sure if I even did the above part correctly, but to find the moment I'm a bit lost and my don't seem to have much in my notes about this...

I think the next step is using cross product, but I'm a bit lost as to which arm to take to find moment about A...

If I use r_BA I get:

M_A = r_BA x F = 6579.44i - 4660.44j - 4934.56k

WELP! Need help!

Cheers LB

 

[SteamKing]

Homework Statement

A (0,0,0)
B(5,6,1)
C(3,0,4)

|F|= 1919N

Homework Equations

The Attempt at a Solution

Cartesian:
B= {5i + 6j + 1k}
C= {3i + 4k}

r_CB ={2i + 6j - 3k}

|r_CB| = sqrt(2² + 6² + 3²) = 7

Unit vector = r_CB / |r_CB| = {2/7i + 6/7j - 3/7k}

This is not the r-vector for use in calculating the moment about point A. What is the r-vector you need instead?

(Hint: What is the Force pulling on?)

F = |F| * Unit vector = 1919 {2/7i + 6/7j - 3/7k} = 548.29i + 1644.86j - 822.43k

Now firstly, I'm not sure if I even did the above part correctly, but to find the moment I'm a bit lost and my don't seem to have much in my notes about this...

You can always find discussions and examples of how to calculate the moment on the web.

I think the next step is using cross product, but I'm a bit lost as to which arm to take to find moment about A...

If I use r_BA I get:

M_A = r_BA x F = 6579.44i - 4660.44j - 4934.56k

WELP! Need help!

Cheers LB

See above. Remember, the problem asks for the magnitude of the moment, so don't forget that!

 

[LeftBrain]

So I need to use r_BC instead?

 

[SteamKing]

So I need to use r_BC instead?

No, you need to use the r-vector which connects point A to the end of the rope pulling on the end of bar AB.

Remember, calculating a Moment requires a Force and some kind of Distance between the force and the axis of rotation caused by the moment.