Statics - Moment using both vector and scalar approaches

AI Thread Summary
The discussion focuses on solving a statics problem involving moments using both vector and scalar approaches. The user details their calculations for moments, including the determination of vectors OA, OB, and AC, and the application of force F. They express uncertainty about their results, suspecting an error in their calculations. Ultimately, they realize the mistake was not converting units to N*m. The conversation emphasizes the importance of unit conversion in statics problems.
Alison A.
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Homework Statement


Capture.PNG


Homework Equations


Mo=Fd
Mo=r x F

The Attempt at a Solution


Alright guys, I did the whole process but I'm pretty sure I just made a little bump somewhere in my calculations which screwed up my answers.

First I found everything I could find
OA = 350j, so the unit vector of OA is 1j

OB = ( 350sin(33°) )i + ( 350 + 350cos(33°) )j
= 191i + 644j

tan(θ) = (300/350), θ = 40.6°

AC = √(300)^2 + (350^2) = 461 mm
OC = 461 sin(33°+40.6°) + (350 + 461cos(33°+40.6°), = 442i + 480j

Then,
AB = OB - OA
= 191i + 644j -350j
= 191i + 294j
Unit vector of AB = 0.545i + 0.839j

Given force is F = 130k

AC = OC - OA
= 442i + 130j

Vector Approach:
MA = AC x F
= (442i + 130j) x (130k)
= 16900i -57460j
In the position of AB = MA * Unit vector AB
MAB = 39000 N * mm

MOA = MA ⋅ Unit vector OA
= (16900, -57460) ⋅ (0,1,0)
= 57500 N * mmScalar Approach:
MAB = F x d
= 130 x 300
= 39000 N * mm

h = AC sin (40.6° + 33°)
= 461 sin (73.6°)
= 442 mm

MOA = F x h
=130 x 442
=57500 N * mm

My answers match, so I'm not sure where I went wrong, any help would be greatly appreciated!
 
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Omg, all I didn't do what convert to N * m, :blushing:
I'm dumb.

Check your units boys and girls.
 

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