Statics - Moment using both vector and scalar approaches

In summary, the conversation involved calculations for finding the moment of a given force (F) applied at point A on an object, using both vector and scalar approaches. The resulting moment was found to be 39000 N * mm and 57500 N * mm respectively. The discussion also touched upon the importance of converting units correctly in calculations.
  • #1
Alison A.
86
2

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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  • #2
Omg, all I didn't do what convert to N * m, :blushing:
I'm dumb.

Check your units boys and girls.
 

Related to Statics - Moment using both vector and scalar approaches

1. What is the difference between vector and scalar approaches in calculating moments in statics?

Vector approach involves representing the moment as a vector quantity with both magnitude and direction, while scalar approach uses only the magnitude of the moment. In vector approach, the direction of the moment is described using the right-hand rule.

2. How do you calculate the moment of a force using the vector approach?

To calculate the moment of a force using the vector approach, you need to determine the magnitude of the force, the perpendicular distance between the force and the axis of rotation, and the direction of the moment using the right-hand rule. The moment is then calculated as the cross product of the force and the distance vector.

3. What is the formula for calculating the moment of a force using the scalar approach?

The formula for calculating the moment of a force using the scalar approach is M = Fd, where M is the moment, F is the magnitude of the force, and d is the perpendicular distance between the force and the axis of rotation.

4. Can you use both vector and scalar approaches to calculate the moment of a force?

Yes, you can use both vector and scalar approaches to calculate the moment of a force. The results will be the same, as long as the calculations are done correctly. However, the vector approach is more accurate and is preferred in most cases.

5. How is the direction of the moment related to the direction of the axis of rotation?

The direction of the moment is always perpendicular to the plane created by the force and the axis of rotation. This means that the moment will be in the same direction as the axis of rotation, and it can be clockwise or counterclockwise depending on the direction of the force and the axis of rotation.

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