1. Statics Test 1 Review
By Caleb

2. Chapter 2 The stuff you should know: Laws of Motion
Finding resultant forces
In 2D
Non-orthogonal axes
Law of Sines, Law of Cosines, Parallelogram law, Head to Tail Addition
Orthogonal
Add Cartesian Vectors(especially if more than 3 forces)
In 3D
Sum Cartesian Vectors to get resultant vector
Use position vectors to get the unit vectors
To get coordinate direction angles, take arccos of the components of unit vector
Use Dot product to get component of force along axis or other components

3. Ch 2 Practice Problem: Dot Product
Find the component of force F acting along BC

4. Ch 2 Practice Problem: Dot Product
Process:
Find uBC and uF
Find Cartesian coordinates of F
Use dot product of uBC and F to get magnitude of the component

5. Chapter 3 Systems in Equilibrium
A lot of the basics from 3 remain the same, but there are some differences:
All problems are in equilibrium, so the total sum of the forces is 0
By extension, the sum of forces in the x, y, and z directions is also 0
Instead of solving for a resultant force, we solve for one of the forces in the system
New components of statics problems are introduced
Springs: F = ks where k is spring constant and s is distance deformed
Pullies: Tension on the rope on both sides of the pulley is the same

6. Ch 3 Practice Problem 3D Vectors
If the bucket has a weight of 20lb and FDA is 10lb, what is the tension in FDB and FDC?

7. Ch 3 Practice Problem 3D Vectors
Process:
Find the unit vectors of FDA and FDC
Find the Cartesian forms of each of the vectors
Sum the forces in the x, y, and z directions to get equations

8. Chapter 4 Moments
Some of you may not have done moments yet, so lets do the basics:
A moment is a force that can cause a body to rotate
The magnitude of the produced moment can represented by the equation M = Fd
F is the force acting perpendicularly to the line of action through the point the moment is being taken about
d is the distance to the perpendicular force from the point the moment is being taken about

9. Ch 4 Examples
M = F * d
So what is the moment about O?

10. Ch 4 Examples M = 100N * (2m) = 200 N*m CCW
Force is a perpendicular distance 2m away from point O

11. Ch 4 Examples
M = F * d

12. Ch 4 Examples M = F * d M = -500N 3 5 * 2m = -600 N*m CW
Since the 500 N is not perpendicular to the line of action through O, we must get the portion of the force that is perpendicular. Forces that act through the line of action do not cause a moment.

13. Ch 4 Examples
M = F * d

14. Ch 4 Examples
M = F * d
M = 500N * 1m – 500N * 2m = (400 – 600)N*m = -200 N*m CW
Both components of the force are perpendicular to the line of action, but they work in opposite directions. The typical conventions make a moment moving Clockwise(CW) negative and Counter Clockwise(CCW) positive. Always label your answer.