1. Aim: How do we add vectors algebraically?

2. Do Now
How can we tell that this system cannot be in equilibrium? Example: The maximum force 20 N and 15 N can produce is 35 N and the minimum force is 5 N. 50 N does not fit in this range.

3. Adding Vectors (Case 1 0º)
You push a couch with a force of 8 N east. I push a couch with a force of 10 N east. Find the resultant N right

4. Adding vectors (Case 2 180º)
You push a couch with a force of 8 N east. I push the same couch with a force of 10 N west. Find the resultant force. 2 N left

5. Adding Vectors (Case 3 90º)
You push a couch with a force of 8 N east. I push a couch with a force of 10 N north. Find the resultant force. Pythagorean Theorem: R2=(8N)2+(10N)2 R2=164 R=12.8N

6. How do you find the resultant force for an arbitrary angle?
How would we find the resultant in the case below where the angle between the 8 N and 10 N forces is 45º:?
10 N
8 N

7. Vector Resolution Review

8. Vector Resolution Review Problem
Find the horizontal and vertical components of the 10 N force.
Ax=Acosθ=10cos(30)=8.67N
Ay=Asinθ=10sin(30)=5N

9. Turn and Talk
Explain what relationship you see between the horizontal component of vector A and the horizontal component of vector B and the horizontal component of the resultant. Explain what relationship you see between the vertical component of vector A and the vertical component of vector B and the vertical component of the resultant

10. Algebraic Addition of Vectors

11. Algebraic Addition of Vectors
When adding vectors A and B algebraically, you must do the following:
Resolve vectors A and B into their horizontal and vertical components; Ax and Ay & Bx and By
Add the horizontal components of A and B to find the horizontal component of the resultant. Add the vertical components of A and B to find the vertical component of the resultant.
Ax + Bx = Rx and Ay + By = Ry
Use the pythagorean theorem, to find the magnitude of the resultant R2 = Rx2 + Ry2
Find the angle and direction of the resultant using
theta = tan-1(Ry/Rx)

12. Example 1-Algebraic Vector Addition
Displacement vector A = 20 m east
Displacement vector B = 50 m 35 degrees north of east.
Find the components of each vector.
Add the components of each vector to find the components of the resultant.
Find the magnitude of the resultant using pythagorean theorem.
Find the angle of the resultant.

14. Example 2-Algebraic Vector Addition
Donald Trump pushes a ballot box with a force of 55 N at an angle of 70 degrees north of west. Bernie Sanders pushes the same ballot box with a 40 N force at an angle of 25 degrees north of east. (Let Trump’s force be vector A and Bernie Sanders’ force be vector B) a) Find the components of each vector. b) Add the components of each vector to find the components of the resultant. c) Find the magnitude of the resultant using pythagorean theorem. d) Find the angle of the resultant.