1. Aim: How do we graphically add force vectors?

2. Review:
A student hands in two vector diagrams A and B but fails to label the resultant. In each diagram, which letter represents the resultant?
(A,B, or C?) A in both

3. Force
A force is defined as a push or a pull. Forces are measured in units called newtons.

4. Turn and Talk:The effect of angle between force vectors on the resultant force vector
Answer these questions:
What is the maximum resultant produced between two 10 N vectors? 20 N
What is the minimum resultant that can be produced between two 10 N vectors? 0N
State the angle between the two force vectors in each of the 6 cases below?
Zero Degrees, Zero Degrees, 180 Degrees, 90 degrees, 90 degrees, and 120 degrees

5. Checkpoint
What happens to the magnitude of the resultant that two vectors produce when the angle between the resultant increases from 0 degrees to 180 degrees? Write a complete sentence. As the angle between the vectors increases from 0 degrees to 180 degrees, the magnitude of the resultant decreases

6. Parallelogram Method of Vector Addition
The parallelogram method of vector addition is identical to the head to tail method of vector addition.
In the parallelogram method of vector addition, the vectors are moved to a common point in which they are placed tail to tail.
A parallelogram is constructed as shown below.
The resultant R is the diagonal of the parallelogram drawn from the common origin.

7. Calculate the resultant between a 12 N and 5 N at the following angles using trigonometry.
0 degrees 90 degrees 180 degrees 17 N 13 N 7 N

8. Find the magnitude of the resultant
When the angle between 5N and 12 N is 30 degrees, predict a possible value range for their resultant? Using the parallelogram method of vector addition, find the resultant vector when the angle between the 5 N and 12 N vector is 30 degrees.

10. Multiple Choice Vectors Problem 1
What resultant could not be produced by two 20 N forces?
0 N
10 N
30 N
50 N

11. Multiple Choice Vectors Problem 2
Which set of forces could produce a resultant of 10 N?
A 4 N and 4 N force
A 6 N and 15 N force
A 5 N and 40 N force
A 20 N and 80 N force

12. Animation for 8 N and 6 N forces

13. Equilibrium and Equilibrant
In physics, equilibrium means that the overall force on an object is 0. The equilibrant is the force which must be applied to an object so that it is at equilibrium.
What is the relationship between the resultant of F1 and F2 and the equilibrant?

14. Equilibrium Question
What is the magnitude and direction of the equilibrant?
71 N northeast
71 N southwest
101 N northeast
101 N southwest

15. Equilibrium Question 2
The three forces below are in equilibrium. What must be the resultant produced by the 45 N and 55 N force? 32 N What must be the resultant produced by the 45 N and 32 N force? 55 N What must be the resultant produced by the 55 N and 32 N force? 45 N

16. Conclusion Explain how this relates to our lesson.
Why are all of the equalities true?
Why is the inequality true?
The range of resultants that can be produced by a 5 N and 12 N force is from 7 N to 17 N. Therfore, an 18 N force could never be produced by a 5 N and 12 N force.