1. Forces II: Addition of Vectors 3N2N The length of the arrow represents the magnitude of the force. The arrows point in the direction in which the force is being exerted. Vector: includes both a magnitude and a direction When we use arrows to represent forces, we are using vectors!

2. Example: Two people are pushing on the same side of a box. One person pushes with a force of 3 N and the other pushes with a force of 2 N. What is the net force on the box? 3N 2N 1. Arrange the arrows so that they are head to tail. 3N2N 2. Then draw a new vector that starts at the tail of the first vector and ends at the head of the last vector. The magnitude and direction of the final vector is the net force. 5 N

3. Example: Two people are pushing on opposite sides of a box. One person pushes from the left with a force of 3 N and the other pushes from the right with a force of 2 N. What is the net force on the box? The net force is +1 N. + x- x 0 12345 -2-3-4-5

4. What is the net force if have 3 N at 0° and 5 N at 90°? Net force = 5.8 N at 60°

5. What is the net force for the two vectors shown below?

6. Note that the x-component of the two vectors cancelled out, and the y-components were added to make the net force vector.

7. What is the net force for the two vectors shown below?

9. If the x and y components of all of the vectors being combined cancel each other out, the net force is zero.

10. What downward force on vector 3 must be used to keep the center point (0,0) from moving? 3 ?

11. 3 Vector 3 must have a magnitude of 2 and be directed down the negative y axis. New notation: -2 y ^ 2 x + 1 y ^^ -2 x + 1 y ^^

12. What is the net force if vectors A and B are added? = 0 A = 3 xB = 2 x ^^ = 5 x ^ A = 3 xB = -2 x ^ ^ = 1 x ^ A = 3 xB = 5 y ^^ = 3 x + 5 y ^^ A = 1 x + 2 yB = -1 x + 2 y ^^^^ A = 4.5 x - 2 yB = -4.5 x - 2 y ^ ^ ^^ A = 2 x + 1 yB = 2 x - 1 y ^^ ^ ^ A = 3 x - 3 yB = -3 x + 3 y ^^^ ^ = 4 y ^ = -4 y ^ = 4 x ^