1. Addition of Vectors PHY 115, 201, and 213 Important points to remember:  Sketch the coordinate system and draw vectors and their components. Label all values including angles.  Pay close attention to signs  Add ‘x’ components together  Add ‘y’ components together  Rectangular form displays a vector’s components

2.  Polar form displays a vector’s magnitude and the angle (CCW from the + ‘x’ axis). Polar form is sometimes referred to as Standard Position.  Calculator should be in ‘degree’ mode.  When solving right triangles, ‘opposite’ is always the side opposite the angle in question.  The resultant ( R ) is the equivalent of the given vectors. If the given vectors are forces, then R is the equivalent force that could replace the given vectors.  The equilibrant (E) is the vector that offsets (cancels) R. Because R represents the given vectors, then E offsets (cancels) the given vectors. Such a situation is referred to as equilibrium and E is the vector that puts the system in equilibrium.

3. The Problem: a)Add these three vectors and find the resultant ( R ): A = 15 LB @ 25 o B = 35 LB @ 130 o C = 20 LB @ 280 o b) Determine the equilibrant (E) needed to put the system of vectors in equilibrium.

4. +y +x A B C A y A x C x C y B x B y 40 o

5. Solve each vector for its components. That is, solve each triangle for the sides. Never mix values when solving a triangle. For example, do not put force units on one side of the triangle and distance units on the other side. Now, sum like components. Add “x” values to “x” values, etc.

6. These components of the Resultant are the sides of the Resultant triangle. +y +x R R y R x

7. Now, solve this triangle for the components of R. This vector, R, could replace vectors A, B, and C.

8. The Equilibrant, E, is 180 o away from R. +y +x R R y R x E