1. ME 221 Statics www.angel.msu.edu (Angel)

2. ME221Lecture 22 Vectors; Vector Addition Define scalars and vectors Vector addition, scalar multiplication 2-D trigonometry Vector components Law of cosines Law of sines Problems

3. ME221Lecture 23 Scalars and Vectors Scalar is a quantity that is represented by a single number –examples: mass, temperature, angle Vectors have both magnitude and direction –Examples: velocity, acceleration, force –Acceleration due to gravity is down not up!

4. ME221Lecture 24 VECTORS Line of Action  Direction Vector A or A x y Magnitude

5. ME221Lecture 25 Vectors Vectors are equal when they have the same magnitude and direction = A B Vectors add by the parallelogram rule A B + B = A C

6. ME221Lecture 26 More on Vectors Vectors are communative A + B = B + A B A C B A Vectors are associative (A + B) + C = A + (B + C)

7. ME221Lecture 27 In order to subtract vectors, first we must understand that if we multiply a vector by (-1) we get a vector equal in length but exactly opposite in direction. Subtraction of Vectors Then we see that B - A = B + (-A) So if we have D = B - A This looks like this: A -A A B D

8. ME221Lecture 28 A B A+B C D Adding More Than Two Vectors A B C  D = A+B+C

9. ME221Lecture 29 Law of Cosines This will be used often in balancing forces c    b a

10. ME221Lecture 210 Law of Sines Again, used throughout this and other classes Start with the same triangle:    c b a

11. ME221Lecture 211 300 lb 200 lb 45 o 25 o Example Determine by trigonometry the magnitude and direction of the resultant of the two forces shown Note: resultant of two forces is the vectorial sum of the two vectors