Vector Refresher Part 2

1. Vector Refresher Part 2 Vector Addition Multiplication by Scalar Quantities Graphical Representations Analytical Methods

2. Vector Addition • A lot of times, it’s important to know the resultant of a set of vectors • The resultant vector can be described as the sum of all the vector quantities you wish to evaluate • We’ll look at graphical and analytical techniques for doing this

3. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Parallelogram method Connect the tails of both vectors to start.

4. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Parallelogram method Create a parallelogram with each vector as one of the sides.

5. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Parallelogram method The resultant goes from the place where 2 tails meet to the place where 2 heads meet

6. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Head-to-tail method With this method, the vectors are added by placing the tail of a vector at the head of another one to make a continuous path.

7. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Head-to-tail method The addition of these vectors results in a vector that starts at the tail of the first vector and ends at the head of the final vector

8. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Head-to-tail method If we had a 3rd vector, we could add it to the previous result

9. Graphical Methods For Vector Addition • 2 ways to look at vector addition graphically • Head-to-tail method If we had a 3rd vector, we could add it to the previous result

10. Multiplying a Vector By a Scalar When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed.

11. Multiplying a Vector By a Scalar When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed. Multiplying a vector by 2 yields a vector with the SAME DIRECTION and twice the length

12. Multiplying a Vector By a Scalar When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed. Multiplying a vector by 1/2 yields a vector with the SAME DIRECTION and half the length

13. Multiplying a Vector By a Scalar When a vector is multiplied by a scalar, the length of the vector can be elongated or shortened. If the scalar is a negative number, the direction is reversed. Multiplying a vector by -1 yields a vector with the OPPOSITE DIRECTION and the same length

14. Example Draw Start by multiplying vector A by 1/2

15. Example Draw Start by multiplying vector A by 1/2

16. Example Draw Next, multiply vector B by -3

17. Example Draw Now add these vectors together

18. Example Draw The resultant vector is shown in green

19. Analytical Method for Vector Addition When vectors are added to each other, the components in each direction are summed.

20. Analytical Method for Vector Addition When vectors are added to each other, the components in each direction are summed.

21. Analytical Method for Vector Addition When vectors are added to each other, the components in each direction are summed.

22. Multiplying a Vector By a Scalar When multiplying a vector by a scalar, the scalar must be applied to each component of the vector Thus, if we multiply by a scalar “k”, we get:

23. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

24. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

25. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

26. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

27. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

28. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

29. Example Determine the resultant force caused by the following 3 force vectors. The first thing to do is determine F3

30. Example Determine the resultant force caused by the following 3 force vectors. Now we can add the 3 vectors together to determine the resultant force

31. Example Determine the resultant force caused by the following 3 force vectors. Now we can add the 3 vectors together to determine the resultant force

32. Example Determine the resultant force caused by the following 3 force vectors. Now we can add the 3 vectors together to determine the resultant force

33. Example Determine the resultant force caused by the following 3 force vectors. Don’t forget the units, they’re as important to the answer as the numbers are

34. Example Determine the resultant force caused by the following 3 force vectors. Don’t forget the units, they’re as important to the answer as the numbers are