Vectors

1
Vectors

• Magnitude and Direction

2
Vector quantities

• Examples displacement, velocity, acceleration,
  and force
• Includes both a magnitude and a direction

3
(No Transcript)
4
Vector Diagrams

• a scale is clearly listed
• an arrow (with arrowhead) is drawn in a specified
  direction
• the magnitude and direction of the vector is
  clearly labeled in this case, the diagram shows
  the magnitude is 20 m and the direction is (30
  degrees West of North).

5
Examples
6
Vectors are drawn to scale
7
Time to practice

• Use vectors to make a map from the science room
  to a location in the school.

8
Vector Addition

• vectors can be added together to determine the
  result (or resultant)

9
Head to Tail Method(Elephant Rule)

• When adding vectors, it is necessary to place the
  head (trunk) of one vector on the tail of
  another. The resultant is drawn from the tail of
  the first vector to the trunk (head) of the last.
  

10
Example
11
Steps for sum of vectors using head to tail method

• 1. Choose a scale and indicate it on a sheet of
  paper (the best choice of scale is one which will
  result in a diagram which is as large as
  possible, yet fits on the sheet of paper).
• 2. Pick a starting location and draw the first
  vector to scale in the indicated direction. Label
  the magnitude and direction of the scale on the
  diagram (e.g., SCALE 1 cm 20 m).
• 3. Starting from where the head of the first
  vector ends, draw the first vector to scale in
  the indicated direction. Label the magnitude and
  direction of the vector on the diagram.
• 4. Repeat steps 2 and 3 for all vectors which are
  to be added
• 5. Draw the resultant from the tail of the first
  vector to the head of the last vector. Label this
  vector as "Resultant" or simply "R."
• 6. Using a ruler, measure the length of the
  resultant and determine its magnitude by
  converting to real units using the scale (4.4 cm
  x 20 m/1 cm 88 m).
• 7. Measure the direction of the resultant using
  the counterclockwise convention.

12
Problem Add the 3 vectors20 m, 45 25 m,
300 15 m, 210 scale 1 cm 5 m
13
Solution vectors may be added in any order
14
Another method for adding vectors

• Only use when
• Adding two (and only 2) vectors
• The 2 vectors make a right angle to each other

15
Practice

• R2 52 10 2
• R2 25 100
• R2 125
• R 11.2 km, NW

16
Practice

• R2 302 402
• R2 2500
• R 50 km, SW