1. Vectors

2. What is a Vector?
Vectors are measured quantities that show magnitude and direction
Examples -

3. Vectors
Vectors are represented by arrows. The size indicates the magnitude.
VECTORS CAN BE MOVED (as long as direction and magnitude do not change)

4. What about everything else?
Scalars
Scalars are quantities that show magnitude only
Examples

5. Representation System of Forces on an object Displacement
A push or a pull
Measured in Newtons
Displacement
How far from a starting point
Measured in Meters

6. Concurrent Vectors
2 or more vectors acting on a single point

7. Resultant Vector
Combined effect of concurrent vectors

8. Example
What is the resultant of the two forces?

9. Vectors at 900
Resultant?

10. Vectors at 900
“Tip-To-Tail”

11. Vectors at 900
Parallelogram

12. Equilibrant
Equal magnitude, but opposite direction of the resultant, to cause equilibrium.
1800 opposite direction

13. 3 ways to solve vector problems
Mathematically – Pythagorean Theorem (Tip-to-Tail)
Graphically – Draw to scale (Tip-to-Tail)
Experimentally – Using force tables with scales

14. Graphically 1st – Make a scale Example – 1 cm = 20 N
Draw according to scale
200 N or 10 cm
40 N or 2 cm

15. Graphically 2nd – Tip-To-Tail or Parallelogram 200 N or 10 cm

16. Graphically
3rd – Draw resultant and measure. Convert back to scale. Measure angle
200 N or 10 cm
40 N or 2 cm

17. Mathematically First - redraw Tip-To-Tail or with Parallelogram 6 N

18. Mathematically
Second – Apply Pythagorean Theorem
6 N
5 N
5 N
6 N

19. Displacement “How far you are from starting point”
Displacement vs. Distance
Distance is how far you traveled

20. Ex – You walk 10 km north and 5 km east. What is your displacement
Ex – You walk 10 km north and 5 km east. What is your displacement? What is your distance?

21. Components of Vectors
Vectors can be broken up into vertical (y) and horizontal (x) components

22. Free Body Diagrams
Represent forces acting on a figure at any given point