Vectors

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

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

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

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

Concurrent Vectors 2 or more vectors acting on a single point

Resultant Vector Combined effect of concurrent vectors

Example What is the resultant of the two forces?

Vectors at 900 Resultant?

Vectors at 900 “Tip-To-Tail”

Vectors at 900 Parallelogram

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

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

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

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

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

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

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

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

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?

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

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