Post on 20-Jan-2016
Scalar & Vector Quantities
SCALAR QUANTITIES
•Described by a single number and unit of measurement.•Gives the magnitude (size)Examples
Mass = 20 gTime = 20.0 sTemperature = 20oC Speed = 20 m/s
VECTOR QUANTITIES••Arrows are usedArrows are used••Described by a single number and aDescribed by a single number and a unit of measurement (scalar)unit of measurement (scalar)••Indicated direction. (head of arrow)Indicated direction. (head of arrow)
ExamplesExamples30 m/s, East30 m/s, East30 m/s, N of E30 m/s, N of E
DETERMINING DIRECTION
B A
CD
N of E
N of W
S of WS of E
ADDITION OF COLLINEAR VECTORS
Resultant vector Resultant vector represent the total of two or more represent the total of two or more
vectorsvectorsdrawn from the tail of the lst vectordrawn from the tail of the lst vector to the head of the last vectorto the head of the last vector
VECTORS ACTING IN THE SAME DIRECTION
Connect them head-to-tail and add
Always indicate the direction of the the resultant
10 km 10 km
R = 20 km, 0o E
VECTORS ACTING IN OPPOSITE DIRECTIONS
Connect them tail to tail Connect them tail to tail
SubtractSubtract
20 km 10 km
R = 10 km, 0o, W
VECTORS ACTING AT ARIGHT ANGLE TO EACH
OTHER
••Connect head-to-tailConnect head-to-tail••Draw resultant from the tail of the lst Draw resultant from the tail of the lst vector to the head of the second vector.vector to the head of the second vector.••Determine resultant using pythagorean Determine resultant using pythagorean theoremtheorem••Determine angular direction by using theDetermine angular direction by using the tan functiontan function
Pythagorean Theorem
• C2 = a2 + b2
• C = hypotenuse
• A & B are sides
20 km
10 km
or20 km
10 km
10 km
20 km
R2 = (10 km)2 + (20 km)2
R = 22 km = 20 km
Determine angle makes with the X-axis.Use the correct number of significant figures.
Tan = Y X
= 20 km 10km
= 2
= 63o = 60o
Trig of the Right Triangle
Ө
hypotenuse
Adjacent side
Opposite side
SOH
Sin Ө = opposite side
hypotenuse
CAH
Cos Ө = adjacent side
hypotenuse
TOA
• Tan Ө = opposite side
adjacent side
NON-COLLINEAR VECTORS
A.A. Draw vectors on x-y axisDraw vectors on x-y axisB.B. Determine the X & Y components of Determine the X & Y components of each vectoreach vector
a. X-component = use Cos functiona. X-component = use Cos function b. Y-component = use Sin functionb. Y-component = use Sin function
c. Theta is 0c. Theta is 0oo if vector is located on X-axis if vector is located on X-axis d. Theta is 90d. Theta is 90oo if vector is located on Y-axis if vector is located on Y-axis
C. Indicate direction of vectors (+) and (-)C. Indicate direction of vectors (+) and (-)
D. Add X-components
E. Add Y-components
F. Draw vectors representing the sum of the components head-to-tail. Signs (+) and (-) represents the direction of vectors.
G. Draw Resultant
H. Calculate R using Pythagorean Theorem
I. Calculate theta
J. Indicate direction relative to N, E, S or W
EXAMPLE
Walk due west for 52 paces, then walk 30.0Walk due west for 52 paces, then walk 30.0oo North of West for 42 paces, and then walkNorth of West for 42 paces, and then walk due north for 25 paces.What are thedue north for 25 paces.What are the magnitude and direction of the magnitude and direction of the resultant, Rresultant, R
VECTOR DIAGRAM
42 25
52
TABLEPACESPACES ØØ XX YY
5252 0.00.0 -52-52 00
4242 30.030.0 -36-36 2121
2525 90.090.0 00 2525
SumSum -88-88 4646
DETERMINING DIRECTION OF RESULTANT
DRAW TRIANGLE USING SUMS OF X- DRAW TRIANGLE USING SUMS OF X- AND Y-COMPONENTSAND Y-COMPONENTS
R
88 Paces
46 Paces N of W
VALUE OF RESULTANT
Use Pythagorean TheoremUse Pythagorean Theorem
RR22 = (88 paces) = (88 paces)22 + (46 paces) + (46 paces)22
R = 99 pacesR = 99 paces
Angular Direction
Use tan functionUse tan function
tan tan = 46 paces = 46 paces 88 paces88 paces
Ø = 28Ø = 28oo
FINAL ANSWER
99 Paces, 2899 Paces, 28oo, N of W, N of W
Units of Measurements
MKS: meters (m), Kilogram (kg), second (s)
kilometer (km), hour (h)
CGS: centimeter (cm), gram (g), second (s)
FPS: foot (ft.), pound (lb.), second (s)
miles (mi.), hour (h)