Kinematics and Dynamics KD1 Vectors

Scalar vs. Vector Scalar-Quantity having magnitude only (no direction) Ex: Temp., mass, time, speed Vector-Quantity having magnitude AND direction Ex: Force, displacement, velocity, acceleration

Examples: Scalar or Vector? 1) 15 m/s up 2) 21 degrees F 3) 100 watts 4) 50 km N of W 5) 75 mi/hr Vector Scalar

3 Ways to Represent Vectors 1. Symbols: 2. Words: 250 m/s East 3. Arrows drawn to scale Need: a) direction indicator b) scale: 1 cm=50 m/s c) directional arrow drawn proper length

Example: Represent 250 m/s E : a) direction indicator b) scale: 1 cm= 50 m/s c) directional arrow drawn proper length 5 (50 m/s)=250 m/s E 5 cm

Vectors Length of arrow=magnitude Head of arrow=direction

Vectors Components-Vectors whose sum is the resultant can be simplified into horizontal (X) and vertical (Y) vectors Resultant-The vector sum of 2 or more components

2 Ways of Finding the Resultant Vector 1. Graphical Method-uses a scale vector drawing Always add vectors “tail” to “head” Resultant is drawn from “tail” of 1st to “head” of last vector EXAMPLES! R

Graphical Method When subtracting vectors, change subtraction to addition A – B = A + (-B) The negative (-B) changes the direction of the vector Negative vectors: ADD the OPPOSITE direction of the original vector

2 Ways of Finding the Resultant Vector 2. Component Method-Uses calculations to find resultant

Trig. Review (Right angles) Sin= Cos= Tan= Pythagorean Theorem Coordinate System Opp / Hyp Adj / Hyp Opp / Adj a2 + b2 = c2

Trig. All vectors can be broken down into horizontal (x) and vertical (y) components Example: F=58 N Fy 30 Fx

Checks Which color of the Triangle represents the hypotenuse? Blue Which color of the Triangle represents the opposite side? Which color of the Triangle represents the adjacent side? Which color represents the X coordinate? Which color represents the Y coordinate? Blue Green Red

Distance vs. Displacement How far something move without regards to the direction (example - 3 miles east and 4 miles north is a total distance of 7 miles) The change in position of something WITH respects to the direction (example - 3 miles east and 4 miles north is a total displacement of 5 miles North East Distance- Displacement-

Steps to Add Vectors by Component Method 1) Break down each vector into x and y components 2) Add similar components Add all “x” components Add all “y” components 3) Use Pythagorean theorem to find magnitude of resultant 4) Use tangent function to find angle and direction of resultant

EXAMPLES! + = – =

Examples Given the scale and the RED arrow, describe the vector in words (use both magnitude and direction) 1 cm = 5 m/s Presume the red arrow is 7 cm Answer = 35 m/s @ 33˚ S of W OR 35 m/s @ 57˚ W of S

Examples Calculate the horizontal (X) and vertical (Y) components. The vector is representing 35 m/s @ 33˚ S of W Sin θ = opp / hyp Sin 33 = opp / 35 .545 = opp / 35 Opp (Y) = 19 m/s Cos θ = adj / hyp Cos 33 = adj / 35 .839 = adj / 35 Adj (X) = 29 m/s