Vector & Scalar Quantities

Characteristics of a Scalar Quantity Only has magnitude Requires 2 things: 1. A value 2. Appropriate units Ex. Mass: 5kg Temp: 21° C Speed: 65 mph

Characteristics of a Vector Quantity Has magnitude & direction Requires 3 things: 1. A value 2. Appropriate units 3. A direction! Ex. Acceleration: 9.8 m/s2 down Velocity: 25 mph West

More about Vectors A vector is represented on paper by an arrow 1. the length represents magnitude 2. the arrow faces the direction of motion 3. a vector can be “picked up” and moved on the paper as long as the length and direction its pointing does not change

Graphical Representation of a Vector The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must: Pick a scale to represent the vectors. Make it simple yet appropriate. Draw the tip of the vector as an arrow pointing in the appropriate direction. Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical.

Vector Directions

Understanding Vector Directions To accurately draw a given vector, start at the second direction and move the given degrees to the first direction. N 30° N of E W E Start on the East origin and turn 30° to the North S

Graphical Representation Practice 5.0 m/s East (suggested scale: 1 cm = 1 m/s) 300 Newtons 60° South of East (suggested scale: 1 cm = 100 N) 0.40 m 25° East of North (suggested scale: 5 cm = 0.1 m)

Graphical Addition of Vectors Tip-To-Tail Method Pick appropriate scale, write it down. Use a ruler & protractor, draw 1st vector to scale in appropriate direction, label. Start at tip of 1st vector, draw 2nd vector to scale, label. Connect the vectors starting at the tail end of the 1st and ending with the tip of the last vector. This = sum of the original vectors, its called the resultant vector.

Graphical Addition of Vectors (cont.) Tip-To-Tail Method 5. Measure the magnitude of R.V. with a ruler. Use your scale and convert this length to its actual amt. and record with units. 6. Measure the direction of R.V. with a protractor and add this value along with the direction after the magnitude.

Graphical Addition of Vectors (cont.) 5 Km Scale: Create a scale! 3 Km Resultant Vector (red) = 6 cm, therefore its 6 km.

Vector Addition Example #1 Use a graphical representation to solve the following: A hiker walks 1 km west, then 2 km south, then 3 km west. What is the sum of his distance traveled using a graphical representation?

Vector Addition Example #1 (cont.) Answer = ????????

Vector Addition Example #2 Use a graphical representation to solve the following: Another hiker walks 2 km south and 4 km west. What is the sum of her distance traveled using a graphical representation? How does it compare to hiker #1?

Vector Addition Example #2 (cont.) Answer = ????????

Mathematical Addition of Vectors Vectors in the same direction: Add the 2 magnitudes, keep the direction the same. Ex. + = 3m E 1m E 4m E

Mathematical Addition of Vectors Vectors in opposite directions Subtract the 2 magnitudes, direction is the same as the greater vector. Ex. 4m S + 2m N = 2m S

Mathematical Addition of Vectors Vectors that meet at 90° Resultant vector will be hypotenuse of a right triangle. Use trig functions and Pythagorean Theorem.