Vectors Physics 30S

How to Get from A to B? Task: Measure the distance from the door hinge to the supply room Materials: – Metre stick – Paper and pencil

How to Get from A to B – Part 2 Task: Confirm your results by measuring again, without a ruler. Your second measurement should be within 5 cm. You may use the length of the tile is ____________. Materials: – Paper and pencil – Calculator

Is it enough? Travel your measured distance. Are you back at the supply room? Will that distance always get you to the supply room?

What is a Vector? What is not a vector? Most numbers so far have not been vectors; they are scalars. – For example: 5, 7.5, ½, -13, π, etc Vectors are different because they have a direction!

Vector Notation On paper, vectors are signified with a half arrow above a capital letter In printed text, vectors are signified with a bolded capital letter – A

Vocabulary Scalar: magnitude only – Example: 4 out of 5, 23°C, 3 Vectors: magnitude and a direction, with a unit – 3 tiles right, 5 metres left, 0.5 cm up

More about Vectors To specify a direction, we need a starting point, called a reference point Reference point: zero location in a coordinate system or frame of reference Position: the location of an object in relation to the reference point

What’s the Difference? Total distance travelled: sum total of actual steps taken; length of the path – scalar Displacement: shortest distance back to the start – vector Speed: how fast an object is moving – scalar Velocity: how fast an object is moving in a specified direction – vector

Homework 1. Write out the directions for how you got to school this morning. There should be enough detail for someone to follow the directions on a map! 2. Identify every vector in your writing in a list following your directions. Label these vectors D 1, D 2, D 3, etc. 3. Vector Worksheet #1, 2

Significant Figures How long is the board? PersonValue measured for length cm cm cm Is there a difference?

Does it Matter? Recreate the net. Base of the square: 7.6 cm Height of the triangle: 10.7 cm

Does it Matter? Here are the actual measurements: Base: 7.6 (7.6200) Height: 10.7 ( )

Significant Figures Significant figures are an attempt to know how exact is a measurement – AKA. Sig figs For example, is the measurement 10.7, 10.67, , or ?

Definition Definition: Significant digits are those digits in a measurement that are known for certain plus one uncertain digit. When taking a measurement, record the last division plus estimate one more digit.

Practice Measurements A) B) Width of your page C) Overhead items

Rules for Sig Figs 1. All non zero digits are significant. – 374 (3 sig figs) – 8.1 (2 sig figs) 2. All zeroes between other significant digits are significant. – (5) – (4) 3. Leading zeroes in a decimal are not significant. – 0.54 (2) – (2) 4. Trailing zeroes are significant if they are to the right of a decimal point. – 2370 (3) – (2) – (4) 5. Without a decimal, trailing zeroes are not significant. – (2)

What to Do About Zeroes? In general: If the zero is a placeholder, it is not significant. If the zero does not need to be there, then it is significant

Scientific Notation What if we know 5000 to 4 significant figures? Use scientific notation: x 10 3 Rule: Count the significant figures in the significand (leading number)

Practice Counting A) 1174 km, NB) 5430 N, up C) 9.8 m/s 2, downD) N, down E) 3.00 x 10 8 m/s, rightF) 909 cm, left G) N, leftH) μm, right Answers: A) 4 B) 3 C) 2 D) 1 E) 3F) 3G) 5H) 7

Using Sig Figs in Calculations The least number of sig figs given is the number of sig figs that should be stated in the answer. Always round sig figs at the end of the question, not at each step!

Practice Calculations A)5.2 x 10.3 = B) = C)65 – = D) / 60 = E)( ) x 10.5 = Answers: A) 54B) 22C) 65D) 10E) 200

Homework Pg.11 Glencoe Physics Study Guide Sig Figs Worksheet – #4-14

Distance vs. Displacement Total distance travelled: sum total of actual steps taken; length of the path – Scalar Displacement: shortest distance back to the start – Vector – Displacement is the final position minus the initial position

Drawing Vectors Vectors are represented by an arrow Length of the arrow = magnitude Arrow points in the direction of the vector Must be drawn to scale – Scale must be indicated Must draw a compass to indicate directions 1 cm = 5 N

Directional Notation Degrees direction (N/S) of direction (E/W) – 25° S of E Direction (N/S) degrees direction (E/W) – S25 ° E Standard position angle

Multiplying Vectors by a Scalar Multiplying by a scalar multiplies the magnitude Multiplying by a negative reverses the direction

Examples Draw a) A b) 2A c) –A d) -3A 1 cm = 10 N

More Examples Draw a) A b) 1.5 A c) -2.5 A 1 cm = 3 m/s

Homework Learning Activity 2.2 – Pg. 15 Handout (Distance Ed)

Adding Vectors Graphically (Tail to Tip method): Draw one vector. Draw the next vector at the tip of the first vector. Draw a new resultant vector from the reference point to the end of the last vector Measure the length and direction of the new resultant vector

Example A + B 1 cm = 5 m/s A + B

Practice Add these vectors using the tail to tip method a) A + B b) A – C c) A + B + C

Adding Vectors Algebraically: 1 Dimension Designate one direction as positive. All vectors going in this direction will be positive. The opposite direction will be negative. All vectors going in this direction will be negative. Sum the magnitude of the vectors together and interpret the direction!

Example A + B Let E be positive. A is positive. B is negative. 1 N - 2N = -1N A + B = -1 N A + B = 1 N, W

Homework Add the following vectors using tail to tip method: 1.A + B 2.C + D Add the following vectors algebraically: 3.A + C 4.B - D

Adding Vectors Algebraically: 2 Dimensional Perpendicular Think back to tail to tip method We can solve for W by using Pythagorean Theorem!

Steps Step 1: Draw a quick sketch. Step 2: Solve for the magnitude using Pythagorean theorem. Step 3: Sketch in the resultant vector. Step 4: Solve for the direction using trigonometry. Step 5: Remember sig figs!

Example 1 A + B Step 1: Draw a quick sketch. Step 2: Solve for the magnitude using Pythagorean theorem. Step 3: Sketch in the resultant vector. Step 4: Solve for the direction using trigonometry. Step 5: Remember sig figs!

Example 2 C + D

Example 3 C - D

Homework Assignment 2.1 (Distance Ed – P.45) #1,2

Vectors Lab

Review A Vector Journey (Distance Ed. Pg ) Done with Sig figs Sig fig practice

The Plan Max Classes: 8 1.What is a vector? 2.Sig figs 3.Drawing vectors/multiply by a scalar 4.Adding vectors (tail to tip and algebraic in one dimension) 5.Adding vectors (2D) 6.Vectors Lab and how to do a lab write up 7.Review 8.Test