Vectors and Scalars

Physics

Bell Ringer 10/13/15 Answer the following on your bell ringer

sheet:

1. Is displacement a vector or scalar? 2. What is the difference between vectors & scalars?

NB: Don’t forget to write your objective in your notebook before we start.

Scalar

A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.

Magnitude – A numerical value

Scalar Example

Magnitude

Speed 20 m/s

Distance 10 m

Age 15 years

Heat 1000 calories

Vector

A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.

Vector Magnitude & Direction

Velocity 20 m/s, N

Acceleration 10 m/s/s, E

Force 5 N, West

Faxv ,,,

Objective

We will use a treasure hunt activity to create a vector addition map

I will map the course taken and add vectors to find the resultant.

3F “ graphical vector addition”

Agenda

Cornell Notes- Essential Questions Vector treasure hunt Vector Map

Cornell Notes Essential Questions:

What is a vector? How do we represent vectors? How do we draw a vector?

What shows the magnitude? What shows the direction?

When should vectors be added? When should vectors be subtracted? What is the resultant vector?

Vectors

Vectors Quantities can be represented with;

1. Arrows2. Signs (+ or -) 1-D motion3. Angles and Definite Directions

(North, South, East, West)

Vectors Every Vector

TailHead

Vectors are illustrated by drawing an ARROW above the symbol. The head of the arrow is used to show the direction and size of the arrow shows the magnitude

Vector AdditionVECTOR ADDITION – If 2 similar vectors point in

the SAME direction, add them.

Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started?

54.5 m, E 30 m, E+

84.5 m, E

Vector Subtraction

VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.

Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?

54.5 m, E

30 m, W-

24.5 m, E

Resultant

The vector representing the sum of two or more vectors is called the resultant vector.

Vector Treasure Hunt Create directions that lead to a specific

object/picture. You must have at least 4 turns. Generate a map from your origin ( door) to

your picture. Write each direction on an index card. Scramble the index cards and follow them

again. Then,( tomorrow) Create a vector map of total

displacement

CompassFront of

room

Back of room

Front door

Teacher Model

Directions to object with at least 4 turns from the front door.

Create a Map

Map drawn to scale.

ExampleYou walk 35 meters east then 20 meters north. You walk another 12 meters west

then 6 meters south. Calculate the Your displacement.

35 m, E

20 m, N

12 m, W

6 m, S

- =23 m, E

- =14 m, N

23 m, E

14 m, NR

Vector Map

Resulta

nt

25 ft South

50 ft

Ea

st

Expectation

Groups of 3-4 2 minutes to find the picture 10 minutes back track steps and create

directions on index cards 2 mins Shuffle cards Try to locate object from directions. 10 mins draw map to scale

Group Pictures

Group1- gorilla Group2- snake Group 3- rat Group 4- eagle Group 5- alligator Group 6- chicken Group 7- pig Group 8- dog

END

10/15/15 Bell Ringer ( 5 minutes!!) Get back to your

groups. 1.On large paper,

create a title, 2. Create a map of

your directions from origin to picture.

3. Create a Vector map by Summing up the vectors to find the horizontal and vertical components. Draw your resultant.

Write your names & turn in to teacher

ExampleYou walk 35 meters east then 20 meters north. You walk another 12 meters west

then 6 meters south. Calculate the Your displacement.

35 m, E

20 m, N

12 m, W

6 m, S

- =23 m, E

- =14 m, N

23 m, E

14 m, NR

Bell Ringer 10/15/15 4 minutes You walked 15 m east

from the door, then you walked 6 m south, then you turned around and walked back west 2 m, and another 6 meters west then you walked North 7 m.

Draw a vector diagram to show the motion and find the resultant.

Lesson objectives

We will use Pythagorean theorem to find the resultant, horizontal, and vertical components of vectors.

I will resolve a vector into its vertical and horizontal components and find the resultant using Pythagorean theorem.

Agenda Bell ringer Problems 1-4

Diagrams only Pythagorean theorem

( Solve for R) Grade papers Right angle triangles & Trig

functions

Note: You Need a calculator today & your notebook

Vector Addition Worksheet

Using Calculators Make sure it is in

degrees Locate the Sin, Cos,

& Tan buttons. Locate the 2nd button. Locate the Tan-1

Button.

Vectors

95 km,E

55 km, N

Start

Finish

A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics

is called the RESULTANT.

Horizontal Component

Vertical Component kmc

c

bacbac

8.10912050

5595Resultant 22

22222

Vectors

95 km,E

55 km, N

Start

Finish

A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics

is called the RESULTANT.

Horizontal Component

Vertical Component kmc

c

bacbac

8.10912050

5595Resultant 22

22222

Vectors

95 km,E

55 km, N

Start

Finish

A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics

is called the RESULTANT.

Horizontal Component

Vertical Component kmc

c

bacbac

8.10912050

5595Resultant 22

22222

BUT……what about the direction?In the previous example, DISPLACEMENT was asked for

and since it is a VECTOR we should include a DIRECTION on our final answer.

NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.

N

S

EW

N of E

E of N

S of W

W of S

N of W

W of N

S of E

E of S

N E

Bell Ringer 10/16/15 Its Friday!!!!! Check your grade in skyward. Write down

your current 2nd 6 weeks grade and your semester grade average.

Turn in Bell Ringer sheet.

Remember: Tests must be made up within a week of the test. Monday 10/19 is the deadline. Also late policy is in effect!

Agenda Review right angle triangle & Trig

functions ( SOH CAH TOA) How to enter Sin,Cos,Tan examples How to enter Sin-1,Cos-1, Tan-1

examples Example problems

How to find missing sides. How to find missing angles

Complete problems on your own

Note: You Need a calculator today

Lesson objectives

We will use trigonometry to find the missing side and the angles from right angle vector diagrams.

I will find the missing angle and missing side using trigonometry: Sine, Cosine, and Tangent functions.

Using Calculators Make sure it is in

degrees Locate the Sin, Cos,

& Tan buttons. Locate the 2nd button. Locate the Tan-1

Button.

Using Calculators Example 1: Use your

calculator to find the sin, cos, or tan or any angle.

Example 2: use your calculator to find the angle using the inverse ( Sin-1, Cos-1,& Tan-1)

Right angle triangle, 90Adjacent- Near the angle

Hypotenuse- the longest side

Opposite- opposite the angle

What if you are missing a side?

Which do I use?

What if you are missing a side?

Which will you use to find the missing sides? Pythagorean theorem or SOHCAH TOA?

Which do I use?

Trig triangles

What if you are looking for the angle? To find the value of the angle we use a Trig

function called the Inverse.

Which sides do we have?Which function do we use?

What if you are looking for the angle? To find the value of the angle we use a Trig

function called the Inverse.

What if you are looking for the angle?

Worksheet: Lesson 1

Reviewing the Primary Trigonometric ratios

Examples

What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What

were his horizontal and vertical components?

65 m25

H.C. = ?

V.C = ?

The goal: ALWAYS MAKE A RIGHT TRIANGLE!

To solve for components, we often use the trig functions since and cosine.

EmCHoppNmCVadj

hypopphypadjhypotenuse

sideoppositehypotenuse

sideadjacent

,47.2725sin65..,91.5825cos65..

sincos

sinecosine

SOH- CAH - TOA!!!!Let’s

identify the sides

What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What

were his horizontal and vertical components?

65 m25

H.C. = ?

V.C = ?

The goal: ALWAYS MAKE A RIGHT TRIANGLE!

To solve for components, we often use the trig functions since and cosine.

EmCHoppNmCVadj

hypopphypadjhypotenuse

sideoppositehypotenuse

sideadjacent

,47.2725sin65..,91.5825cos65..

sincos

sinecosine

SOH- CAH - TOA!!!!

What if you are missing a component?Suppose a person walked 65 m, 25 degrees East of North. What

were his horizontal and vertical components?

65 m25

H.C. = ?

V.C = ?

The goal: ALWAYS MAKE A RIGHT TRIANGLE!

To solve for components, we often use the trig functions since and cosine.

EmCHoppNmCVadj

hypopphypadjhypotenuse

sideoppositehypotenuse

sideadjacent

,47.2725sin65..,91.5825cos65..

sincos

sinecosine

BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough

for the direction. We MUST find the VALUE of the angle.

N of E

55 km, N

95 km,E

To find the value of the angle we use a Trig function called the Inverse.

30)5789.0(

5789.09555

1

Tan

sideadjacentsideoppositeTan

109.8 km

So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough

for the direction. We MUST find the VALUE of the angle.

N of E

55 km, N

95 km,E

To find the value of the angle we use a Trig function called the Inverse.

30)5789.0(

5789.09555

1

Tan

sideadjacentsideoppositeTan

109.8 km

109.8 km, 30 degrees North of East

BUT…..what about the VALUE of the angle???Just putting North of East on the answer is NOT specific enough

for the direction. We MUST find the VALUE of the angle.

N of E

55 km, N

95 km,E

.

30)5789.0(

5789.09555

1

Tan

sideadjacentsideoppositeTan

109.8 km

So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

ExampleA bear, searching for food wanders 35 meters east then 20 meters north.

Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.

35 m, E

20 m, N

12 m, W

6 m, S

- =23 m, E

- =14 m, N

23 m, E

14 m, N

3.31)6087.0(

6087.2314

93.262314

1

22

Tan

Tan

mR

The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST

R

ExampleA boat moves with a velocity of 15 m/s, N in a river which

flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.

15 m/s, N

8.0 m/s, W

Rv

1.28)5333.0(

5333.0158

/17158

1

22

Tan

Tan

smRv

The Final Answer : 17 m/s, @ 28.1 degrees West of North

ExampleA plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate

the plane's horizontal and vertical velocity components.

63.5 m/s

32

H.C. =?

V.C. = ?

SsmCVoppEsmCHadj

hypopphypadjhypotenuse

sideoppositehypotenuse

sideadjacent

,/64.3332sin5.63..,/85.5332cos5.63..

sincos

sinecosine

ExampleA storm system moves 5000 km due east, then shifts course at 40

degrees North of East for 1500 km. Calculate the storm's resultant displacement.

NkmCVoppEkmCHadj

hypopphypadjhypotenuse

sideoppositehypotenuse

sideadjacent

,2.96440sin1500..,1.114940cos1500..

sincos

sinecosine

5000 km, E

40

1500 km

H.C.

V.C.

5000 km + 1149.1 km = 6149.1 km

6149.1 km

964.2 kmR

91.8)364.0(

157.01.6149

2.96414.62242.9641.6149

1

22

Tan

Tan

kmR

The Final Answer: 6224.14 km @ 8.91 degrees, North of East

Hmm. That was good.

Holy Snakes!!!

It’s a bird, it’s a plane, It’s Super Rat!

Do I look like I’m playing?

Gator’s anyone?

Don’t be a chicken??

Do you think I’m cute? Yes or Nah? Yessss!!!!

What a time to be alive?