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Vectors and Scalars AP Physics B Vectors and Scalars AP Physics B

Vectors and Scalars AP Physics B - PowerPoint Presentation

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Vectors and Scalars AP Physics B - PPT Presentation

Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE but NOT a direction associated with it Magnitude A numerical value with units Scalar Example Magnitude Speed 20 ms ID: 642991

north east vectors direction east north direction vectors meters calculate magnitude degrees answer displacement velocity vector final components west

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Slide1

Vectors and Scalars

AP Physics BSlide2

Scalar

A

SCALAR

is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.Magnitude – A numerical value with units.

Scalar Example

Magnitude

Speed

20 m/s

Distance

10 m

Age

15 years

Heat

1000 caloriesSlide3

Vector

A

VECTOR

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

Vector

Magnitude & Direction

Velocity

20 m/s, NAcceleration10 m/s/s, EForce5 N, West

Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.Slide4

Applications of Vectors

VECTOR ADDITION (Graphically)

– If 2 similar vectors point in the SAME direction,

draw them tip to tail, then measure RESULTANT.

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

Notice that the SIZE of the arrow conveys

MAGNITUDE

and the way it was drawn conveys DIRECTION.Slide5

Applications of Vectors

VECTOR ADDITION (mathematically)

– 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

Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.Slide6

Applications of Vectors

VECTOR SUBTRACTION (Graphically)

- If 2 vectors are going in opposite directions, you

draw them tip to tail them measure the RESULTANT.Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?Slide7

Applications of Vectors

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, ESlide8

Non-Collinear Vectors - Graphically

When 2 vectors are

perpendicular

, you must use the Tip to tail method still.

95 km,E

55 km, N

Start

FinishA man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics is called the RESULTANT.

The LEGS of the triangle are called the COMPONENTS

Horizontal Component

Vertical ComponentSlide9

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

Tip to tail

.

N

SEW

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 of ESlide10

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

qSlide11

Non-Collinear Vectors - Mathematically

When 2 vectors are

perpendicular

, you must use the Pythagorean theorem.

95 km,E

55 km, N

Start

FinishA man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.The hypotenuse in Physics is called the RESULTANT.

The LEGS of the triangle are called the COMPONENTS

Horizontal Component

Vertical ComponentSlide12

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 TANGENT.

q

109.77 km

So the COMPLETE final answer is :

109.77

km,

30.07

degrees North of EastSlide13
Slide14

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 m

25

H.C. = ?

V.C = ?

The goal:

ALWAYS MAKE A RIGHT TRIANGLE!To solve for components, we often use the trig functions sine and cosine.Slide15

Example

A 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

The Final Answer:

26.93 m, 31.3 degrees NORTH of EAST

R

qSlide16

Example

A 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

R

v

q

The Final Answer : 17 m/s, @ 28.07 degrees West of NorthSlide17

Example

A 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. = ?Slide18

Example

A 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.

5000 km, E

40

1500 km

H.C.

V.C.

5000 km + 1149.1 km = 6149.1 km

6149.1 km

964.2 km

R

q

The Final Answer:

6224.14 km @ 8.91 degrees, North of EastSlide19

.

 

                                                                                                      

First, let’s talk about Mr Morris’s boat…

If the boat has a speed of 10 m/s

in still water and

the current is 5 m/s, what is the resultant velocity of the boat? Slide20

If the boat has a speed of 10

m/s in still water

and the current is

5

m/s, what is the resultant velocity of the

boat with respect to the riverbank?

10 m/s across

5 m/s downstreamVRVR =√10 2 + 52 = 11.18 m/s

Θ

Θ

=

Tan

-1

(10/5)

=

63.43º

w/riverbankSlide21

How long to travel across the 120 m wide river?

The time to cross depends on the

speed across

the river.

t =

d

v

= 120 m 10m/s = 12 secHow far downstream will the boat land on the far bank?The distance downstream depends on the downstream current speed and the time in the water.d = vt= (5 m/s)(12sec) = 60 m downstream