Chapter 1 Notes - Wikispacesphysics3310.wikispaces.com/file/view/Chapter 1 Notes.pdf/174904455... · What is PHYSICS •Chapter 1. Introduction to Physics. Physics 3310 Chapter 1

Physics 3310 Chapter 1 Notes

Mr. Kim 1

Chapter 1 NotesBy: Mr. Kim

Physics 3310-xx

• Physics is a study of natural phenomenon.• By studying natural phenomenon Physics help predict how nature will behave in one situation based on the results of experimental data obtained in another situation.

• Physics has developed out of the efforts of men and women to explain our physical environment.

What is PHYSICS•Chapter 1. Introduction to Physics


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• The first step in ensuring accuracy and reproducibility is defining the units in which the measurements are made.

• These measurements should be accurate and reproducible.

• Units are standardized values from which we make measurements

Importance of UNITS•Chapter 1. Vectors & Scalars

• On a thermometer, the algebraic signs simply mean that the temperature is either above or below 0oC and have nothing to do with east, west, or any other physical direction.

• Temperature, therefore, is not a vector. • Temperature is a scalar!

Plus and Minus Signs•Chapter 3. Vectors & Scalars


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•

3 Major Systems of Units•Chapter 1. Vectors & Scalars

SI (System International) British cgs (centimeter, gram, sec.)

1. Time ‐ second (s) 1. Time ‐ second (s) 1. Time ‐ second (s)

2. Mass ‐ kilograms (kg) 2. Mass – slug 2. Mass ‐ grams (g)

3. Length ‐meters (m) 3. Length ‐ foot (ft.) 3. Length ‐ centimeters (cm)

4. Temp. ‐ Kelvin (K) 4. Temp. ‐ Fahrenheit (F) 4. Temperature ‐ Kelvin (K)

5. Current ‐ Ampere (A) 5. Current ‐ Ampere (A) 5. Current ‐ Ampere (A)

6. Amount ‐mole (mol) 6. Amount – mole (mol) 6. Amount ‐mole (mol)

7. Luminous Intensity ‐Candela (cd)

7. Luminous Intensity ‐ ? 7. Luminous Intensity ‐ ?

•unit of length: meter (m)

•unit of mass: kilogram (kg)

•unit of time: second (s)

SI Units•Chapter 1. Intro to Physics


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METER•Chapter 1. Intro to Physics

KILOGRAM•Chapter 1. Intro to Physics


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SECOND•Chapter 1. Intro to Physics

• The fundamental unit for length is METERS.• The fundamental unit for time is SECONDS.• The fundamental unit for mass is KILOGRAMS.

Fundamental Units•Chapter 1. Intro to Physics


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• The derived unit are combination of fundamental units.

• Example: m/s, kg m/s, etc

Derived Units•Chapter 1. Intro to Physics

• Vector A, with magnitude of 3.5 m along the y-axis can be represented as 3.5 m times the unit vector along the y-axis.

Unit Vectors•Chapter 3. Vectors & Scalars

x

y

z

= 3.5 m, along y-axis

= (3.5 m)

=


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Scalar times Unit Vectors•Chapter 3. Vectors & Scalars

= (3.5 m) ̂

x

y

z

= (2.9 m

)

• To add vectors graphically in 1-D, one must add the tail of the adding vector to the head of the vector one is adding to.

Example of Vector Addition in 1-D•Chapter 3. Vectors & Scalars

A BStart Finish

R

Tail of B to head of A

N


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• R = A + B• R = 275 m, due east + 125 m, due east• R = 400 m, due east

Example of Vector Addition in 1-D•Chapter 3. Vectors & Scalars

A=275m B=125mStart Finish

R=400m

Tail of B to head of A

N

• Vectors can be added.• One must take into account both the magnitude and direction of the vectors when adding.

• = +

Vector Addition in 1-D•Chapter 3. Vectors & Scalars

= +3.5 m = +6.5 m

= +10.0 m

= + = +3.5 m +(+6.5 m ) = +10.0 m


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• The sum of the total vector is often called the resultant vector, .

• Notice the direction of + .

Vector Addition in 1-D•Chapter 3. Vectors & Scalars

= +3.5 m = +6.5 m

= +10.0 m

• Vectors can be subtracted.• One must take into account both the magnitude and direction of the vectors when adding.

• =

Vector Subtraction in 1-D•Chapter 3. Vectors & Scalars

= = +3.5 m (+6.5 m ) = 3.0 m

= +3.5 m= +6.5 m

= 3.0 m


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RECALL: Vectors Multiplied by a Scalar•Chapter 3. Vectors & Scalars

A

2A

-3A

• Negative vector can be added.• One must take into account both the magnitude and direction of the vectors when adding.

• = +

Adding a Negative Vector in 1-D•Chapter 3. Vectors & Scalars

= +3.5 m= 6.5 m

= 3.0 m

= + = +3.5 m +( 6.5 m ) = 3.0 m


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• Notice how subtracting a positive vector is same as adding a negative vector with same magnitude.

• Notice the same Resultant of = 3.0 m .

Vector Addition/Subtraction in 1-D•Chapter 3. Vectors & Scalars

= = +3.5 m (+6.5 m ) = 3.0 m

= + = +3.5 m +( 6.5 m ) = 3.0 m

= +3.5 m

= +3.5 m= 6.5 m

= +6.5 m

• To add vectors graphically in 2D, one must add the tail of the adding vector to the head of the vector one is adding to.

• A + B = R

Vector Addition in 2-D Graphically•Chapter 3. Vectors & Scalars

A

B A

BR


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• To add vectors graphically in 2D, add the tail of the adding vector to the head of the vector one is adding to.


y

x90o

= +3.0 m

= +4.0 m

= +3.0 m

= +4.0 m

= +

• The RESULTANT is drawn from the tail of the first vector to the head of the vector being added.


y

x

90o

= +3.0 m

= +4.0 m

= +

= 3.0 m 4.0 m

= +3.0 m

= +4.0 m

Cartesian Form!!


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• BUT… What about the magnitude of the RESULTANT ?

Vector in Polar Form•Chapter 3. Vectors & Scalars

y

x

90o

= +3.0 m

= +4.0 m

= +

= 3.0 m 4.0 m

represents the MAGNITUDE of

3.0 4.0

9.0 16.0

25.0 .

•BUT… What about the direction of the RESULTANT ?

Vector in Polar Form•Chapter 3. Vectors & Scalars

y

x

90o

= +3.0 m

= +4.0 m

tan

tan

tan43

.


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• Therefore!!! • The RESULTANT can be written as…

Vector in Cartesian & Polar Form•Chapter 3. Vectors & Scalars

y

x

90o

= +3.0 m

= +4.0 m

= +

= 3.0 m 4.0 m

= ,

=5.0 , 53.0

Cartesian Form!!

Polar Form!!

• Any vector may be expressed in terms of its components.• An arbitrary vector and its vector components x and y.

Vector Components•Chapter 3. Vectors & Scalars

y

x

90o

= x+ yCartesian Form!!

y

x

= R R


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• A vector can be resolved into its components.• But, how do we calculate the scalar values of R and R ?

Vector Components•Chapter 3. Vectors & Scalars

y

x

90o

y

x

= R R

• But, how can we calculate the scalar values of R and R when the magnitude, , & the direction, , of the Resultant, , is given?

Calculating Vector Components•Chapter 3. Vectors & Scalars

y

x

90o

y

x

= R R

= ,


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• If a vector, , is given in a Polar form then we can calculate the scalar values of R and R to convert it to a Cartesian form.


y

x

90o

= ,

=15.0 , 53.0Polar Form!!

y

x

Example:

• Calculating the scalar values of R .Calculating Vector Components

•Chapter 3. Vectors & Scalars

y

x

90o

=15.0 , 53.0

y

x

cosR

R cos

R 15.0 cos 53.0

R 9.0


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y

x

90o

=15.0 , 53.0

y

x

sinR

R sin

R 15.0 sin 53.0

R 12.0

• Thus, =15.0 , 53.0 can be written as… Vector in Component Form


y

x

90o

y

x

= (9.0 12.0 )m

Cartesian Form!!


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• =15.0 , 150.0Example #2 of Vector Components


y

-x

90o

y

x



y

-x

90o

=15.0 , 150.0

y

x

cosR

R cos

R 15.0 cos 150.0

R 13.0


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y

-x

90o

=15.0 , 150.0

y

x

sinR

R sin

R 15.0 sin 150.0

R 7.5

• Thus, =15.0 , 150.0 can be written as…


= ( 13.0 7.5 )my

-x

90o

y

x


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• Vectors can be added by adding their components.Adding Components of a Vector


y

x

90o

y

x90o

= A A

A A

= B B

B

B

• RECALL that to add vectors graphically in 2D, one must add the tail of the adding vector to the head of the vector one is adding to.

• A + B = R


A

B A

BR


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• Adding vectors in a component form.Adding Components of a Vectors


y

x

90o

= A A

A A

= B B

B

B

=

= (A A B B

= (A B A B

= (A B A B



y

x90o

= A A

A A

= B B

B

B

=

= (A A B B

= (A B A B

= (A B A B


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y

x

90o

A A

B

B R = A B

R = (A B

A B

A



y

x

90o

A A

B

B

R = A B

= (A B A B

= (R R

R = (A B

A B


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• An EXAMPLE of adding vectors in a component form.Adding Components of a Vectors


In Figure on the next slide, a position vector, , has a magnitude of 145 m and is oriented 20.0o clockwise from the vertical. Another position vector, , has a magnitude of 105 m and points 35.0o below the horizontal. Determine the magnitude and direction of the resultant vector, , by means of components. =



=

20.0o

35.0o

+x

+y

Ay

Ax Bx

By


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Vector x Component y Component

Ax = (145 m) sin 20.0o

Ax = 49.6 m

Ay = (145 m) cos 20.0o

Ay = 136 m

Bx = (105 m) cos -35.0o

Bx = 86.0 m

By = (105 m) sin -35.0o

By = -60.2 m

Rx = Ax + Bx

Rx = 135.6 m

Ry = Ay + By

Ry = 75.8 m

• Thus, can be written as… Adding Vector Components


= (135.6 75.8 )m

+x

+y

= (R R

R

R


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• Now let’s convert to polar form… Cartesian to Polar Form


= (135.6 75.8 )m+y

+x

R

R

represents the MAGNITUDE of

R R

135.6 75.8

18387.4 5745.6

24133.0

.

Cartesian to Polar Form•Chapter 3. Vectors & Scalars

= (135.6 75.8 )m

+y

+x

R

R

• BUT!!! • What about the direction of the RESULTANT ?

tanR

R

tanR

R

tan75.8135.6

.


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• Thus, can be written as… Adding Vector Components


= (135.6 75.8 )m

= . , .

=

+x

+y

• Strategy 1:Strategies for Adding Vector Components


Determine the x and y components for each vector to be added.

Be sure to take into consideration the directions of the components by using plus and minus signs to denote whether the components point along the positive or negative axis.


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Find the algebraic sum of the x components, which is the x component of the resultant vector.

Similarly, find the algebraic sum of the ycomponents, which is the y component of the resultant vector.

Write the resultant vector in a Cartesian Form.



Use the x and y components of the resultant vector and the Pythagorean theorem to determine the magnitude of the resultant vector.


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Use either the inverse sine, inverse cosine, or inverse tangent function to find the angle that specifies the direction of the resultant vector.

END of Chapter 3 Vector Notes

Please make sure that your Homework Packet is completed before the unit test!

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Chapter 1 Notes - Wikispacesphysics3310.wikispaces.com/file/view/Chapter 1 Notes.pdf/174904455... · What is PHYSICS •Chapter 1. Introduction to Physics. Physics 3310 Chapter 1