6/28/2011

1

PHY 2053: College Physics

� Chapters 1 to Chapters 9

� Three tests: Every Thursday

� Test I: Chapters 1 - 3

�Test II : Chapters 4 - 6

�Test III : Chapters 7 - 9

WebAssign: Homework every week

Laboratory: 11% of the total grade

Text:

Cutnell & Johnson, 8e

Instructor: Aniket Bhattacharyawww.physics.ucf.edu/~aniket/phy2053.html

Physics

Physics is an old subject

Physics tries to explain physical ( and

more recently biological ) world in

terms of a small number laws

Technology <=> physics

Understanding fundamental

principles of physics is important for

better technology, better living

Historical Facts

Planetary Motions: Galileo, Copernicus, Newton

Transportation, machines, rockets ….

Electromagnetism : James Clark Maxwell

Telecommunication, Medical application (X-ray

and Imaging)

Physics plays the most important role in

developing technologies

Chapter 1:

� Units

� Review of algebra and trigonometry

� scalars and vectors

� Addition and subtraction of vectors

Test-I will cover chapters 1, 2, and 3

(Thursday July 7: 3:00 pm – 4:40 pm)

Measurements & Units

To begin we need three things to measure:

�How long (large) is some object ? (length)

�How heavy or light it is (weight)

�How fast does it move (time elapsed)

Other quantities (as we will see later) can be

derived from these three basic quantities

What do we measure ?

Units of measurements

1 meter = 100 cm

1 cm = 1/100 meter = 0.01 meter

1 foot = 0.3048 meter= 381/1250 meter

1 meter = 3.28 feet

1 kilogram = 1000 gram

1 gram = 1/1000 kilogram = 0.001 kilogram

I slug = 14.59 kilogram

1 kilogram = 0.0685 slug

6/28/2011

2

Abbreviation

gram -> g

kilogram -> kg

meter -> m

kilometer -> km

second - > s

International Systems (SI) of Units

Unit of length: Meter (m)The meter is the length of the path travelled by light in vacuum during a

time interval of 1/299792458 = 1/(30000000) of a second.

Unit of mass: Kilogram (kg)The kilogram is the unit of mass; it is equal to the mass of the

international prototype of the kilogram.

Unit of time: second (s)

http://physics.nist.gov/cuu/Units/current.html

the second is the duration of 9 192 631 770 periods of the radiation

corresponding to the transition between the two hyperfine levels of the

ground state of the cesium 133 atom.

Unit of length

The standard Platinum-Irridium metal bar

Different units of length

Unit of mass

This international prototype, made of platinum-iridium

Time: Atomic Clock

The second is the duration of 9 192 631 770 periods of the radiation

corresponding to the transition between the two hyperfine levels of

the ground state of the cesium 133 atom.

The atomic clock (NIST-FI) is

considered to be one of the most

accurate clock. It keeps time with an

uncertainty of one second in twenty

million years.

6/28/2011

3

Physical quantities and dimension

Examples: A car is moving with a certain speed, say 60 miles per hour

Speed is a physical quantity that one can measure. How do we

measure ? Well, we take a stop watch, let the car go for a certain

distance and measure the distance and the time elapsed.

What is the dimension of speed ?

distance [L]speed

time elapsed [T]

Length

Time= = =

Speed has the dimension of (length / time)

Other examples

Physical Quantity Dimension Unit

Area [L2] m2

Volume [L3] m3

Mass density M/L3 Kg/m3

1 ft = 0.3048 m

1 mi = 1.609 km

1 hp = 746 W

1 liter = 10-3 m3

The conversion of unitsThe same dimension can be expressed

in different units !

Question

A highschool playground has a length of 100 m and 80 m wide.

What is its area square meter ?

Express the length in kilometer

The highest waterfall in the world is Angel Falls in Venezuela,

with a total drop of 979.0 m.

Express this drop in feet

Example: The World’s highest Waterfall

1 Meter = 3.281 feet

979 m = 979.0 X 3,281 ft

= 3212 ft.

Height of the Washington Monument

The value of the height h of the Washington Monument is h = 169 m =

555 ft. Here h is the physical quantity, its value expressed in the unit

"meter," unit symbol m, is 169 m, and its numerical value when

expressed in meters is 169. However, the value of h expressed in the unit

"foot," symbol ft, is 555 ft, and its numerical value when expressed in feet

is 555 (from http://physics.nist.gov/cuu/Units/introduction.html)

6/28/2011

4

Problem: chapter 1

1. A student sees a newspaper ad for an apartment that has

1330 square feet (ft2 ). How many square foot of area are

there ?

Answer: Area = 1330 ft2 = 124 m2

Hint: 1 m = 3.28 ft

2Area = 1330 ft( ) 1 m

3.28 ft

1 m

3.28 ft

2124 m

=

Problem: chapter 1

2. A man’s scalp hair grows at a rate of 0.35 mm per day.

What is this growth rate in feet per century?

Answer: 42 ft /century

Hint: 1 m = 3.28 ft

1 mm = (1/1000) m = 0.001 m

1 year = 365 days

mmGrowth rate 0.35=

d 3

1 m

10 mm

1 ft

0.3048 m

365.24 d 1 y

100 y

42 ft/centurycentury

=

Problem: chapter 1

4. Bicyclists in the Tour de France reach speeds of 34.0

miles per hour (mi/h) on flat sections of the road. What is

this speed in (a) kilometers per hour (km/h) and (b)

meters per second (m/s)?

Hint: 1 mile = 1609 m = 1.609 km

1 h = 3600 s

( )mi mi

Speed = 34.0 1 34.0h

=

1.609 km

h 1 mi

km54.7

h

=

( ) ( )mi mi

Speed = 34.0 1 1 34.0h

=

h

1609m

1 mi

1 h

m15.2

3600s s

=

Review of Trigonometry

0 0

-1 -1 -10 a 0

a

sin θ cos θ tan θ

h h hθ = sin θ = cos θ = tan

h h h

a

a

h h h

h h h= = =

ApplicationFrom the length of the shadow a and the angle ,

the height of the building can be determined

0

0

0

tan θ

tan

(67.2 m)(tan 50.0 ) 80.0 m

a

a

h

h

h h θ

=

=

= =

Another example

What is the depth d at a distance 22.0 m ?

6/28/2011

5

Problem: chapter 1

5. Given the quantities a = 9.7 m, b = 4.2 s, c = 69 m/s,

what is the value of the quantity (a3/cb2)

Problem: chapter 1

10. A partly full paint can has 0.67 U.S. gallons of paint left

in it. (a) What is the volume of the paint in cubic meters?

(b) If all the remaining paint is used to coat a wall evenly

(wall area 5 13 m2), how thick is the layer of wet paint?

Give your answer in meters.

Please note: 1 US gallon = 3.785 X 10-3 m3

Problem: chapter 1

15. The corners of a square lie on a circle of diameter D =

0.35 m. Each side of the square has a length L. Find L.

Problem: chapter 1

17. The drawing shows sodium and chloride ions

positioned at the corners of a cube that is part of the

crystal structure of sodium chloride (common table salt).

The edge of the cube is 0.281 nm (1 nm 5 1 nanometer 5

1029 m) in length. Find the distance (in nanometers)

between the sodium ion located at one corner of the cube

and the chloride ion located on the diagonal at the

opposite

Scalars and Vectors

Mass, length, density: examples of scalar quantities. We only need a

number to specify these.

Not every physical quantity can be specified by a number ; such as

quantities which require directions, for example, displacement,

velocity. Typically we need a length (magnitude) and an angle

(direction)

How do we draw a vector ?

A vector has a magnitude (length) and a direction

As long as we keep the length and the direction the same it does not

matter where do we start drawing the vector. In the above examples all

three purple vectors represent the same vector A which is 8 units long and

directed along East. Likewise, all the three green vectors represent the

same vector B which is 6 units long and points toward North

6/28/2011

6

What happens when the vector points in the opposite direction ?

Two vectors of the same length but pointing in opposite

directions differ only by a negative sign. In the above example

please note that the vectors B and –B are two different vectors.

Scalars and Vectors

http://www.grc.nasa.gov/WWW/K-12/airplane/vectors.html

Vector pointing along arbitrary direction

In general, a vector which has the same magnitude but different

directions are two different vectors. In example above, all the

vectors with different colors have same magnitude but different

directions. Therefore, they are all different vectors.

Vector Addition

Addition Subtraction

Components of a vector How do we add two vectors ?

6/28/2011

7

Addition of vectors by means of components Problem: chapter 1

27. Consider the following four force vectors:

F1 = 50.0 newtons, due east

F2 = 10.0 newtons, due east

F3 = 40.0 newtons, due west

F4 = 30.0 newtons, due west

Which two vectors add together to give a resultant with

the smallest magnitude, and which two vectors add to give

a resultant with the largest magnitude? In each case

specify the magnitude and direction of the resultant.