Physics 2001 Introduction:

What is Physics

The scientific study of the basic properties of matter and energy

Science

An organized method of study using the scientific method:

Observation

Hypothesis

Experiment

Modification of Hypothesis

Parts of Science

Consists of Physical Sciences, Life Sciences, Social Sciences

Physical, Social and Life Sciences

Life Sciences

Biology, Anatomy,Physiology,…

Physical Sciences

Physics, Geology, Chemistry,…

Social Sciences:

Psychology, Sociology..

Physics 2001

Chapter 1

Motion

Drag Racing-an example of the importance of acceleration and average speed

In drag racing the first car to the end of the course wins.

This usually means the one with the fastest acceleration

However one car can accelerate faster at the beginning and the other might still win if it accelerates more at the end.

3 Basic Aspects of Nature

Space

Time

Matter

3 Fundamental Physical Quantities

Distance

Time

Mass

Units

Size or amount used in measuring something (physical quantity)

Based on standard,

Standard: something of known size, e.g. Length of Kings Foot = “Ruler”, or foot.

Aspect vs Quantity

Space vs Distance…Distance=how space is measured feet, meters, miles, etc.

Time vs. Time in seconds, min.,etc

Matter vs mass, mass=how matter is measured kilogram, gram, slug, etc.

Exponents

An exponent is a number telling us the other number is multiplied by itself this many time.

10²= 10 x 10 =100

10⁴= 10 x 10 x 10 x 10

Negative exponents are 1 divided by the number

10^-2= 1/10 x 1/10 or .01 (2 decimal places)

10^-4= 1/(10 x 10 x 10 x 10) = .0001 (4 dec. places)

Prefixes

A word put in front of another word to alter the meaning of the word.

Example word: boat,

Prefix: life

New word: lifeboat

In physics we use prefixes frequently, especially in units.

Metric System

A special system of units, consisting of units for all the known physical quantities and concepts used by science.

Example length: meter

Mass: Gram

Time: second

Prefix: kilo = 1 thousand, kilometer = 1000 meters; kilogram = 1000 grams.

Common Prefixes in the Metric System

Deci = 1/10^th

Deca = 10 times

Centi = 1/100^{th =}10^-2

Milli = 1/1000^{th =}10^-3

Micro = 1/1000,000^{th =}10^-6

Mega = 1,000,000 times = 10⁺⁶

Giga = 1,000,000,000 times ⁼10⁺⁹

Physical Objects

Measurement

Length, Time

The Breath Experiment

Metric vs. British System

Conversions

To convert from one unit to another

Get the conversion factor

Multiply it by the number of units

E.g. 1 m = 3.28 ft

12 m = 12 x 3.28 = 39.36 ft

Cycle and Period:

A cycle is one complete phase of something

Period (T) The time for one complete cycle of a periodic process.

Frequency (f)

The number of cycles of a periodic process that occur per unit time.

The unit of measure of frequency is the hertz (Hz). (s-¹ =1/sec)

To get frequency from period, divide 1 by period. T=12(s), f = 1/12(Hz)

Mass (m) .

A measure of an object's resistance to acceleration. A measure of the quantity of matter in an object

Measured in grams, kg (SI units), slugs (British Units)

Speed (v)

Rate of movement. Rate of change of distance from a reference point. The distance that something travels divided by the time elapsed.

V= Δd/Δt (Δ = greek letter delta, = change in something).

Δd/Δt = change in distance/change in time (time for the change to happen)

Calculating Speed

An object is 8 ft from the door, 3 seconds later it is 23 feet from the door,

Δd=final-original=23-8=15 ft

The object moves 15 feet in 3 seconds

V= Δd/Δt = 15/3 = 5 ft/sec

Velocity

Velocity is Speed with direction.

E.G. 90 meters/second North

30 meters/second South West

80 mph South, etc.

Vectors vs Scalars

Vectors have size and direction, e.g. 90 meters North

Scalars have only size, e.g. 90 meters.

Vector 120 miles per hour (mph) East (E).

Scalar 120 miles per hour

We draw vectors on paper to represent them.

Drawing Vectors

When representing a vector we must use a grid, the grid shows direction, like North, South, East, and West, and size.

For example the size of 1 inch on the grid may stand for 10 miles per hour of velocity. This is the “scale”

Something 2 inches long would be 20 miles per hour.

One Dimensional Vector Addition

Back and forth in the same direction.

Two Dimensional Vector Addition,

To add vectors:

Draw the first vector, A

Draw the second vector,B, with it’s tail starting at the head of the first vector

The answer, or resultant is drawn from the tail of the first to the head of the last.

Vector Addition Example

Average Speed Vs Instantaneous Speed, Velocity,

Average speed is speed over some time or distance, but it may be changing, to know it exactly we need to know it at a very short “instant” in time. This is the instantaneous speed or velocity.

Trigonometry,

Pythagorean Theorem, Right Triangles,

c² = a² + b²

Hypotenuse squared = sum of the squares of the sides in a right triangle

Pythagorean Theorem

30 deg. triangle

3-4-5 Right Triangle

3-4-5 Right Triangle

Acceleration

Rate of change of velocity.

The change in velocity divided by the time elapsed.

Δv/Δt = change in velocity/change in time (time for the change to happen)

Example of Acceleration Problem

Velocity 9 m/s E

After 2 sec. v= 15 m/s E

Change in v=(final-original)15-9 or 6 m/s E

a=Δv/Δt

a = 6m/s/2sec = 3 m/s/s(m/s²) E

Determining v from a and t

When a is constant, v = a x t

a = 5 m/s² t = 20 s

v = 5 m/s² x 20 s = 100 m/s

Centripetal Acceleration

Acceleration of an object moving along a circular path.

It is directed toward the center of the circle.

a = v²/r = square of velocity divided by the radius of the circle.

Example Cent. Acc.

Particle moves in a circle of radius 5 m

Speed is 12 m/s. What is Cent. Acc.?

Cent. Acc. = v²/r = (12 m/s)²/ 5 m

= 144 m²/s² / 5m = 28.8 m/s²

Simple Types of Motion:

Zero Velocity, Constant Velocity

d = v x t when v=constant

E.g. v = 10 m/s; t = 5 s

d = 10 m/s x 5 s = 50 m

Distance vs. Time Graphs,

Slope of the distance vs time graph = velocity

Constant Speed Graphs

Speed vs. time, plots a straight line.

Accelerated motion,

When velocity is changing we have accelerated motion.

The simplest case is when acceleration is constant, such as the acceleration of gravity near the earth’s surface.

Speed vs. Time Graphs.

When speed is constant the graph is a straight horizontal line.

When speed is accelerated uniformly (constant acceleration) the graph is a straight line at an angle.

The slope is the acceleration. See fig. 1.26

Constant Acceleration,

Acceleration of Gravity

g = acceleration of gravity = 9.8 m/sec/sec.

d = ½ at² (½ x a x t x t)

D = ½ at²Problem

a = 9.8 m/s²

t = 5 sec. What is d?

½ at²= ½ x 9.8 m/s² x 5 s x 5 s

= 4.9 x 25 m /s²x s^{2 =}122.5 m

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Back to Physics


	What is Physics
		The scientific study of the basic properties of matter and energy


	An organized method of study using the scientific method:
		Observation
		Hypothesis
		Experiment
		Modification of Hypothesis


	Consists of Physical Sciences, Life Sciences, Social Sciences


	Life Sciences
		Biology, Anatomy,Physiology,…
	Physical Sciences
		Physics, Geology, Chemistry,…
	Social Sciences:
		Psychology, Sociology..


	In drag racing the first car to the end of the course wins.
	This usually means the one with the fastest acceleration
	However one car can accelerate faster at the beginning and the other might still win if it accelerates more at the end.


	Size or amount used in measuring something (physical quantity)
	Based on standard,
	Standard: something of known size, e.g. Length of Kings Foot = “Ruler”, or foot.


	Space vs Distance…Distance=how space is measured feet, meters, miles, etc.
	Time vs. Time in seconds, min.,etc
	Matter vs mass, mass=how matter is measured kilogram, gram, slug, etc.


	An exponent is a number telling us the other number is multiplied by itself this many time.
	10²= 10 x 10 =100
	10⁴= 10 x 10 x 10 x 10
	Negative exponents are 1 divided by the number
	10^-2= 1/10 x 1/10 or .01 (2 decimal places)
	10^-4= 1/(10 x 10 x 10 x 10) = .0001 (4 dec. places)


	A word put in front of another word to alter the meaning of the word.
	Example word: boat,
	Prefix: life
	New word: lifeboat
	In physics we use prefixes frequently, especially in units.


	A special system of units, consisting of units for all the known physical quantities and concepts used by science.
	Example length: meter
	Mass: Gram
	Time: second
	Prefix: kilo = 1 thousand, kilometer = 1000 meters; kilogram = 1000 grams.


	Deci = 1/10^th
	Deca = 10 times
	Centi = 1/100^{th =}10^-2
	Milli = 1/1000^{th =}10^-3
	Micro = 1/1000,000^{th =}10^-6
	Mega = 1,000,000 times = 10⁺⁶
	Giga = 1,000,000,000 times ⁼10⁺⁹


	To convert from one unit to another
		Get the conversion factor
		Multiply it by the number of units
		E.g. 1 m = 3.28 ft
		12 m = 12 x 3.28 = 39.36 ft


	A cycle is one complete phase of something
	Period (T) The time for one complete cycle of a periodic process.


	The number of cycles of a periodic process that occur per unit time.
	The unit of measure of frequency is the hertz (Hz). (s-¹ =1/sec)
	To get frequency from period, divide 1 by period. T=12(s), f = 1/12(Hz)


	A measure of an object's resistance to acceleration. A measure of the quantity of matter in an object
	Measured in grams, kg (SI units), slugs (British Units)


	Rate of movement. Rate of change of distance from a reference point. The distance that something travels divided by the time elapsed.
	V= Δd/Δt (Δ = greek letter delta, = change in something).
	Δd/Δt = change in distance/change in time (time for the change to happen)


	An object is 8 ft from the door, 3 seconds later it is 23 feet from the door,
	Δd=final-original=23-8=15 ft
	The object moves 15 feet in 3 seconds
	V= Δd/Δt = 15/3 = 5 ft/sec


	Velocity is Speed with direction.
	E.G. 90 meters/second North
	30 meters/second South West
	80 mph South, etc.


	Vectors have size and direction, e.g. 90 meters North
	Scalars have only size, e.g. 90 meters.
	Vector 120 miles per hour (mph) East (E).
	Scalar 120 miles per hour
	We draw vectors on paper to represent them.


	When representing a vector we must use a grid, the grid shows direction, like North, South, East, and West, and size.
	For example the size of 1 inch on the grid may stand for 10 miles per hour of velocity. This is the “scale”
	Something 2 inches long would be 20 miles per hour.


	To add vectors:
		Draw the first vector, A
		Draw the second vector,B, with it’s tail starting at the head of the first vector
		The answer, or resultant is drawn from the tail of the first to the head of the last.


	Average speed is speed over some time or distance, but it may be changing, to know it exactly we need to know it at a very short “instant” in time. This is the instantaneous speed or velocity.


	c² = a² + b²
	Hypotenuse squared = sum of the squares of the sides in a right triangle


	Rate of change of velocity.
	The change in velocity divided by the time elapsed.
	Δv/Δt = change in velocity/change in time (time for the change to happen)


	Velocity 9 m/s E
	After 2 sec. v= 15 m/s E
	Change in v=(final-original)15-9 or 6 m/s E
	a=Δv/Δt
	a = 6m/s/2sec = 3 m/s/s(m/s²) E


	When a is constant, v = a x t
	a = 5 m/s² t = 20 s
	v = 5 m/s² x 20 s = 100 m/s


	Acceleration of an object moving along a circular path.
	It is directed toward the center of the circle.
	a = v²/r = square of velocity divided by the radius of the circle.


	Particle moves in a circle of radius 5 m
	Speed is 12 m/s. What is Cent. Acc.?
	Cent. Acc. = v²/r = (12 m/s)²/ 5 m
	= 144 m²/s² / 5m = 28.8 m/s²


	Zero Velocity, Constant Velocity
	d = v x t when v=constant
	E.g. v = 10 m/s; t = 5 s
	d = 10 m/s x 5 s = 50 m


	When velocity is changing we have accelerated motion.
	The simplest case is when acceleration is constant, such as the acceleration of gravity near the earth’s surface.