Regents Physics PowerPoint Presentation

	Compiled summer 2004
	Joan Jakubowski

Physics Units

	I. Physics Skills
	II. Mechanics
	III. Energy
	IV. Electricity and Magnetism
	V. Waves
	VI. Modern Physics

I. Physics Skills

	A. Scientific Notation
	B. Graphing
	C. Significant Figures
	D. Units
	E. Prefixes
	F. Estimation

A. Scientific Notation

	Use for very large or very small numbers
	Write number with one digit to the left of the decimal followed by an exponent (1.5 x 105)
	Examples: 2.1 x 103 represents 2100 and 3.6 x 10-4 represents 0.00036

Scientific Notation Problems

	1. Write 365,000,000 in scientific notation
	2. Write 0.000087 in scientific notation

Answers

	1.) 3.65 x 108
	2.) 8.7 x 10-5

B. Graphing

	Use graphs to make a “picture” of scientific data
	“independent variable”, the one you change in your experiment is graphed on the “x” axis and listed first in a table
	“dependent variable”, the one changed by your experiment is graphed on the “y” axis and listed second in a table

"Best fit “line”"

	Best fit “line” or “curve” is drawn once points are plotted. Does not have to go through all points. Just gives you the “trend” of the points
	The “slope” of the line is given as the change in the “y” value divided by the change in the “x” value

Types of Graphs

	1. Direct Relationship means an increase/decrease in one variable causes an increase/decrease in the other
	Example below

"2."

	2. Inverse(indirect) relationship means that an increase in one variable causes a decrease in the other variable and vice versa
	Examples

"3."

	3. Constant proportion means that a change in one variable doesn’t affect the other variable
	Example;

"4."

	4. If either variable is squared(whether the relationship is direct or indirect), the graph will curve more steeply.

C. Significant figures

	Uncertainty in measurements is expressed by using significant figures
	The more accurate or precise a measurement is, the more digits will be significant

Significant Figure Rules

	1. Zeros that appear before a nonzero digit are not significant (examples: 0.002 has 1 significant figure and 0.13 has 2 significant figures)
	2. Zeros that appear between nonzero digits are significant (examples: 1002 has 4 significant figures and 0.405 has 3 significant figures)

Significant figures rules(cont.)

	3. zeros that appear after a nonzero digit are significant only if they are followed by a decimal point (20. has 2 sig figs) or if they appear to the right of the decimal point (35.0 has 3 sig figs)

Sig Fig problems

	1. How many significant figures does 0.050900 contain?
	2. How many significant figures does 4800 contain?

Answers

	1. 5 sig figs
	2. 2 sig figs

D. Units

	1. Fundamental units are units that can’t be broken down
	2. Derived units are made up of other units and then renamed
	3. SI units are standardized units used by scientists worldwide

Fundamental Units

	Meter (m)– length, distance, displacement, height, radius, elongation or compression of a spring, amplitude, wavelength
	Kilogram (kg)– mass
	Second (s)– time, period
	Ampere (A)– electric current
	Degree (o)– angle

Derived Units

	Meter per second (m/s)– speed, velocity
	Meter per second squared (m/s2)– acceleration
	Newton (N)– force
	Kilogram times meter per second (kg.m/s)– momentum
	Newton times second (N.s)-- impulse

Derived Units (cont.)

	Joule (J)– work, all types of energy
	Watt (W)– power
	Coulomb (C)– electric charge
	Newton per Coulomb (N/C)– electric field strength (intensity)
	Volt (V)- potential difference (voltage)
	Electronvolt (eV)– energy (small amounts)

Derived Units (cont.)

	Ohm (Ω)– resistance
	Ohm times meter (Ω.m)– resistivity
	Weber (Wb)– number of magnetic field (flux) lines
	Tesla (T)– magnetic field (flux) density
	Hertz (Hz)-- frequency

E. Prefixes

	Adding prefixes to base units makes them smaller or larger by powers of ten
	The prefixes used in Regents Physics are tera, giga, mega, kilo, deci, centi, milli, micro, nano and pico

Prefix Examples

	A terameter is 1012 meters, so… 4 Tm would be 4 000 000 000 000 meters
	A gigagram is 109 grams, so… 9 Gg would be 9 000 000 000 grams
	A megawatt is 106 watts, so… 100 MW would be 100 000 000 watts
	A kilometer is 103 meters, so… 45 km would be 45 000 meters

Prefix examples (cont.)

	A decigram is 10-1 gram, so… 15 dg would be 1.5 grams
	A centiwatt is 10-2 watt, so… 2 dW would be 0.02 Watt
	A millisecond is 10-3 second, so… 42 ms would be 0.042 second

Prefix examples (cont.)

	A microvolt is 10-6 volt, so… 8 µV would be 0.000 008 volt
	A nanojoule is 10-9 joule, so… 530 nJ would be 0.000 000 530 joule
	A picometer is 10-12 meter, so… 677 pm would be 0.000 000 000 677 meter

Prefix Problems

	1.) 16 terameters would be how many meters?
	2.) 2500 milligrams would be how many grams?
	3.) 1596 volts would be how many gigavolts?
	4.) 687 amperes would be how many nanoamperes?

Answers

	1.) 16 000 000 000 000 meters
	2.) 2.500 grams
	3.) 1596 000 000 000 gigavolts
	4.) 0.000 000 687 amperes

F. Estimation

	You can estimate an answer to a problem by rounding the known information
	You also should have an idea of how large common units are

Estimation (cont.)

	2 cans of Progresso soup are just about the mass of            1 kilogram
	1 medium apple weighs          1 newton
	The length of an average Physics student’s leg is 1 meter

Estimation Problems

	1.) Which object weighs approximately one newton?  Dime, paper clip, student, golf ball
	2.) How high is an average doorknob from the floor?  101m, 100m, 101m, 10-2m

Answers

	1.) golf ball
	2.) 100m

II. Mechanics

	A. Kinematics; vectors, velocity, acceleration
	B. Kinematics; freefall
	C. Statics
	D. Dynamics
	E. 2-dimensional motion
	F. Uniform Circular motion
	G. Mass, Weight, Gravity
	H. Friction
	I. Momentum and Impulse

Kinematics; vectors, velocity, acceleration

	In physics, quantities can be vector or scalar
	VECTOR quantities have a magnitude (a number), a unit and a direction
	Example; 22m(south)

"SCALAR quantities only have a..."

	SCALAR quantities only have a magnitude and a unit
	Example; 22m

"VECTOR quantities;"

	VECTOR quantities; displacement, velocity, acceleration, force, weight, momentum, impulse, electric field strength
	SCALAR quantities; distance, mass, time, speed, work(energy), power

Distance vs. Displacement

	Distance is the entire pathway an object travels
	Displacement is the “shortest” pathway from the beginning to the end

Distance/Displacement Problems

	1.) A student walks 12m due north and then 5m due east. What is the student’s resultant displacement? Distance?
	2.) A student walks 50m due north and then walks 30m due south. What is the student’s resultant displacement? Distance?

Answers

	1.) 13m (NE) for displacement
	17 m for distance
	2.) 20m (N) for displacement 80 m for distance

Speed vs. Velocity

	Speed is the distance an object moves in a unit of time
	Velocity is the displacement of an object in a unit of time

Average Speed/Velocity Equations

Symbols

Speed/Velocity Problems

	1.) A boy is coasting down a hill on a skateboard. At 1.0s he is traveling at 4.0m/s and at 4.0s he is traveling at 10.0m/s. What distance did he travel during that time period? (In all problems given in Regents Physics, assume acceleration is constant)

Answers

	1.) You must first find the boy’s average speed/velocity before you are able to find the distance

Answers (cont.)

Acceleration

	The time rate change of velocity is acceleration (how much you speed up or slow down in a unit of time)
	We will only be dealing with constant (uniform) acceleration

Symbols (cont.)

Constant Acceleration Equations

Constant Acceleration Problems

	1.) A car initially travels at 20m/s on a straight, horizontal road. The driver applies the brakes, causing the car to slow down at a constant rate of 2m/s2 until it comes to a stop. What was the car’s stopping distance? (Use two different methods to solve the problem)

Answers

	First Method
	vi=20m/s
	vf=0m/s
	a=2m/s2
	Use  vf2=vi2+2ad to find “d”
	d=100m

Answer (cont.)

	Second Method

B. Kinematics: freefall

	In a vacuum (empty space), objects fall freely at the same rate
	The rate at which objects fall is known as “g”, the acceleration due to gravity
	On earth, the “g” is 9.81m/s2

Solving Freefall Problems

	To solve freefall problems use the constant acceleration equations
	Assume a freely falling object has a vi=0m/s
	Assume a freely falling object has an a=9.81m/s2

Freefall Problems

	1.) How far will an object near Earth’s surface fall in 5s?
	2.) How long does it take for a rock to fall 60m? How fast will it be going when it hits the ground
	3.) In a vacuum, which will hit the ground first if dropped from 10m, a ball or a feather?

Answers

	1.)

Answers (cont.)

	2.)

Answers (cont.)

	3.) Both hit at the same time because “g” the acceleration due to gravity is constant. It doesn’t depend on mass of object because it is a ratio

Solving Anti??? Freefall Problems

	If you toss an object straight up, that is the opposite of freefall.
	So…
	vf  is now 0m/s
	a is -9.8lm/s2
	Because the object is slowing down not speeding up

Antifreefall Problems

	1.) How fast do you have to toss a ball straight up if you want it reach a height of 20m?
	2.) How long will the ball in problem #1 take to reach the 20m height?

Answers

	1.)

Answers (cont.)

	2.)

C. Statics

	The study of the effect of forces on objects at rest
	Force is a push or pull
	The unit of force is the newton(N) (a derived vector quantity)

Adding forces

	When adding concurrent (acting on the same object at the same time) forces follow three rules to find the resultant (the combined effect of the forces)
	1.) forces at 00, add them
	2.) forces at 1800, subtract them
	3.) forces at 900, use Pythagorean Theorem

Force Diagrams

	Forces at 00
	Forces at 1800
	Forces at 900

Composition of Forces Problems

	1.) Find the resultant of two 5.0N forces at 00? 1800? And 900?

Answers

	1.) 00
	5N  5N    =    10N

Answers (cont.)

	1.) 1800
	5N     5N     =    0N

Answers (cont.)

	1.) 900
	5N                       =
	5N                        7.1N

Resolution of forces

	The opposite of adding concurrent forces.
	Breaking a resultant force into its component forces
	Only need to know components(2 forces) at a 900 angle to each other

Resolving forces using Graphical Method

	To find the component forces of the resultant force
		1.) Draw x and y axes at the tail of the resultant force
		2.) Draw lines from the head of the force to each of the axes
		3.) From the tail of the resultant force to where the lines intersect the axes, are the lengths of the component forces

Resolution Diagram

	Black arrow=resultant force
	Orange lines=reference lines
	Green arrows=component forces
	y
	x

Resolving Forces Using Algebraic Method

Equilibrium

	Equilibrium occurs when the net force acting on an object is zero
	Zero net force means that when you take into account all the forces acting on an object, they cancel each other out

Equilibrium (cont.)

	An object in equilibrium can either be at rest or can be moving with constant (unchanging) velocity
	An “equilibrant” is a force equal and opposite to the resultant force that keeps an object in equilibrium

Equilibrium Diagram

	Black arrows=components
	Blue arrow=resultant
	Red arrow=equilibrant
	=
	+

Problems

	1.) 10N, 8N and 6N forces act concurrently on an object that is in equilibrium. What is the equilibrant of the 10N and 6N forces? Explain.
	2.) A person pushes a lawnmower with a force of 300N at an angle of 600 to the ground. What are the vertical and horizontal components of the 300N force?

Answers

	1.) The 8N force is the equilibrant (which is also equal to and opposite the resultant) The 3 forces keep the object in equilibrium, so the third force is always the equilibrant of the other two forces.

Answers (cont.)

	2.)

C. Dynamics

	The study of how forces affect the motion of an object
	Use Newton’s Three Laws of Motion to describe Dynamics

Newton’s 1^st Law of Motion

	Also called the law of inertia
	Inertia is the property of an object to resist change. Inertia is directly proportional to the object’s mass
	“An object will remain in equilibrium (at rest or moving with constant speed) unless acted upon by an unbalanced force”

Newton’s Second Law of Motion

	“When an unbalanced (net) force acts on an object, that object accelerates in the direction of the force”
	How much an object accelerates depends on the force exerted on it and the object’s mass (See equation)

Symbols

	Fnet=the net force exerted on an object (the resultant of all forces on an object) in newtons (N)
	m=mass in kilograms (kg)
	a=acceleration in m/s2

Newton’s Third Law of Motion

	Also called law of action-reaction
	“When an object exerts a force on another object, the second object exerts a force equal and opposite to the first force”
	Masses of each of the objects don’t affect the size of the forces (will affect the results of the forces)

Free-Body Diagrams

	A drawing (can be to scale) that shows all concurrent forces acting on an object
	Typical forces are the force of gravity, the normal force, the force of friction, the force of acceleration, the force of tension, etc.

Free-body Forces

	Fg is the force of gravity or weight of an object (always straight down)
	FN is the “normal” force (the force of a surface pushing up against an object)
	Ff is the force of friction which is always opposite the motion
	Fa is the force of acceleration caused by a push or pull

Free-Body Diagrams

	If object is moving with constant speed to the right….
	Black arrow=Ff
	Green arrow=Fg
	Yellow arrow=FN
	Blue arrow=Fa

Free-Body Diagrams on a Slope

	When an object is at rest or moving with constant speed on a slope, some things about the forces change and some don’t
	1.) Fg is still straight down
	2.) Ff is still opposite motion
	3.) FN is no longer equal and opposite to Fg
	4.) Ff is still opposite motion
	More……

Free-Body Diagrams on a Slope

	Fa=Ff=Ax=Acosθ
	FN=Ay=Asinθ
	Fg=mg (still straight down)
	On a horizontal surface, force of gravity and normal force are equal and opposite
	On a slope, the normal force is equal and opposite to the “y” component of the force of gravity

Free-Body Diagram on a Slope

	Green arrow=FN
	Red arrow=Fg
	Black arrows=Fa and Ff
	Orange dashes=Ay
	Purple dashes=Ax

Dynamics Problems

	1.) Which has more inertia a 0.75kg pile of feathers or a 0.50kg pile of lead marbles?
	2.) An unbalanced force of 10.0N acts on a 20.0kg mass for 5.0s. What is the acceleration of the mass?

Answers

	1.) The 0.75kg pile of feathers has more inertia because it has more mass. Inertia is dependent on the “mass” of the object

Answers (cont.)

	2.)

More Problems

	3.)  A 10N book rests on a horizontal tabletop. What is the force of the tabletop on the book?
	4.) How much force would it take to accelerate a 2.0kg object 5m/s2? How much would that same force accelerate a 1.0kg object?

Answers

	1.) The force of the tabletop on the book is also 10N (action/reaction)

Answers (cont.)

	2.)

E. 2-Dimensional Motion

	To describe an object moving 2-dimensionally, the motion must be separated into a “horizontal” component and a “vertical” component (neither has an effect on the other)
	Assume the motion occurs in a “perfect physics world”; a vacuum with no friction

Types of 2-D Motion

	1.) Projectiles fired horizontally
	an example would be a baseball tossed straight horizontally away from you

Projectile Fired Horizontally

	Use the table below to solve these type of 2-D problems

Types of 2-D Motion

	2.) Projectiles fired at an angle
	an example would be a soccer ball lofted into the air and then falling back onto the ground

Projectile Fired at an Angle

	Use the table below to solve these type of 2-D problems
	Ax=Acosθ and Ay=Asinθ

2-D Motion Problems

	1.) A girl tossed a ball horizontally with a speed of 10.0m/s from a bridge 7.0m above a river. How long did the ball take to hit the river? How far from the bottom of the bridge did the ball hit the river?

Answers

	1.) In this problem you are asked to find time and horizontal distance (see table on the next page)

Answers (cont.)

Answers (cont.)

	Use

More 2-D Motion Problems

	2.) A soccer ball is kicked at an angle of 600 from the ground with an angular velocity of 10.0m/s. How high does the soccer ball go? How far away from where it was kicked does it land? How long does its flight take?

Answers

	2.) In this problem you are asked to find vertical distance, horizontal distance and horizontal time. Finding vertical time is usually the best way to start. (See table on next page)

Answers (cont.)

Answers (cont.)

	Find vertical “t” first using
	vf=vi+at     with….
	vf=0.0m/s
	vi=8.7m/s
	a=-9.81m/s2
	So…vertical “t”=0.89s  and horizontal “t” is twice that
	and equals 1.77s

Answers (cont.)

	Find horizontal “d” using

Answers (cont.)

	Find vertical “d” by using

F. Uniform Circular Motion

	When an object moves with constant speed in a circular path
	The force (centripetal) will be constant towards the center
	Acceleration (centripetal) will only be a direction change towards the center
	Velocity will be tangent to the circle in the direction of movement

Uniform Circular Motion Symbols

	Fc=centripetal force, (N)
	v=constant velocity (m/s)
	ac=centripetal acceleration (m/s2)
	r=radius of the circular pathway (m)
	m=mass of the object in motion (kg)

Uniform Circular Motion Diagram

Uniform Circular Motion Equations

Uniform Circular Motion Problems

	1.) A 5kg cart travels in a circle of radius 2m with a constant velocity of 4m/s. What is the centripetal force exerted on the cart that keeps it on its circular pathway?

Answers

	1.)

G. Mass, Weight and Gravity

	Mass is the amount of matter in an object
	Weight is the force of gravity pulling down on an object
	Gravity is a force of attraction between objects

Mass

	Mass is measured in kilograms (kg)
	Mass doesn’t change with location (for example, if  you travel to the moon your mass doesn’t change)

Weight

	Weight is measured in newtons (N)
	Weight “does” change with location because it is dependent on the pull of gravity
	Weight is equal to mass times the acceleration due to gravity

Weight/Force of Gravity Equations

Gravitational Field Strength

	g=acceleration due to gravity but it is also equal to “gravitational field strength”
	The units of acceleration due to gravity are m/s2
	The units of gravitational field strength are N/kg
	Both quantities are found from the equation:

Mass, Weight, Gravity Problems

	1.) If the distance between two masses is doubled, what happens to the gravitational force between them?
	2.) If the distance between two objects is halved and the mass of one of the objects is doubled, what happens to the gravitational force between them?

Answers

	1.) Distance has an inverse squared relationship with the force of gravity.
	So…since r is multiplied by 2 in the problem, square 2……so….22=4, then take the inverse of that square which equals ¼….so….the answer is “¼ the original Fg”

Answers (cont.)

	2.) Mass has a direct relationship with Fg  and distance has an inverse squared relationship with Fg.
	First…since m is doubled so is Fg and since r is halved, square ½ , which is ¼ and then take the inverse which is 4.
	Then…combine 2x4=8
	So…answer is “8 times Fg”

More Problems

	3.) Determine the force of gravity between a 2kg and a 3kg object that are 5m apart.
	4.) An object with a mass of 10kg has a weight of 4N on Planet X. What is the acceleration due to gravity on Planet X? What is the gravitational field strength on Planet X?

Answers

	3.)
	4.)

H. Friction

	The force that opposes motion measured in newtons (N)
	Always opposite direction of motion
	“Static Friction” is the force that opposes the “start of motion”
	“Kinetic Friction” is the force of friction between objects in contact that are in motion

Coefficient of Friction

	The ratio of the force of friction to the normal force (no unit, since newtons cancel out)
	Equation
	Ff= μFN
	μ=coefficient of friction
	Ff=force of friction
	FN=normal force

Coefficient of Friction

	The smaller the coefficient, the easier the surfaces slide over one another
	The larger the coefficient, the harder it is to slide the surfaces over one another
	Use the table in the reference tables

Coefficient of Friction Problems

	1.) A horizontal force is used to pull a 2.0kg cart at constant speed of 5.0m/s across a tabletop. The force of friction between the cart and the tabletop is 10N. What is the coefficient of friction between the cart and the tabletop? Is the friction force kinetic or static? Why?

Answers

	1.)
	The friction force is kinetic because the cart is moving over the tabletop

I. Momentum and Impulse

	Momentum is a vector quantity that is the product of mass and velocity (unit is kg.m/s)
	Impulse is the product of the force applied to an object and time (unit is N.s)

Momentum and Impulse Symbols

	p=momentum
	Δp=change in momentum= (usually) m(vf-vi)
	J=impulse

Momentum and Impulse Equations

	p=mv
	J=Ft
	J=Δp
	pbefore=pafter

Momentum and Impulse Problems

	1.) A 5.0kg cart at rest experiences a 10N.s (E) impulse. What is the cart’s velocity after the impulse?
	2.)  A 1.0kg cart at rest is hit by a 0.2kg cart moving to the right at 10.0m/s. The collision causes the 1.0kg cart to move to the right at 3.0m/s. What is the velocity of the 0.2kg cart after the collision?

Answer

	1.) Use J=Δp    so……
	J=10N.s(E)=Δp=10kg.m/s(E)
	and since original p was 0kg.m/s and Δp=10kg.m/s(E),
	new p=10kg.m/s(E)
	then use….. p=mv     so……..
	10kg.m/s(E)=5.0kg x v    so….
	v=2m/s(E)

Answers (cont.)

	2.) Use pbefore=pafter
	Pbefore=0kg.m/s + 2kg.m/s(right)
	=2kg.m/s(right)
	Pafter=2kg.m/s(right)=3kg.m/s +
	P(0.2kg cart)  so….p of 0.2kg cart must be -1kg.m/s or 1kg.m/s(left)
	more…..

Answers (cont.)

	So if p after collision of 0.2kg cart is 1kg.m/s(left) and
	p=mv
	1kg.m/s(left)=0.2kg x v
	And v=5m/s(left)

III. Energy

	A. Work and Power
	B. Potential and Kinetic Energy
	C. Conservation of Energy
	D. Energy of a Spring

A. Work and Power

	Work is using energy to move an object a distance
	Work is scalar
	The unit of work is the Joule (J)
	Work and energy are manifestations of the same thing, that is why they have the same unit of Joules

Work and Power (cont.)

	Power is the rate at which work is done so there is a “time” factor in power but not in work
	Power and time are inversely proportional; the less time it takes to do work the more power is developed
	The unit of power is the watt (W)
	Power is scalar

Work and Power Symbols

	W=work in Joules (J)
	F=force in newtons (N)
	d=distance in meters (m)
	ΔET=change in total energy in Joules (J)
	P=power in watts (W)
	t=time in seconds (s)

Work and Power Equations

	W=Fd=ΔET
	***When work is done vertically, “F” can be the weight of the object Fg=mg

Work and Power Problems

	1.) A 2.5kg object is moved 2.0m in 2.0s after receiving a horizontal push of 10.0N. How much work is done on the object? How much power is developed? How much would the object’s total energy change?
	2.) A horizontal 40.0N force causes a box to move at a constant rate of 5.0m/s. How much power is developed? How much work is done against friction in 4.0s?

Answers

	1.) to find work use W=Fd
	So…W=10.0N x 2.0m=20.0J
	To find power use P=W/t
	So…P=20.0J/2.0s=10.0W
	To find total energy change it’s the same as work done so……
	ΔET=W=20.0J

Answers (cont.)

	2.) To find power use
	So… P=40.0N x 5.0m/s=200W
	To find work use P=W/t so…200W=W/4.0s
	So….W=800J

More problems

	3.) A 2.0kg object is raised vertically 0.25m. What is the work done raising it?
	4.) A lift hoists a 5000N object vertically, 5.0 meters in the air. How much work was done lifting it?

Answers

	3.) to find work use W=Fd with F equal to the weight of the object
	So…..W=mg x d
	So...W=2.0kgx9.81m/s2x0.25m
	So…W=4.9J

Answers (cont.)

	4.) to find work use W=Fd
	Even though it is vertical motion, you don’t have to multiply by “g” because weight is already given in newtons
	So…W=Fd=5000N x 5.0m
	And W=25000J

B. Potential and Kinetic Energy

	Gravitational Potential Energy is energy of position above the earth
	Elastic Potential Energy is energy due to compression or elongation of a spring
	Kinetic Energy is energy due to motion
	The unit for all types of energy is the same as for work the Joule (J). All energy is scalar

Gravitational Potential Energy Symbols and Equation

	ΔPE=change in gravitational potential energy in Joules (J)
	m=mass in kilograms (kg)
	g=acceleration due to gravity in (m/s2)
	Δh=change in height in meters (m)
	Equation    ΔPE=mgΔh
	***Gravitational PE only changes if there is a change in vertical position

Gravitational PE Problems

	1.) How much potential energy is gained by a 5.2kg object lifted from the floor to the top of a 0.80m high table?
	2.) How much work is done in the example above?

Answers

	1.) Use ΔPE=mgΔh to find potential energy gained so ΔPE=5.2kgx9.81m/s2x0.80m
	So…ΔPE=40.81J
	2.) W=ΔET so..W is also 40.81J

Kinetic Energy Symbols and Equation

	KE=kinetic energy in Joules (J)
	m=mass in kilograms (kg)
	v=velocity or speed in (m/s)

Kinetic Energy Problems

	1.) If the speed of a car is doubled, what happens to its kinetic energy?
	2.) A 6.0kg cart possesses 75J of kinetic energy. How fast is it going?

Answers

	1.) Using KE=1/2mv2 if v is doubled, because v if squared KE will be quadrupled.
	2.) Use KE=1/2mv2  so…..
	75J=1/2 x 6.0kg x v
	And…..v=5m/s

C. Conservation of Energy

	In a closed system the total amount of energy is conserved
	Total energy includes potential energy, kinetic energy and internal energy
	Energy within a system can be transferred among different types of energy but it can’t be destroyed

Conservation of Energy in a Perfect Physics World

	In a perfect physics world since there is no friction there will be no change in internal energy so you don’t have to take that into account
	In a perfect physics world energy will transfer between PE and KE

In the “Real” World

	In the real world there is friction so the internal energy of an object will be affected by the friction (such as air resistance)

Conservation of Energy Symbols

	ET=total energy of a system
	PE=potential energy
	KE=kinetic energy
	Q=internal energy
	***all units are Joules (J)

Conservation of Energy Equations

	In a real world situation, ET=KE+PE+Q because friction exists and may cause an increase in the internal energy of an object
	In a “perfect physics world” ET=KE+PE   with KE+PE equal to the total “mechanical energy of the system object

Conservation of Energy Examples (perfect physics world)

	position #1
	position #2
	position #3                     more..

Conservation of Energy Examples (cont.)

Conservation of Energy Examples (cont.)

	Position #1
	Position #2
	Position #3

Conservation of Energy (perfect physics world)

	Position #1  the ball/bob has not starting falling yet so the total energy is all in gravitational potential energy
	Position #2 the ball/bob is halfway down, so total energy is split evenly between PE and KE
	Position #3 the ball/bob is at the end of its fall so total energy is all in KE

Conservation of Energy Problems

	1.) A 2.0kg block starts at rest and then slides along a frictionless track. What is the speed of the block at point B?
	A
	7.0m
	B

Answer

	Since there is no friction, Q does not need to be included
	So…use ET=PE+KE
	At position B, the total energy is entirely KE
	Since you cannot find KE directly, instead find PE at the beginning of the slide and that will be equal to KE at the end of the slide        more…..

Answer (cont.)

	PE (at position A) =mgΔh=2.0kgx9.81m/s2x7.0m =137.3J
	KE (at position A) =0J because there is no speed
	So ET (at position A)=137.3J
	At position B there is no height so the PE is 0J
	More….

Answer (cont.)

	At position B the total energy still has to be 137.3J because energy is conserved and because there is no friction no energy was “lost” along the slide
	So….ET(position B)=137.3J=0J+KE
	So…KE also equals 137.3J at position B
	More…

Answer (cont.)

	Use KE=1/2mv2
	So…KE=137.3J=1/2x2.0kgxv2
	So v (at position B)=11.7m/s

More Conservation of Energy Problems

	position #1
	position #2
	position #3
	1.) From what height must you drop the 0.5kg ball so that the it will be traveling at 25m/s at position #3(bottom of the fall)?
	2.)How fast will it be traveling at position #2 (halfway down)?
	*Assume no friction

Answers

	1.) At position #3, total energy will be all in KE because there is no height and no friction
	So…use ET=KE=1/2mv2
	KE=1/2 x 0.5kg x (25m/s)2
	So…KE=156.25J=PE (at position#1)
	So…ΔPE=156.25J=mgΔh
	And Δh=31.86m

Answers (cont.)

	2.) Since position #2 is half way down total energy will be half in PE and half in KE
	So…KE at position #2 will be half that at position #3
	So…KE at position #2 is 78.125J
	Then use KE (at #2)=78.125J =1/2 x 0.5kg x v2
	v=17.68m/s at position #2

D. Energy of a Spring

	Energy stored in a spring is called “elastic potential energy”
	Energy is stored in a spring when the spring is stretched or compressed
	The work done to compress or stretch a spring becomes its elastic potential energy

Spring Symbols

	Fs=force applied to stretch or compress the spring in newtons (N)
	k=spring constant in (N/m) ***specific for each type of spring
	x=the change in length in the spring from the equilibrium position in meters (m)

Spring Equations

	Fs=kx
	PEs=1/2kx2

Spring Diagrams

Spring Problems

	1.) What is the potential energy stored in a spring that stretches 0.25m from equilibrium when a 2kg mass is hung from it?
	2.) 100J of energy are stored when a spring is compressed 0.1m from equilibrium. What force was needed to compress the spring?

Answers

	1.) Using PEs=1/2kx2  you know “x” but not “k”
	You can find “k” using Fs=kx
	With Fs equal to the weight of the hanging mass
	So… Fs=Fg=mg=2kgx9.81m/s2
	Fs=19.62N=kx=k x 0.25m
	k=78.48N/m
	More…

Answers (cont.)

	Now use PEs=1/2kx2
	PEs=1/2 x 78.48N/m x (0.25m)2
	So PEs=2.45J

Answers (cont.)

	2.) To find the force will use Fs=kx, but since you only know “x” you must find “k” also
	Use PEs=1/2kx2 to find “k”
	PEs=100J=1/2k(0.1m)2
	k=20 000N/m
	use Fs=kx=20 000N/m x 0.1m
	Fs=2000N

Examples of Forms of Energy

	1.) Thermal Energy is heat energy which is the KE possessed by the particles making up an object
	2.) Internal Energy is the total PE and KE of the particles making up an object
	3.) Nuclear Energy is the energy released by nuclear fission or fusion
	4.) Electromagnetic Energy is the energy associated with electric and magnetic fields

IV. Electricity and Magnetism

	A. Electrostatics/Electric Fields
	B. Current Electricity
	C. Series Circuits
	D. Parallel Circuits
	E. Electric Power and Energy
	F. Magnetism and Electromagnetism

A. Electrostatics

	Atomic Structure—the atom consists of proton(s) and neutron(s) in the nucleus and electrons outside the nucleus.
	The proton and neutron have similar mass (listed in reference table)
	The electron has very little mass (also in reference table)

"A proton has a positive..."

	A proton has a positive charge that is equal in magnitude but opposite in sign to the electron’s negative charge
	A neutron has no charge so it is neutral

"The unit of charge is..."

	The unit of charge is the coulomb (C)
	Each proton or each electron has an “elementary charge” (e) of 1.60x10-19C
	The magnitude of the charge on both an electron and a proton are the same, only the signs are different

"An object has a neutral..."

	An object has a neutral charge or no net charge if there are equal numbers of protons and neutrons
	An object will have a net “negative” charge if there are more electrons than protons
	An object will have a net “positive” charge if there are less electrons than protons

"Transfer of charge occurs only..."

	Transfer of charge occurs only through movement of electrons
	If an object loses electrons, it will have a net positive charge
	If an object gains electrons, it will have a net negative charge

"When the 2 spheres touch"

	When the 2 spheres touch
	Next….

"And then are pulled apart"

	And then are pulled apart. This is what happens

"On the previous page,"

	On the previous page, only charge is transferred
	Total charge stays the same
	So charge is always conserved
	There is “CONSERVATION OF CHARGE” just like with energy and momentum

Transfer of Charge Problem

	1.) Sphere #1 touches sphere #2 and then is separated. Then sphere #2 touches #3 and is separated. What are the final charges on each sphere?

Answer

	1.) #1 has a charge of +2e
	#2 has a charge of +3e
	#3 has a charge of  +3e

Electrostatic Symbols and Constants

	Fe=electrostatic force in newtons (N) can be attractive or repulsive
	k=electrostatic constant 8.99x109N.m2/C2
	q=charge in coulombs (C)
	r=distance of separation in meters (m)
	E=electric field strength in (N/C)

Electrostatic Equations

Electric Fields

	An electric field is an area around a charged particle in which electric force can be detected
	Electric fields are detected and mapped using “positive” test charges
	Field lines are the imaginary lines along which a positive test charge would move (arrows show the direction)

Electric Field Line Diagrams

	Negative charge   Positive charge
	Parallel Plates
	+
	-

Electric Field Line Diagrams

	Negative and positive charges
	Field lines

Electric Field Line Diagrams

	Two positive charges
	Field lines

Electric Field Line Diagrams

	Two negative charges
	Field lines

Electrostatics Problems

	1.) What is the magnitude of the electric field strength when an electron experiences a 5.0N force?
	2.) Is a charge of 4.8x10-19C? possible? A charge of
	5.0x10-19C?
	3.) What is the electrostatic force between two 5.0C charges that are 1.0x10-4m apart?

Answers

	1.) Use

Answers (cont.)

	2.) Only whole number multiples of the elementary charge are possible. To find out if charge is possible, divide by 1.60x10-19C.
	4.8x10-19C is possible because when it is divided you get 3, which is a whole number.
	5.0x10-19C is not possible because when it is divided you get 3.125 which is not a whole number.

Answers (cont.)

	3.) Use

B. Current Electricity

	Current is the rate at which charge passes through a closed pathway (a circuit)
	The unit of current is ampere (A)

Conditions needed for a Circuit

	Must have a “potential difference” supplied by a battery or power source
	Must have a “pathway” supplied by wires
	Can have a resistor(s)
	Can have meters (ammeters, voltmeters, ohmmeters)

Current Electricity Quantities

	Current is the flow of charge past a point in a circuit in a unit of time. Measured in amperes (A)
	Potential Difference is the work done to move a charge between two points. Measured in volts (V)
	Resistance is the opposition to the flow of current. Measured in ohms (Ω)

Current Electricity Symbols

	I=current in amperes (A)
	Δq=charge in coulombs (C)
	t=time in seconds (s)
	V=potential difference in volts (V)
	W=work in Joules (J)
	R=resistance in ohms (Ω)
	ρ=resistivity in (Ω.m)
	L=length of wire in meters (m)
	A=cross-sectional area of wire in square meters (m2)

Current Electricity Equations

Conductivity

	A material is a “good” conductor if electric current flows easily through it
	Metals are good conductors because they have many electrons available and they are not tightly bound to the atom
	If a material is an extremely poor conductor, it is called an “insulator

Resistivity

	Resistivity is an property inherent to a material (and its temperature) that is directly proportional to the resistance of the material
	Use the “short, thick, cold” rule to remember what affects resistance
	Short, thick, cold wires have the lowest resistance (best conduction)

Current Electricity Problems

	1.) How many electrons pass a point in a wire in 2.0s if the wire carries a current of 2.5A?
	2.) A 10 ohm resistor has 20C of charge passing through it in 5s. What it the potential difference across the resistor?

Answers

	1.)

Answers (cont.)

	2.)

Resistivity Problem

	3.) What is the resistance of a 5.0m long aluminum wire with a cross-sectional area of 2.0x10-6m2 at 200C?

Answer

	3.)

C. Series Circuits

	Series circuit is a circuit with a single pathway for the current
	Current stays the same throughout the circuit
	Resistors share the potential difference from the battery (not necessarily equally)
	The sum of the resistances of all resistors is equal to the equivalent resistance of the entire circuit

Series Circuit Equations

Meters

	Ammeter measures the current in a circuit
	Voltmeter measures the potential difference across a resistor or battery
	Ohmmeter measures the resistance of a resistor

Circuit Diagram Symbols

	Cell
	Battery
	Switch
	Voltmeter
	ammeter

More Circuit Diagram Symbols

	Resistor
	Variable Resistor
	Lamp

Series Circuit Diagram Example

Series Circuit Problems

	1.) Two resistors with resistances of 4Ω and 6Ω are connected in series to a 25V battery. Determine the potential drop through each resistor, the current through each resistor and the equivalent resistance.

Answers

	1.) You can use R=V/I as soon as you have 2 pieces of information at each resistor. You can also use the series circuit laws.
	First, use Req=R1+R2 to find Req
	4Ω+6Ω=10Ω=Req (use this as the R at the battery)
	More…

Answers (cont.)

	Then use R=V/I at the battery to find I at the battery
	So…10Ω=25V/I  and I=2.5A and all currents are equal in a series circuit, so I1and I2=2.5A
	More….

Answers (cont.)

	Now that you have 2 pieces of information at each resistor, you can use R=V/I to find potential differences
	At the 4Ω resistor, 4Ω=V/2.5A
	so V1=10V
	At the 6Ω resistor, 6Ω=V/2.5A
	So…V2=15V

D. Parallel Circuits

	Parallel circuits have more than one pathway that the current can pass through
	Current is shared (not necessarily equally) among the pathways
	Voltage is the same in each pathway as across the battery
	Equivalent resistance is the sum of the reciprocal resistances of the pathways (Req is always less than R of any individual pathway)

Parallel Circuit Equations

Parallel Circuit Diagram Example

Parallel Circuit Problems

	1.) Three resistors of 2Ω, 4Ω and 4Ω are connected in parallel to an applied potential difference of 20V. Determine equivalent resistance for the circuit, the potential difference across each resistor and the current through each resistor.

Answers

	1.)
	So equivalent resistance=1Ω
	More…..

Answers (cont.)

	Use V=V1=V2=V3
	So since V=20V, V1=V2=V3=20V
	More……

Answers (cont.)

	Using R=V/I, substitute the potential differences and resistances for each resistor to find the current for each resistor
	I=20A
	I1=10A
	I2=5A
	I3=5A

E. Electric Power and Energy

	Electric power is the product of potential difference and current measured in watts just like mechanical power
	Electric energy is the product of power and time measured in joules just like other forms of energy

Electric Power and Energy Equations

Electric Energy and Power Problems

	1.) How much time does it take a 60W light bulb to dissipate 100J of energy?
	2.) What is the power of an electric mixer while operating at 120V, if it has a resistance of 10Ω?
	3.) A washing machine operates at 220V for 10 minutes, consuming 3.0x106J of energy. How much current does it draw during this time?

Answers

	1.) Use W=Pt
	So…100J=60Wxt
	So…t=0.6s
	2.) Use
	So…P=1440W

Answers (cont.)

	3.) Use W=VIt    but first need to change the 10 minutes to 600 seconds.
	So…3.0x106J=220V(I)600s
	So…I=22.7A

F. Magnetism and Electromagnetism

	Magnetism is a force of attraction or repulsion occurring when spinning electrons align
	A magnet has two ends called “poles”
	The “N” pole is “north seeking”
	The “S” pole is “south seeking”
	Like “poles” repel
	Unlike “poles” attract

"If you break a magnet"

	If you break a magnet, the pieces still have N and S poles
	The earth has an “S” pole at the North Pole
	The earth has a “N” pole at the South Pole
	The “N” pole of a compass will point towards earth’s “S” pole which is the geographic North pole

"There is a “field"

	There is a “field” around each magnet
	Imaginary magnetic field or flux lines show where a magnetic field is
	You can use a compass to map a magnetic field

Units for Magnetic Field

	The weber (Wb) is the unit for measuring the number of field lines
	The tesla (T) is the unit for magnetic field or flux density
	1T=1Wb/m2

Magnetic Field Diagrams

Magnetic Field Diagrams (cont.)

Magnetic Field Diagrams (cont.)

Electromagnetism

	Moving a conductor through a magnetic field will induce a potential difference which may cause a current to flow (conductor must “break” the field lines for this to occur)
	A wire with a current flowing through it creates a magnetic field
	So…magnetism creates electricity and electricity creates magnetism

Electromagnetism Diagram

	Must move wire into and out of page to induce potential current by breaking field lines

v. Waves

	A.) Wave Characteristics
	B.) Periodic Wave Phenomena
	C.) Light
	D.) Reflection and Refraction
	E.) Electromagnetic Spectrum

A. Wave Characteristics

	A wave is a vibration in a “medium” or in a “field”
	Sound waves must travel through a medium (material)
	Light waves may travel in either a medium or in an electromagnetic field
	Waves transfer energy only, not matter

"A pulse is a single..."

	A pulse is a single disturbance or vibration
	A periodic wave is a series of regular vibrations

Types of Waves

	1.) Longitudinal Waves are waves that vibrate parallel to the direction of energy transfer. Sound and earthquake p waves are examples.

Types of Waves

	2.) Transverse waves are waves that vibrate perpendicularly to the direction of energy transfer. Light waves and other electromagnetic waves are examples.

Frequency

	Frequency is how many wave cycles per second
	The symbol for frequency is f
	The unit for frequency is hertz (Hz)
	1Hz=1/s
	Frequency is pitch in sound
	Frequency is color in visible light

Frequency (cont.)

	High frequency wave
	Low frequency wave

Period

	Period is the time required for one wave cycle
	The symbol for period is T
	The unit for period is the second (s)
	The equation for period is T=1/f
	Period and frequency are inversely proportional

Period (cont.)

	Short period wave
	Long period wave

Amplitude

	The amplitude of a wave is the amount of displacement from the equilibrium line for the wave (how far crest or trough is from the equilibrium line)
	Symbol for amplitude is A
	Unit for amplitude is meter (m)
	Amplitude is loudness in sound
	Amplitude is brightness in light

Amplitude (cont.)

	High amplitude wave
	Low amplitude wave

Wavelength

	Wavelength is the distance between points of a complete wave cycle
	Symbol for wavelength is λ
	Unit for wavelength is meter (m)
	A wave with a high frequency will have short wavelengths and short period

Wavelength (cont.)

	Short wavelength    λ
	λ
	Long wavelength

Phase

	Points that are at the same type of position on a wave cycle (including same direction from equilibrium and moving in same direction) are “in phase”

Phase (cont.)

	Points that are in phase are whole wavelengths apart (i.e., 1λ apart, 2λ apart, 3λ apart, etc.)
	Points that are in phase are multiples of 360 degrees apart (i.e., 360 degrees apart, 720 degrees apart, 1080 degrees apart, etc.)

Phase (cont.)

	A             B             C
	D               E             F
	Points A, B and C are in phase
	Points D, E and F are in phase
	Points A and B are 360 degrees apart and 1λ apart
	Points D and F are 720 degrees apart and 2λ apart

Phase (cont.)

	A                                 C
	D
	B
	Points A and B are 180 degrees apart and ½ λ apart (not in phase)
	Points C and D are 90 degrees apart and ¼ λ apart (not in phase)

Speed

	Speed of a wave is equal to the product of wavelength and frequency
	Symbol for speed is v
	Unit for speed is m/s
	Equation for speed is v=fλ
	Can also use basic speed equation v=d/t if needed

Speed (cont.)

	The speed of a wave depends on its “type” and the medium it is traveling through
	The speed of light (and all electromagnetic waves) in a vacuum and in air is 3.00x108m/s
	The speed of sound in air at STP (standard temperature and pressure) is 331m/s

Wave Characteristics Problems

	1.) A wave has a speed of 7.5m/s and a period of 0.5s. What is the wavelength of the wave?
	2.) If the period of a wave is doubled, what happens to its frequency?
	3.) Points on a wave are 0.5λ apart, 7200 apart, 4λ apart. Which points are in phase?

Answers

	1.) First use T=1/f to find f, then use v=fλ to find λ
	So…0.5s=1/f and f=2.0Hz
	Then…7.5m/s=2.0Hz(λ) and λ=3.75m
	2.) T and f are inversely related so if T is doubled f is halved.

Answers (cont.)

	3.) Points are in phase only if they are whole wavelengths apart or multiples of 360 degrees apart. So..the points that are 720 degrees apart are in phase and the points that are 4λ apart are in phase. The points that are 0.5λ apart are not in phase.

More problems

	5.0m
	4.) What is the wavelength of the wave shown above?

Answer

	4.) The wave is 5.0m long and contains 2.5 cycles. You want to know the length of 1 cycle.
	So…5.0m/2.5 cycles=2.0m/cycle
	So…λ=2.0m

B. Periodic Wave Phenomena

	When waves interact with one another many different “phenomena” result
	Those phenomena are the doppler effect, interference, standing waves, resonance and diffraction

Circular Waves

	Some phenomena are easier to explain using circular waves
	A is the λ from
	crest to crest
	is the
	wavefront (all
	points on the
	circle are in              A       A
	phase)

Doppler Effect

	If the source of waves is moving relative to an observer, the observed frequency of the wave will change (actual f produced by the source doesn’t change and movement must be fast for observer to notice)

Doppler Effect (cont.)

	If source is moving towards the observer, f will increase (higher pitch if sound wave, shift towards blue if light wave)
	If source is moving away from the observer, f will decrease (lower pitch if sound wave, shift towards red if light wave)

Doppler Effect (cont.)

	Joe                                     Shmoe
	more….

Doppler Effect (cont.)

	In the diagram on the previous page, the wave source is moving towards Joe
	In the diagram on the previous page, the wave source is moving away from Shmoe

Doppler Effect (cont.)

	The effect on Joe is that the f of the wave will be higher for him (shorter λ and T, higher pitch or bluer light)
	The effect on Shmoe is that the f of the wave will be lower for him (longer λ and T, lower pitch or redder light)

Interference

	When waves travel in the same region and in the same plane at the same time (superposition) they can interfere with each other
	In “constructive” interference, waves build on one another to increase amplitude
	In “destructive” interference, waves destroy on another to decrease amplitude

Interference (cont.)

	Maximum constructive interference occurs when waves are in phase
	Maximum destructive interence occurs when waves are 180 degrees out of phase

 Maximum Constructive Interference

	Above results in

 Maximum Destructive Interference

	Above results in

Standing Waves

	Standing waves occur when waves having same A and same f travel in opposite directions. Vibrates so that it looks like waves are stationary

Resonance

	A body with an ability to vibrate has a natural frequency at which it will vibrate
	If you put an object that is vibrating with that same natural frequency next to that body, the body will also start vibrating (don’t need to touch)
	This is called “resonance”

Resonance (cont.)

	Examples of resonance:
	Find the “Tacoma Narrows Bridge” video on the internet
	A singer being able to break a glass with her voice

Diffraction

	When waves bend behind a barrier instead of going straight through that is called diffraction
	Wave
	fronts

C. Light

	Light is the part of the electromagnetic spectrum that is visible to humans
	The speed of light symbol is c
	The speed of light is constant, 3.00x108m/s in air or a vacuum
	Instead of using v=fλ, when it’s light you can substitute c=fλ

Light (cont.)

	No object can travel faster than the speed of light (one of Einstein’s ideas)
	The speed of light in a material is always less than c

Light Problems

	1.) Determine the wavelength in a vacuum of a light wave having a frequency of 6.4x1014Hz.
	2.) What is the frequency of a light wave with a wavelength of 5.6x10-7m?

Answers

	1.) Use c=fλ
	3.00x108m/s=6.4x1014Hz(λ)
	So… λ=4.7x10-7m
	2.) Use c=fλ
	3.00x108m/s=f(5.6x10-7m)
	So…f=5.4x1014Hz

D. Reflection and Refraction

	Reflection occurs when a ray of light hits a boundary and bounces back into the same medium
	Refraction occurs when a ray of light enters a new medium and changes direction because of a change in speed

More Reflection

	The law of reflection
	θi    θr
	Dotted line is the “normal”
	(reference line)

More Reflection

	In a mirror the image of an object is flipped laterally (your right hand is your left hand in a mirror image)
	To view an object in a plane mirror, you need a minimum of ½ the height of the object for the height of the mirror

More Refraction

	When light enters a different medium, the change in direction depends on the density of the new medium
	If new medium is denser, the light will slow down and bend towards the normal
	If new medium is less dense, the light will speed up and bend away from the normal

More Refraction

	Refraction Equations

More Refraction

	Symbols
			n=index of refraction (no units)
			v=speed of the wave in m/s
			λ=wavelength in m
			c=speed of light in a vacuum (3.00x108m/s)
			θ1=angle of incidence
			θ2=angle of refraction

Refraction Diagram

	θ1
	air
	glass        θ2
	Light travels from air into glass which is more dense so it slows down and bends towards the normal

Refraction Diagram

	θ1
	air
	glass         θ2
	Light travels from glass into air which is less dense so it speeds up and bends away from the normal

Absolute Index of Refraction

	Absolute index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a specific medium
	The symbol is n
	The higher the “n” number the denser the medium
	The lower the “n” number the less dense the medium

Absolute Index of Refraction (cont.)

	Higher “n” means slower v of light in the medium
	Lower “n” means higher v of light in the medium
	Use reference tables to find “n” numbers

Problems

	1.) What is the speed of light in diamond?
	2.) What is the ratio of the speed of light in corn oil to the speed of light in water?

Problems (cont.)

	3.) A ray of monochromatic light having a frequency of 5.09x1014Hz is traveling through water. The ray is incident on corn oil at an angle of 600 to the normal. What is the angle of refraction in corn oil?

Answers

	1.)

Answers (cont.)

	2.)

Answers (cont.)

	3.) Use Snell’s Law

E. Electromagnetic Spectrum

	Electromagnetic waves include gamma rays, x rays, ultraviolet rays, infrared rays, microwaves, t.v. and radio waves, long waves
	Electromagnetic waves are produced by accelerating charges (produce alternating electric and magnetic fields)

Electromagnetic Spectrum (cont.)

	High energy electromagnetic waves have high f and small λ
	Low energy electromagnetic waves have low f and long λ
	Energy in a wave can be increased by increasing f, decreasing λ and T and increasing the duration of the wave

Electromagnetic Spectrum (cont.)

	In the visible light spectrum, the violet end is high f, short λ and high energy
	In the visible light spectrum, the red end is low f, long λ and low energy

VI. Modern Physics

	A. Quantum Theory
	B. Atomic Models
	C. Nucleus
	D. Standard Model
	E. Mass-Energy

A. Quantum Theory

	E-m energy is absorbed and emitted in specific amounts called “quanta” according to the quantum theory
	A photon is the basic unit of
	e-m energy (particle of light)
	In wave theory E-m energy is emitted continuously
	Energy of a photon is directly related to its frequency

Quantum Theory (cont.)

	Light acts like a wave during diffraction, interference and the doppler effect
	Light acts like a particle (quantum idea) during the photoelectric effect and atomic spectra

Quantum Theory (cont.)

	Equation
	Ephoton=energy of a photon in joules (J)
	h=Planck’s constant
	(6.63x10-34J.s)
	f=frequency in hertz (Hz)
	λ=wavelength in meters (m)
	c=speed of light in vacuum 3.00x108m/s

Quantum Theory (cont.)

	Photoelectric Effect—Einstein used the particle idea of light (quantum theory) to explain why light incident on a photosensitive metal would only cause electrons to be emitted if its frequency was high enough

Quantum Theory (cont.)

	When light acts like a particle, it has momentum just like a particle
	Compton Effect—when an e-m photon hits an electron, the photon transfers some of its energy and momentum to the electron
	Particles can also act like waves by having a wavelength (usually too small to detect)