Download Electricity, Sound, and Light

Name:
Date:
8.1
Benjamin Franklin
Benjamin Franklin overcame a lack of formal education to become a prominent businessman, community
leader, inventor, scientist, and statesman. His study of “electric fire” changed our basic understanding of how
electricity works.
An eye toward inventiveness
Benjamin Franklin was born in
Boston in 1706. With only one
year of schooling he became an
avid reader and writer. He was
apprenticed at age 12 to his
brother James, a printer. The
siblings did not always see eye
to eye, and at 17, Ben ran away
to Philadelphia.
In his new city, Franklin
developed his own printing and
publishing business. Over the years, he became a
community leader, starting the first library, fire
department, hospital, and fire insurance company. He
loved gadgets and invented some of his own: the
Franklin stove, the glass armonica (a musical
instrument), bifocal eyeglasses, and swim fins.
‘Electric fire’
In 1746, Franklin saw some demonstrations of static
electricity that were meant for entertainment. He
became determined to figure out how this so-called
“electric fire” worked.
Undeterred by his lack of science education, Franklin
began experimenting. He generated static electricity
using a glass rod and silk cloth, and then recorded
how the charge could attract and repel lightweight
objects.
Franklin read everything he could about this “electric
fire” and became convinced that a lightning bolt was a
large-scale example of the same phenomenon.
Father and son experiment
In June 1752, Franklin and his 21-year-old son,
William, conducted an experiment to test his theory.
Although there is some debate over the details, most
historians agree that Franklin flew a kite on a stormy
day in order to collect static charges.
Franklin explained that he and his son constructed a
kite of silk cloth and two cedar strips. They attached a
metal wire to the top. Hemp string was used to fly the
kite. A key was tied near the string’s lower end. A silk
ribbon was affixed to the hemp, below the key.
Shocking results
It is probable that Franklin and his son were under
some sort of shelter, to keep the silk ribbon dry. They
got the kite flying, and once it was high in the sky they
held onto it by the dry silk ribbon, not the wet hemp
string. Nothing happened for a while. Then they
noticed that the loose threads of the hemp suddenly
stood straight up.
The kite probably was not struck directly by lightning,
but instead collected charge from the clouds. Franklin
touched his knuckle to the key and received a static
electric shock. He had proved that lightning was a
discharge of static electricity.
Those are charged words
Through his experiments, Franklin determined that
“electric fire” was a single “fluid” rather than two
separate fluids, as European scientists had thought.
He proposed that this “fluid” existed in two states,
which he called “positive” and “negative.” Franklin
was the first to explain that if there is an excess
buildup of charge on one item, such as a glass rod, it
must be exactly balanced by a lack of charge on
another item, such as the silk cloth. Therefore, electric
charge is conserved. He also explained that when
there is a discharge of static electricity between two
items, the charges become balanced again.
Many of Franklin’s electrical terms remain in use
today, including battery, charge, discharge, electric
shock, condenser, conductor, plus and minus, and
positive and negative.
Reading reflection
1.
Although Ben Franklin had only one year of schooling, he became a highly educated person. Describe how
Franklin learned about the world.
2.
What hypothesis did Franklin test with his kite experiment?
3.
Describe the results and conclusion of Franklin’s kite experiment.
4.
Franklin’s kite experiment was dangerous. Explain why.
5.
Silk has an affinity for electrons. When you rub a glass rod with silk, the glass is left with a positive charge.
Make a diagram that shows the direction that charges move in this example. Illustrate and label positive and
negative charges on the silk and glass rod in your diagram. Note: Show the same number of positive and
negative charges in your diagram.
6.
Research: Among Franklin’s many inventions is the lightning rod. Find out how this device works, and
create a model or diagram to show how it functions.
Name:
Date:
8.1
Lewis Latimer
Latimer, often called a “Renaissance Man,” was an accomplished African-American inventor receiving seven
U.S. patents. His professional and personal achievements define him as a humanitarian, artist, and scientist.
Son of former slaves
An enlightened inventor
Lewis Howard Latimer
was born on September 4,
1848
in
Chelsea,
Massachusetts. Latimer's
parents escaped from
slavery in Virginia and
moved north. Once in
Boston, Latimer's father,
George, was arrested and
jailed for being a fugitive.
The
Massachusetts
Supreme Court ruled that
he belonged to his owner.
The people of Boston protested and local supporters
paid for his release. George was now free. George
and his wife settled in Chelsea where they started
their family. In 1858, George, fearing he would be
forced to return to slavery, went underground leaving
his family behind.
Young Lewis Latimer attended grammar school in
Chelsea and was a very good student. During the
Civil War, teenager Lewis lied about his age to join the
Union Navy. After four years of military service,
Latimer was honorably discharged at the end of the
war.
Drafting a career
Latimer looked for work in Boston and finally found a
job as an office boy with a patent law firm, Crosby and
Gould. He earned $3.00 per week. At the firm, Lewis
studied the detailed patent drawings prepared by the
draftsmen. He never went to school to learn drafting,
but taught himself using any available tools and
books.
Latimer showed his drawings to his boss and secured
a job as a draftsman earning $20.00 per week. He
eventually became chief draftsman and worked at the
firm for eleven years.
During this time, Latimer created patent drawings for
Alexander Graham Bell. He completed the drawings
and submitted them only hours before a competing
inventor. Bell was awarded the telephone patent in
1876 due to Latimer's hard work and drafting skills.
Latimer was not only a talented draftsman, but also a
successful inventor. While at Crosby and Gould, he
developed
his
first
invention—mechanical
improvements for railroad train water closets (also
known as toilets!).
After Crosby and Gould, Latimer worked as a
draftsman at the Follandsbee Machine Shop. Here he
met Hiram Maxim and was hired to work at Maxim's
company, U.S. Electric Lighting. Maxim was an
inventor searching for ways to improve Thomas
Edison’s light bulb. Edison held the patent for the light
bulb, but the life span of the bulb was very short.
Maxim wanted to extend the life of the light bulb and
turned to Latimer for help.
Latimer taught himself the details of electricity. In
1881, he invented carbon filaments to replace paper
filaments in light bulbs. He then went on to improve
the manufacturing process of carbon filaments. Now
light bulbs lasted longer, were more affordable, and
had more uses. Latimer oversaw the installation of
electric street lights in North America and London. He
became chief electrical engineer for U.S. Electric
Lighting and supervised The Maxim-Westin Electric
Lighting Company in London.
Edison and beyond
In 1885, Thomas Edison hired Latimer to work in the
legal department of Edison Electric Light Company.
Latimer was the chief draftsman and patent authority
working to protect Edison's patents. He wrote the
widely acclaimed electrical engineering book called
Incandescent Electric Lighting: A Practical Description
of the Edison System. Latimer became one of only 28
members of the “Edison Pioneers” and the only
African- American member. Edison Pioneers were the
most highly regarded men in the electrical field.
Edison's company eventually became the General
Electric Company.
Latimer's additional inventions included an early
version of the air conditioner; a locking rack for hats,
coats, and umbrellas; and a book support. He was
also a poet, musician, playwright, painter, civil rights
activist, husband, and father. Latimer died in 1928 at
age 80.
Reading reflection
1.
How did Lewis Latimer become a draftsman and electrical engineer?
2.
List Latimer's major inventions. What was his most important invention and why?
3.
Research: What is a “Renaissance Man”? Why is Latimer referred to as a Renaissance man?
4.
Research: Latimer was an accomplished poet. Locate and identify the names of two of his poems.
5.
Research: When did the Edison Pioneers first meet? Locate an excerpt from the obituary published by the
Edison Pioneers honoring Lewis Latimer.
Page 2 of 2
Name:
Date:
Voltage, Current, and Resistance
8.2
Electricity is one of the most fascinating topics in physical science. It’s also one of the most useful to understand,
since we all use electricity daily. This skill sheet reviews some of the important terms in the study of electricity.
In the reading section, you’ll find questions that check your understanding. If you’re not sure of the answer, go
back and read that section again. In the practice section, you will have an opportunity to show that you know how
voltage, current, and resistance are related in real-world situations.
What is voltage?
You know that water will flow from a higher tank through a hose into a
lower tank. The water in the higher tank has greater potential energy than the
water in the lower tank. A similar thing happens with the flow of charges in
an electric circuit.
Charges flow in a circuit when there is a difference in energy level from one
end of the battery (or any other energy source) to the other. This energy
difference is measured in volts. The energy difference causes the charges to
move from a higher to a lower voltage in a closed circuit.
Think of voltage as the amount of “push” the electrical source supplies to the
circuit. A meter is used to measure the amount of energy difference or
“push” in a circuit. The meter reads the voltage difference (in volts) between
the positive and the negative ends of the power source (the battery). This
voltage difference supplies the energy to make charges flow in a circuit.
1.What is the difference between placing a 1.5-volt battery in a circuit and
placing a 9-volt battery in a circuit?
What is current?
Current describes the flow of electric charges. Current is the actual measure of how many charges are flowing
through the circuit in a certain amount of time. Current is measured in units called amperes.
Just as the rate of water flowing out of a faucet can be fast or slow, electrical current can move at different rates.
The type, length, and thickness of wire all effect how much current flows in a circuit. Resistors slow the flow of
current. Adding voltage causes the current to speed up.
2.
What could you do to a closed circuit consisting of a battery, a light bulb, and a switch that would increase
the amount of current? Explain your answer.
3.
What could you do to a closed circuit consisting of a battery, a light bulb, and a switch that would decrease
the amount of current? Explain your answer.
Voltage, Current, and Resistance
What is resistance?
Resistance is the measure of how easily charges flow through a circuit. High resistance means it is difficult for
charges to flow. Low resistance means it is easy for charges to flow. Electrical resistance is measured in units
called ohms (abbreviated with the symbol Ω).
Resistors are items that reduce the flow of charge in a circuit. They act like “speed bumps” in a circuit. A light
bulb is an example of a resistor.
4.
Describe one thing that you could do to the wire used in a circuit to decrease the amount of resistance
presented by the wire.
How are voltage, current, and resistance related?
When the voltage (push) increases, the current (flow of charges) will also increase, and when the voltage
decreases, the current likewise decreases. These two variables, voltage and current, are said to be directly
proportional.
When the resistance in an electric circuit increases, the flow of charges (current) decreases. These two variables,
resistance and current, are said to be inversely proportional. When one goes up, the other goes down, and vice
versa.
The law that relates these three variables is called Ohm’s Law. The formula is:
Voltage (volts)
Current (amps) = ---------------------------------------------Resistance (ohms, Ω)
5.
In your own words, state the relationship between resistance and current, as well as the relationship between
voltage and current.
•
In a circuit, how many amps of current flow through a resistor such as a 6-ohm light bulb when using four
1.5-volt batteries as an energy supply?
Solution:
4 × 1.5 volts 6 volts
Current = --------------------------- = --------------6 ohms
6 ohms
Current = 1 amp
Page 2 of 3
Page 3 of 3
8.2
Now you will have the opportunity to demonstrate your understanding of the relationship between current,
voltage and resistance. Answer each of the following questions and show your work.
1.
How many amps of current flow through a circuit that includes a 9-volt battery and a bulb with a resistance
of 6 ohms?
2.
How many amps of current flow through a circuit that includes a 9-volt battery and a bulb with a resistance
of 12 ohms?
3.
How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms of
resistance?
4.
How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 amps?
Name:
Date:
Electrical Power
8.2
How do you calculate electrical power?
In this skill sheet you will review the relationship between electrical power and Ohm’s law. As you work through
the problems, you will practice calculating the power used by common appliances in your home.
During everyday life we hear the word watt mentioned in reference to things like light bulbs and electric bills.
The watt is the unit that describes the rate at which energy is used by an electrical device. Energy is never created
or destroyed, so “used” means it is converted from electrical energy into another form such as light or heat. Since
energy is measured in joules, power is measured in joules per second. One joule per second is equal to one watt.
To calculate the electrical power “used” by an electrical component, multiply the voltage by the current.
Current x Voltage = Power, or P = IV
A kilowatt (kWh) is 1,000 watts or 1,000 joules of energy per second. On an electric bill you may have noticed
the term kilowatt-hour. A kilowatt-hour means that one kilowatt of power has been used for one hour. To
determine the kilowatt-hours of electricity used, multiply the number of kilowatts by the time in hours.
.
•
You use a 1,500 watt heater for 3 hours. How many kilowatt-hours of electricity did you use?
1 kilowatt
= 1.5 kilowatts
1,000 watts
1.5 kilowatts × 3 hours = 4.5 kilowatt-hours
1,500 watts ×
You used 4.5 kilowatt-hours of electricity.
1.
2.
3.
Your oven has a power rating of 5,000 watts.
a.
How many kilowatts is this?
b.
If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh) are used?
c.
If your town charges $0.15 per kWh, what is the cost to use the oven to bake the cookies?
You use a 1,200-watt hair dryer for 10 minutes each day.
a.
How many minutes do you use the hair dryer in a month? (Assume there are 30 days in the month.)
b.
How many hours do you use the hair dryer in a month?
c.
What is the power of the hair dryer in kilowatts?
d.
How many kilowatt-hours of electricity does the hair dryer use in a month?
e.
If your town charges $0.15 per kWh, what is the cost to use the hair dryer for a month?
Calculate the power rating of a home appliance (in kilowatts) that uses 8 amps of current when plugged into
a 120-volt outlet.
Electrical Power
4.
Calculate the power of a motor that draws a current of 2 amps when connected to a 12 volt battery.
5.
Your alarm clock is connected to a 120 volt circuit and draws 0.5 amps of current.
a.
Calculate the power of the alarm clock in watts.
b.
Convert the power to kilowatts.
c.
Calculate the number of kilowatt-hours of electricity used by the alarm clock if it is left on for one year.
d.
Calculate the cost of using the alarm clock for one year if your town charges $0.15 per kilowatt-hour.
6.
Using the formula for power, calculate the amount of current through a 75-watt light bulb that is connected
to a 120-volt circuit in your home.
7.
The following questions refer to the diagram.
a. What is the total voltage of the circuit?
b. What is the current in the circuit?
c. What is the power of the light bulb?
8.
9.
A toaster is plugged into a 120-volt household circuit. It draws 5 amps of
current.
a.
What is the resistance of the toaster?
b.
What is the power of the toaster in watts?
c.
What is the power in kilowatts?
A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit.
a.
What is the current through the dryer?
b.
What is the resistance of the dryer?
c.
How many kilowatt-hours of electricity are used by the dryer if it is used for 4 hours in one week?
d.
How much does it cost to run the dryer for one year if it is used for 4 hours each week at a cost of $0.15
per kilowatt-hour?
10. A circuit contains a 12-volt battery and two 3-ohm bulbs in series.
a.
Calculate the total resistance of the circuit.
b.
Calculate the current in the circuit.
c.
Calculate the power of each bulb.
d.
Calculate the power supplied by the battery.
11. A circuit contains a 12-volt battery and two 3-ohm bulbs in parallel.
a.
What is the voltage across each branch?
b.
Calculate the current in each branch.
c.
Calculate the power of each bulb.
d.
Calculate the total current in the circuit.
e.
Calculate the power supplied by the battery.
Page 2 of 2
Name:
Date:
Ohm's Law
8.2
A German physicist, Georg S. Ohm, developed this mathematical relationship, which is present in most circuits.
This relationship is known as Ohm's law. It states that if the voltage in a circuit increases, so does the current. If
the resistance increases, the current decreases.
Voltage (volts)
Current (amps) = ---------------------------------------------Resistance (ohms, Ω)
To work through this skill sheet, you will need the symbols used to depict circuits in
diagrams. The symbols that are most commonly used for circuit diagrams are
provided to the right.
If a circuit contains more than one battery, the total voltage is the sum of the
individual voltages. A circuit containing two 6 V batteries has a total voltage of 12 V.
[Note: The batteries must be connected positive to negative for the voltages to add.]
•
If a toaster produces 12 ohms of resistance in a 120-volt circuit, what is the
amount of current in the circuit?
Solution:
I =
V 120 volts
=
= 10 amps
R
12 ohms
The current in the toaster circuit is 10 amps.
Note: If a problem asks you to calculate the voltage or resistance, you must rearrange the equation to solve for V
or R. All three forms of the equation are listed below.
I =
V
R
V = IR
R =
V
I
Answer the following question using Ohm’s law. Don’t forget to show your work.
1.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 3 ohms?
2.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 12 ohms?
3.
A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.
4.
A circuit contains two 1.5 volt batteries and a bulb with a resistance of 3 ohms. Calculate the current.
5.
What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?
6.
A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?
Ohm's Law
7.
How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms of
resistance?
8.
How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 amps?
9.
An alarm clock draws 0.5 A of current when connected to a 120 volt circuit. Calculate its resistance.
10. A portable CD player uses two 1.5 V batteries. If the current in the CD player is 2 A, what is its resistance?
11. You have a large flashlight that takes 4 D-cell batteries. If the current in the flashlight is 2 amps, what is the
resistance of the light bulb? (Hint: A D-cell battery has 1.5 volts.)
12. Use the diagram below to answer the following problems.
a.
What is the total voltage in each circuit?
b.
How much current would be measured in each circuit if the light bulb has a resistance of 6 ohms?
c.
How much current would be measured in each circuit if the light bulb has a resistance of 12 ohms?
d.
Is the bulb brighter in circuit A or circuit B? Why?
13. What happens to the current in a circuit if a 1.5-volt battery is removed and is replaced by a 9-volt battery?
14. In your own words, state the relationship between resistance and current in a circuit.
15. In your own words, state the relationship between voltage and current in a circuit.
16. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to increase the
current? Explain your answer.
17. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to decrease the
current? Explain your answer.
18. You have four 1.5 V batteries, a 1 Ω bulb, a 2 Ω bulb, and a 3 Ω bulb. Draw a circuit you could build to
create each of the following currents. There may be more than one possible answer for each.
a.
1 ampere
b.
2 amperes
c.
3 amperes
d.
6 amperes
Page 2 of 2
Name:
Date:
8.2
George Westinghouse
George Westinghouse was both an imaginative tinkerer and a bold entrepreneur. His inventions had a profound
effect on nineteenth-century transportation and industrial development in the United States. His air brakes and
signaling systems made railway systems safer at higher speeds, so that railroads became a practical method of
transporting goods across the country. He promoted alternating current as the best means of providing electric
power to businesses and homes, and his method became the worldwide standard. Westinghouse obtained 361
patents over the course of his life.
A boyhood among machines
George Westinghouse was
born October 6, 1846, in
Central Bridge, New York.
When he was 10, his family
moved to Schenectady,
where his father opened a
shop that manufactured
agricultural
machinery.
George spent a great deal
of time working and
tinkering there.
Long-distance electricity
Next,
Westinghouse
became
interested
in
transmitting electricity over long distances. He saw
the potential benefits of providing electric power to
individual homes and businesses, and in 1884 formed
the Westinghouse Electric Company. Westinghouse
learned that Nikola Tesla had developed alternating
current and he persuaded Tesla to join the company.
After serving in both the Union Army and Navy in the
Civil War, Westinghouse attended college for three
months. He dropped out after receiving his first patent
in 1865, for a rotary steam engine he had invented in
his father’s shop.
Initially, Westinghouse met with resistance from
Thomas Edison and others who argued that direct
current was a safer alternative. But direct current
could not be transmitted over distances longer than
three miles. Westinghouse demonstrated the potential
of alternating current by lighting the streets of
Pittsburgh, Pennsylvania, and, in 1893, the entire
Chicago World’s Fair. Afterward, alternating current
became the standard means of transmitting electricity.
An inventive train of thought
From waterfalls to elevated railway
In 1866, Westinghouse was aboard a train that had to
come to a sudden halt to avoid colliding with a
wrecked train. To stop the train, brakemen manually
applied brakes to each individual car based on a
signal from the engineer.
Also in 1893, Westinghouse began yet another new
project: the construction of three hydroelectric
generators to harness the power of Niagara Falls on
the New York-Canada border. By November 1895,
electricity generated there was being used to power
industries in Buffalo, some 20 miles away.
Westinghouse believed there could be a safer way to
stop these heavy trains. In April 1869, he patented an
air brake that enabled the engineer to stop all the cars
in tandem. That July he founded the Westinghouse
Air Brake Company, and soon his brakes were used
by most of the world’s railways.
The new braking system made it possible for trains to
travel safely at much higher speeds. Westinghouse
next turned his attention to improving railway
signaling and switching systems. Combining his own
inventions with others, he created the Union Switch
and Signal Company.
Another Westinghouse interest was alternating
current locomotives. He introduced this new
technology first in 1905 with the Manhattan Elevated
Railway in New York City, and later with the city’s
subway system.
An always inquiring mind
The financial panic of 1907 caused Westinghouse to
lose control of his companies. He spent much of his
last years in public service. Westinghouse died in
1914 and left a legacy of 361 patents in his name—
the final one received four years after his death.
Reading reflection
1.
Where did George Westinghouse first develop his talent for inventing things?
2.
How did Westinghouse make it possible for trains to travel more safely at higher speeds?
3.
Why did Westinghouse promote alternating current over direct current for delivering electricity to
businesses and homes?
4.
How did Westinghouse turn public opinion in favor of alternating current?
5.
Together with a partner, explain the difference between direct and alternating current. Write your
explanation as a short paragraph and include a diagram.
6.
How did Westinghouse provide electrical power to the city of Buffalo, New York?
7.
Ordinary trains in Westinghouse’s time were coal-powered steam engines. How were Westinghouse’s
Manhattan elevated trains different?
8.
Research: Westinghouse had a total of 361 patents to his name. Use a library or the Internet to find out
about three inventions not mentioned in this brief biography, and describe each one.
Name:
Date:
Open and Closed Circuits
8.2
Where is the current flowing?
You have built and tested different kinds of circuits in the lab. Now you can use what you learned to make
predictions about circuits you haven’t seen before. Use the circuit diagrams pictured below to answer the
questions. You may wish to write on the diagrams in order to keep track where the current is flowing. As a result,
each diagram is repeated several times.
1.
Which devices (A, B, C, or D) in the circuit pictured below will be on when the following conditions are
met? For your answer, give the letter of the device or devices.
a. Switch 3 is open, and all other switches are closed.
b. Switch 2 is open, and all other switches are closed.
c. Switch 4 is open, and all other switches are closed.
d. Switch 1 is open, and all other switches are closed.
e. Bulb C blows out, and all switches are closed.
f. Bulb A blows out, and all switches are closed.
.
g. Switches 2 and 4 are open, and switches 1 and 3 are closed.
h. Switches 2 and 3 are open, and switches 1 and 4 are closed.
Open and Closed Circuits
.
i. Switches 2, 3, and 4 are open, and switch 1 is closed.
j. Switches 1 and 2 are open, and switches 3 and 4 are closed.
2. Which of the devices (A-G) in the circuit below will be on when the following conditions are met? For your
answer, give the letter of the device or devices.
a. Switch 5 is open, and all other switches are closed.
b. Switch 6 is open, and all others are closed.
c. Switch 7 is open, and all others are closed.
.
d. Switch 4 is open, and all others are closed.
e. Switch 3 is open, and all others are closed.
f. Switch 2 is open, and all others are closed.
g. Switch 1 is open, and all others are closed.
h. Switches 2 and 4 are open, and all others are closed.
Page 2 of 3
Page 3 of 3
i. Switches 4 and 6 are open, and all others are closed.
8.2
j. Switches 4 and 7 are open, and all others are closed.
k. Switches 5 and 7 are open, and all others are closed.
l. Switches 2 and 3 are open, and all others are closed.
m. Bulb D blows out with all switches closed.
.
3.
4.
5.
n. Bulbs A and B blow out with all switches closed.
o. Bulbs A and D blow out with all switches closed.
Use arrows to draw the direction of the current in each of the circuits below. Make sure to show current
direction in all paths of the circuits within each diagram.
How many possible paths are there in circuit diagrams in questions (1) and (2)?
Draw a circuit of your own. Use one battery, show at least 4 devices (bulbs and bells), and divide the current
at some point in the circuit. Finally, use arrows to show the direction of the current in all parts of your circuit.
Name:
Date:
Electric Circuit Project
8.2
The Steady Hand Game
Do you have a steady hand? This easy-to-build game challenges your manual dexterity. Can you move a small
loop of wire over a complicated maze without tripping the light bulb? Try it and see!
Gather these materials
•
Electric Circuits Set: electricity table, one battery with holder, one light bulb with holder, one long
connecting wire (brown)
•
1 meter of 12-gauge copper wire. Wire must not have an insulated coating. This wire can be purchased
where picture hanging supplies are sold.
•
50 centimeter-long piece of 16-gauge insulated copper wire. This wire can be purchased at a hardware store.
•
Electrical tape
•
Wire stripper tool
•
Permanent-ink marking pen
•
Metric ruler or measuring tape
Electric Circuit Project
How to build the game
1.
2.
3.
4.
5.
6.
7.
8.
9.
Place the battery, light bulb, and long connecting wire on the electricity table as shown in the diagram on the
previous page.
Cut a 20-centimeter piece from one end of the 1 meter-long piece of 12-gauge copper wire.
Bend one end of the 20-cm piece in to a loop with a diameter no larger than a dime. The smaller the loop, the
more challenging the game! Twist the wire to secure the loop. You have just constructed the wand for your
game board.
Strip 2 cm of plastic coating from each end of the 50 cm length of 16 gauge wire. (Your teacher may help
with this part).
Wrap one end of the exposed wire around the base of your wand and secure with electrical tape.
Wrap the other end of the exposed copper wire around the right front corner post of the electricity table. (The
light bulb wire should also be connected to this post). Secure with electrical tape.
Measure 15 cm in from each end of your remaining 80 cm piece of 12 gauge copper wire. Mark the two
spots with permanent ink. DO NOT cut the wire.
Make a 90° bend in the wire at each spot so that the wire is shaped like a wide, upside-down U.
Bend the long horizontal section of the wire into a series of hills and valleys (see illustration). Adjust the
bends until the two 15 cm “legs” of the wire are 23 cm apart.
10. Place one of the 15-centimeter “legs” alongside the left, rear post of the electricity grid. The long connecting
wire should be attached to this post. Secure the leg with electrical tape.
11. Slide the loop of your wand over the other leg of the 12-gauge wire.
12. Use electrical tape to secure this leg to the right, rear post of the electricity grid. Make sure that the tape
covers the entire post.
13. Make sure that the loop in the wand will slide down the post. The loop should be placed in this position
when the game is not in use.
14. Now you are ready to play! Using one hand, move the loop in the wand over the hills and valleys—but don’t
let the loop touch the copper wire! Try to make it all the way across without lighting the bulb.
Variation: Inexpensive buzzers can be purchased at electronic or hobby stores and placed in the circuit alongside
the bulb.
Page 2 of 2
Name:
Date:
8.3
Michael Faraday
Despite little formal schooling, Michael Faraday rose to become one of England’s top research scientists of the
nineteenth century. He is best known for his discovery of electromagnetic induction, which made possible the
large-scale production of electricity in power plants.
Reading his way to a job
Michael Faraday was born
on September 22, 1791, in
Surrey, England, the son of
a blacksmith. His family
moved to London, where
Michael
received
a
rudimentary education at a
local school.
At 14, he was apprenticed
to a bookbinder. He
enjoyed
reading
the
materials he was asked to
bind, and found himself
mesmerized by scientific
papers that outlined new
discoveries.
A wealthy client of the bookbinder noticed this
voracious reader and gave him tickets to hear
Humphry Davy, the British chemist who had
discovered potassium and sodium, give a series of
lectures to the public.
Faraday took detailed notes at each lecture. He
bound the notes and sent them to Davy, asking him
for a job. In 1812, Davy hired him as a chemistry
laboratory assistant at the Royal Institution, London’s
top scientific research facility.
Despite his lack of formal training in science or math,
Faraday was an able assistant and soon began
independent research in his spare time. In the early
1820s, he discovered how to liquefy chlorine and
became the first to isolate benzene, an organic
solvent with many commercial uses.
The first electric motor
Faraday also was interested in electricity and
magnetism. After reading about the work of Hans
Christian Oersted, the Danish physicist, chemist, and
electromagnetist, he repeated Oersted’s experiments
and used what he learned to build a machine that
used an electromagnet to cause rotation—the first
electric motor.
Next, he tried to do the opposite, to use a moving
magnet to cause an electric current. In 1831, he
succeeded.
Faraday’s
discovery
is
called
electromagnetic induction, and it is used by power
plants to generate electricity even today.
The Faraday effect
Faraday first developed the concept of a field to
describe magnetic and electric forces, and used iron
filings to demonstrate magnetic field lines. He also
conducted important research in electrolysis and
invented a voltmeter.
Faraday was interested in finding a connection
between magnetism and light. In 1845 he discovered
that a strong magnetic field could rotate the plane of
polarized light. Today this is known as the Faraday
effect.
A scientist’s public education
Faraday was a teacher as well as a researcher. When
he became director of the Royal Institution laboratory
in 1825, he instituted a popular series of Friday
Evening Discourses. Here paying guests (including
Prince Albert, who was Queen Victoria’s husband)
were entertained with demonstrations of the latest
discoveries in science.
A series of lectures on the chemistry and physics of
flames, titled “The Natural History of a Candle,” was
among the original Christmas Lectures for Children,
which continue to this day.
Named in his honor
Faraday continued his work at the Royal Institution
until just a few years before his death in 1867. Two
units of measure have been named in his honor: the
farad, a unit of capacitance, and the faraday, a unit of
charge.
Reading reflection
1.
What did Michael Faraday do to get a job with Humphry Davy? Why was this effort important in getting
Faraday started in science?
2.
Research benzene and list two modern-day commercial uses for this chemical.
3.
Based on the reading, define electromagnetic induction.
4.
In your own words, describe the Faraday effect. In your description, explain the term “polarized light.”
5.
How did Faraday contribute to society during his time as the director of the Royal Institution laboratory?
6.
Name two ways in which Faraday’s work affects your own life in the twenty-first century.
7.
Imagine you could go back in time to see one of Faraday’s demonstrations. Explain why you would like to
attend one of his demonstrations.
8.
Activity: Use iron filings and a magnet to demonstrate magnetic field lines, or prepare a simple
demonstration of electromagnetic induction for your classmates.
Name:
Date:
Magnetic Earth
8.3
Earth’s magnetic field is very weak compared with the strength of the field on the surface of the ceramic magnets
you probably have in your classroom. The gauss is a unit used to measure the strength of a magnetic field. A
small ceramic permanent magnet has a field of a few hundred up to 1,000 gauss at its surface. At Earth’s surface,
the magnetic field averages about 0.5 gauss. Of course, the field is much stronger nearer to the core of the planet.
1.
What is the source of Earth’s magnetic field according to what you have read in chapter 8?
2.
Today, Earth’s magnetic field is losing approximately 7 percent of its strength every 100 years. If the
strength of Earth’s magnetic field at its surface is 0.5 gauss today, what will it be 100 years from now?
3.
Describe what you think might happen if Earth’s magnetic field continues to lose strength.
4.
The graphic to the right illustrates one piece of evidence that proves the
reversal of Earth’s poles during the past millions of years. The ‘crust’ of
Earth is a layer of rock that covers Earth’s surface. There are two kinds of
crust—continental and oceanic. Oceanic crust is made continually (but
slowly) as magma from Earth’s interior erupts at the surface. Newly formed
crust is near the site of eruption and older crust is at a distance from the site.
Based on what you know about magnetism, why might oceanic crust rock
be a record of the reversal of Earth’s magnetic field? (HINT: What happens
to materials when they are exposed to a magnetic field?)
5.
The terms magnetic south pole and geographic north pole refer to locations
on Earth. If you think of Earth as a giant bar magnet, the magnetic south
pole is the point on Earth’s surface above the south end of the magnet. The
geographic north pole is the point where Earth’s axis of rotation intersects
its surface in the northern hemisphere. Explain these terms by answering the
following questions.
6.
a.
Are the locations of the magnetic south pole and the geographic north
pole near Antarctica or the Arctic?
b.
How far is the magnetic south pole from the geographic north pole?
c.
In your own words, define the difference between the magnetic south pole and the geographic north
pole.
A compass is a magnet and Earth is a magnet. How does the magnetism of a compass work with the
magnetism of Earth so that a compass is a useful tool for navigating?
Magnetic Earth
7.
The directions—north, east, south, and west—are arranged on a compass so that they align with 360 degrees.
This means that zero degrees (0°) and 360° both represent north. For each of the following directions by
degrees, write down the direction in words. The first one is done for you.
a.
45°
b.
180°
c.
270°
d.
90°
e.
135°
f.
315°
Answer: The direction is northeast.
Magnetic declination
Earth’s geographic north pole (true north) and magnetic south pole are located near each other, but they are not at
the same exact location. Because a compass needle is attracted to the magnetic south pole, it points slightly east
or west of true north. The angle between the direction a compass points and the direction of the geographic north
pole is called magnetic declination. Magnetic declination is measured in degrees and is indicated on
topographical maps.
8.
Let’s say you were hiking in the woods and relying on a map and compass to navigate. What would happen
if you didn’t correct your compass for magnetic declination?
9.
Are there places on Earth where magnetic declination equals 0°? Use the Internet or your local library to find
out where on Earth there is no magnetic declination.
Page 2 of 2
Name:
Date:
Transformers
8.3
A transformer is a device used to change voltage and current. You may have
noticed the gray electrical boxes often located between two houses or
buildings. These boxes protect the transformers that “step down” high voltage
from power lines (13,800 volts) to standard household voltage (120 volts).
How a transformer works:
1.
The primary coil is connected to outside power lines. Current in
the primary coil creates a magnetic field through the secondary
coil.
2.
The current in the primary coil changes frequently because it is
alternating current.
3.
As the current changes, so does the strength and direction of the
magnetic field through the secondary coil.
4.
The changing magnetic field through the secondary coil induces
current in the secondary coil. The secondary coil is connected to
the wiring in your home.
Transformers work because the primary and secondary coils have different numbers of turns. If the secondary
coil has fewer turns, the induced voltage in the secondary coil is lower than the voltage applied to the primary
coil. You can use the proportion below to figure out how number of turns affects voltage:
Transformers
A transformer steps down the power line voltage (13,800 volts) to standard household voltage (120 volts). If the
primary coil has 5,750 turns, how many turns must the secondary coil have?
Solution:
V1 N1
=
V 2 N2
13,800 volts 5750 turns
=
120 volts
N2
N2 = 50 turns
1.
In England, standard household voltage is 240 volts. If you brought your own
hair dryer on a trip there, you would need a transformer to step down the voltage
before you plug in the appliance. If the transformer steps down voltage from 240
to 120 volts, and the primary coil has 50 turns, how many turns does the
secondary coil have?
2.
You are planning a trip to Singapore. Your travel agent gives you the proper
transformer to step down the voltage so you can use your electric appliances
there. Curious, you open the case and find that the primary coil has 46 turns and
the secondary has 24 turns. Assuming the output voltage is 120 volts, what is the
standard household voltage in Singapore?
3.
A businessman from Zimbabwe buys a transformer so that he can use his own electric appliances on a trip to
the United States. The input coil has 60 turns while the output coil has 110 turns. Assuming the input voltage
is 120 volts, what is the output voltage necessary for his appliances to work properly? (This is the standard
household output voltage in Zimbabwe.)
4.
A family from Finland, where standard household voltage is 220 volts, is planning a trip to Japan. The
transformer they need to use their appliances in Japan has an input coil with 250 turns and an output coil
with 550 turns. What is the standard household voltage in Japan?
5.
An engineer in India (standard household voltage = 220 volts) is designing a transformer for use on her
upcoming trip to Canada (standard household voltage = 120 volts). If her input coil has 240 turns, how many
turns should her output coil have?
6.
While in Canada, the engineer buys a new electric toothbrush. When she returns home she designs another
transformer so she can use the toothbrush in India. This transformer also has an input coil with 240 turns.
How many turns should the output coil have?
Page 2 of 2
Name:
Date:
Significant Differences in Measurement
8.3
When people conduct experiments, how can they be certain the results are accurate? The short answer is that they
can never be certain the results are accurate. This is why experiments are usually performed multiple times, and
then analyzed to determine the amount of the error. The error is estimated by calculating the largest difference
between the average and a measured value. Once you know the amount of error, it can be used to determine
whether two results should be considered the same. If two measurements or results differ by an amount that is
less than or equal to the amount of error, they are considered to be the same.
One hot summer day, Dave and Chris decided to have a toy boat race in their little sisters’ wading pool. The boats
are identical, except for the sails. Dave’s boat has a rectangular sail, and Chris’ boat has a triangular sail. They
borrow their father’s timer to get the most accurate measurement possible. They raced the boats 5 times. The
results are given below.
Dave’s Boat ([])
Time (seconds)
0.528
0.532
0.530
0.526
0.533
Chris’ Boat (Δ)
Time (seconds)
0.525
0.530
0.529
0.520
0.529
Chris claims that since his boat won every race; that proves that his boat is the faster boat. Is this correct?
In order to determine if Chris’ claim is correct, you must decide if the times they have collected are significantly
different. If there is no significant difference between the times of the boats, then there is no evidence to support
that either boat is faster. Follow these steps to determine whether the difference is significant:
+ 0.532 + 0.530 + 0.526 + 0.533- = 0.530
Dave’s boat’s average time = 0.528
-------------------------------------------------------------------------------------------5
+ 0.530 + 0.529 + 0.520 + 0.529- = 0.527
Chris’ boat’s average time = 0.525
-------------------------------------------------------------------------------------------5
1.
Find the average time it took each boat to complete the race course. Remember that the average is found by
dividing the sum of a data set by the number of items in the data set.
2.
Find the amount of error for each data set. To calculate the error, find the greatest difference between the
average (found in #1) and any item in the data set.
a.
Find the error for Dave’s boat: The difference between Dave’s boat’s average (0.530) and its slowest
time (0.533) is 0.003; the difference between the average and the fastest time (0.526) is 0.004. The
largest difference is 0.004, so the amount of error is ± 0.004.
Significant Differences in Measurement
b.
Find the error for Chris’ boat: The difference between Chris’ boat’s average (0.527) and its slowest time
(0.530) is 0.003; the difference between the average and the fastest time (0.520) is 0.007. The largest
difference is 0.007, so the amount of error is ± 0.007.
3.
Determine whether the difference is significant. First, find the difference between the averages for each set
of data. Here, the difference is found by subtracting the average time of Chris’ boat (0.527) from the average
time of Dave’s boat (0.530). Since 0.530 - 0.527 = 0.003, and 0.003 is not greater than the amount of error
found in #2, there is no significant difference between the two sets of data. In other words, scientifically, the
data are the same. It is impossible to determine which boat is faster.
1.
A toy car and a toy truck of about the same size are started down identical ramps. The distance traveled by
each vehicle on each of four attempts is recorded below. Is it true that the truck will always travel farther
than the car? [Hint: follow the steps explained in the example]
Toy Car
Distance (m)
1.57
1.45
1.55
1.48
Average
Toy Truck
Distance (m)
1.77
1.90
1.85
2.00
Average
Error
Error
2.
The water pressure in the sinks at Sean’s house is constant. Sean wants to compare the water pressure in the
kitchen sink with the water pressure in the bathroom sink. He does this by recording the amount of time it
takes to fill a 1-cup measure with water from each sink. He performs this experiment a total of five times. Is
it possible to determine which sink has the greatest water pressure (fills the cup the quickest)? If so, which
sink has the greater water pressure?
Bathroom Sink
Time (seconds)
3.42
3.50
3.45
3.49
3.47
Average
Kitchen Sink
Time (seconds)
3.12
3.15
3.12
3.10
3.13
Average
Error
Error
Page 2 of 3
Page 3 of 3
3.
After school one day, Antonio and Earnest were playing with a slingshot. Antonio’s mother said it
8.3
would be OK as long as they stayed in the back yard, and used only pencil erasers for ammunition.
Antonio had a pink, rectangular eraser, while Earnest had a smaller white, square one. The table below
shows the distance traveled by each eraser on 8 attempts. From only the given data, can you support
(scientifically) Earnest’s claim that his eraser will always go farther? Explain why or why not.
Antonio’s (pink) eraser
Distance (m)
3.12
3.20
3.55
3.04
3.48
3.60
3.16
3.35
4.
While cleaning the kitchen sink one Saturday, Joanne noticed that her yellow sponge seemed to be a little
heavier than the pink one when they were both saturated with water, even though when the sponges were
dry, they seemed to have the same mass. Joanne found the mass of both sponges when they were dry. She
was right, each sponge had a mass of 31.50 grams. She saturated each sponge with plain water several times,
and recorded the data below. Does the data show (scientifically) that the yellow sponge absorbs more water
than the pink one? Explain why or why not.
Yellow Sponge
Mass (g)
94.25
93.45
92.40
92.22
92.20
5.
Earnest’s (white) eraser
Distance (m)
3.20
3.75
3.22
3.05
3.58
3.63
3.18
3.41
Pink Sponge
Mass (g)
75.62
75.60
75.55
75.50
75.00
At Valley View Middle School, the girls’ 4 × 100 m relay team is set. Coach Davis still needs to determine
who the fastest runner is, so she can decide in what order they should run. The four girls on the relay team
run time trials twice each day for three days. Their times are given in the table below. Is it possible
(scientifically speaking) to determine who is the fastest? If so, which girl is the fastest?
Tara
Time (seconds)
12.70
12.99
13.00
12.88
12.75
12.80
Sammie
Time (seconds)
12.59
12.45
12.40
12.60
12.54
12.42
Joan
Time (seconds)
13.02
13.01
13.00
12.95
13.05
13.11
Lexy
Time (seconds)
12.77
12.80
12.78
12.99
12.94
12.90
Name:
Date:
Model Maglev Train Project
8.3
Magnetically levitating (Maglev) trains use electromagnetic force to lift the
train above the tracks. This system greatly reduces wear because there are few
moving parts that carry heavy loads. It’s also more fuel efficient, since the
energy needed to overcome friction is greatly reduced. Although maglev
technology is still in its experimental stages, many engineers believe it will
become the standard for mass transit systems over the next 100 years.
This project will give you an opportunity to create a model maglev train. You
can even experiment with different means of providing power to your train.
Materials
•
•
•
•
•
•
52 one-inch square magnets with north and south poles on the faces, rather than ends (found at hobby shops)
One strip of 1/4-inch thick foam core, 24 inches long by 4 inches wide
Two strips of 1/4-inch thick foam core, 24 inches long by 2.5 inches wide
One strip of 1/4-inch thick foam core, 6 inches long by 3.75 inches wide
Hot melt glue and glue gun
Masking tape
Directions
1.
Cut a strip of masking tape 24 inches long. Press a line of 24 magnets onto the tape, north sides up.
2.
Hold an additional magnet north side down and run it along the strip to make sure that the entire “track” will
repel the magnet. Flip over any magnets that attract your test magnet.
3.
Glue the magnet strip along one long side of the 24-by-4-inch foam core rectangle.
4.
Repeat steps 1-2, then glue the
second magnet strip along the
opposite side to create the other
track.
5.
Place a bead of hot glue along the
cut edge and attach one 24-by-2.5
inch foam core rectangle to form a
short wall.
6.
Repeat step 5 to form the opposite wall. This keeps the train from sliding sideways off the track.
7.
To create your train, glue the south side of a magnet to each corner of the small foam core rectangle.
8.
Turn the train over so that the north side of its magnets face the tracks. Place your train above the track
and watch what happens!
8.3
Extensions:
1.
Experiment with various means to propel your train along the tracks. Consider using balloons, rubber
bands and toy propellers, small motors (available at hobby stores) or even jet propulsion using vinegar
and baking soda as fuel.
2.
Build a longer, more permanent track using plywood shelving. Use clear, flexible plastic for the front
wall so that you can see the train floating above the track.
3.
Find out how much weight your train can carry. Are some propulsion systems able to carry more weight
than others? Why?
4.
Have a design contest to see who can build the fastest train, or the train that can carry the most weight
from one end of the track to the other.
Page
Projects
Name:
Date:
Stopwatch Math
9.1
What do horse racing, competitive swimming, stock car racing, speed skating, many track and field events, and
some scientific experiments have in common? The need for some sort of stopwatch, and people to interpret the
data. For competitive athletes in speed-related sports, finishing times (and split times taken at various intervals of
a race) are important to help the athletes gauge progress and identify weaknesses so they can adjust their training
and improve their performance.
Three girls ran the following times for one mile in their gym class: Julie ran 9:3 3 .2 (nine minutes,
33.2 seconds), Maggie ran 9 : 4 4 . 2 4 (nine minutes, 44.24 seconds), and Mel ran 9 : 3 3 . 2 7 (nine minutes,
33.27 seconds. In what order did they finish?
The girl who came in first is the one with the fastest (smallest) time. Compare each time digit by digit, starting
with the largest place-value. Here, that would be the minutes place:
There is a “9” in the minutes’ place of each time, so next, compare the seconds’ place. Since Maggie’s time has
larger numbers in the seconds’ place (4 4 ) than Julie or Mel (3 3 ), her time is larger (slower) than the other two.
We know Maggie finished third out of the three girls. Now, comparing Julie’s time (9 : 3 3 . 2 ) to Mel’s
(9 : 3 3 . 2 7 ), it is helpful to rewrite Julie’s time (9:3 3 .2 ) so that it has the same number of places as Mel’s.
Julie’s time needs one more digit, so adding a zero onto the end of her time, it becomes 9 : 3 3 . 2 0 . Notice that
Mel’s time is larger (slower) than Julie’s (2 7 > 2 0 ). This means that Julie’s time was fastest (smallest), so she
finished first, followed by Mel, and Maggie’s time was the slowest (largest).
1.
Put each set of times in order from fastest to slowest.
a.
5.5
5.05
5
5.2
5 .15
Fastest
b.
6:06.04
Fastest
Slowest
6:06
6:06.4
6:06.004
Slowest
Stopwatch Math
2.
The table below gives the winners and their times from eight USA track and field championship races in the
men’s 100 meter run. Rewrite the table so that the times are in order from fastest to slowest. Please include
the times and the years. Please note that the “w” that occurs next to some times indicates that the time was
wind aided.
Year
2005
2004
2003
2002
2001
2000
1999
1998
Time
10 . 0 8
9 . 91
10 .1 1
9.88w
9.95w
10.01
9 . 97 w
9.88w
Name
Justin
Gatlin
Maurice
Greene
Bernard
Williams
Maurice
Greene
Tim
Montgomery
Maurice
Greene
Dennis
Mitchell
Tim
Harden
Time
Year
3.
The following times were recorded during an experiment with battery powered cars. Please put them in
order from fastest to slowest.
a.
1:22.4
1 : 2 4 . 0 07
1:25
1:22.04
1 : 2 3 .1 1 7
1:23 .2
1:24
Fastest
b.
1:18.3
Slowest
1:20.22
1 : 2 1. 0 0 3
1:20
1 : 1 7. 9 9
1 : 2 1. 2
1 : 18 . 2 2
Fastest
c.
1:25
Fastest
4.
1:33
Slowest
1:24.99
1:24.099
1 : 2 5 . 0 01
1 : 2 4 . 9 9 01
1:24.9899
Slowest
Write a set of five times (in order from fastest to slowest) that are all between 2 6 : 15 . 2 and 2 6 : 15 . 2 4 . Do
not include the given numbers in your set.
Page 2 of 2
Name:
Date:
Averaging
9.1
The most common type of average is called the mean. To find the mean, just add all the data, then divide the total
by the number of items in the data set. This type of average is used daily by many people; teachers and students
use it to average grades, meteorologists use it to average normal high and low temperatures for a certain date, and
sports statisticians use it to calculate batting averages, among many other things.
Seven students in Mrs. Ramos’ homeroom have part time jobs on the weekends. Some of them baby sit, some
mow lawns, and others help their parents with their businesses. They all listed their hourly wages to see how their
own pay compares to that of the others. Here is the list: $11.00, $4.50, $12.20, $5.25, $8.77, $15.33, $5.75. What
is the average (mean) hourly wage earned by students in Mrs. Ramos’ homeroom?
1.
Find the sum of the data: $11.00 + $4.50 + $12.20 + $5.25 + $8.77 + $15.33 + $5.75 = $62.80
2.
Divide the sum ($62.80) by the number of items in the data set (7): $62.80 ÷ 7 ≈ $8.97
3.
Solution: The average hourly wage of the students in Mrs. Ramos’ homeroom is $8.97.
1.
Jill’s test grades in science class so far this grading period are: 77%, 64%, 88%, and 82%. What is her
average test grade so far?
2.
The total team salaries in 2005 for teams in a professional baseball league are as follows: Team One,
$63,015,833 (24 players); Team Two, $48,107,500 (24 players); Team Three, $81,029,500 (29 players);
Team Four, $62,888,192 (22 players); Team Five, $89,487,426 (18 players). What is the average amount of
money spent by a team in this league on players salaries in 2005?
3.
During a weekend landscaping job, Raul worked 8 hours, Ben worked 15 hours, Michelle worked 22 hours,
Rosa worked 5 hours, and Sammie worked 15 hours. What was the average number of hours worked by one
person during this landscaping job? If each worker was paid $12.00 an hour, what was the average pay per
person for the job?
4.
The 8th grade girls basketball team at George Washington Carver Middle School played the team from
Rockwood Valley Middle School last night. The Rockwood Valley team won, 53-37. Altogether, there were
three girls who scored 11 points each, four who scored 8 points each, one who scored 6 points, two who
scored 4 points each, four who scored 2 points each, three who scored one point each, and two girls who did
not score at all. What is the average number of points scored by a player on either team?
5.
During a weekend car trip that covered 220 miles each way, Rowan kept track of the price per gallon of
regular unleaded gasoline at different gas stations along the way. Here is the list he kept: $2.79, $3.23, $3.99,
$2.89, $3.09, $2.99, $2.97, $3.11, $2.88, $3.01, $3.00, $2.99. What was the average price per gallon of gas
among the different gas stations on the list?
Name:
Date:
Period and Frequency
9.1
The period of a pendulum is the time it takes to move through one
cycle. As the ball on the string is pulled to one side and then let go, the
ball moves to the side opposite the starting place and then returns to
the start. This entire motion equals one cycle.
Frequency is a term that refers to how many cycles can occur in one
second. For example, the frequency of the sound wave that
corresponds to the musical note “A” is 440 cycles per second or 440 hertz. The unit hertz (Hz) is defined as the
number of cycles per second.
The terms period and frequency are related by the following equation:
1.
A string vibrates at a frequency of 20 Hz. What is its period?
2.
A speaker vibrates at a frequency of 200 Hz. What is its period?
3.
A swing has a period of 10 seconds. What is its frequency?
4.
A pendulum has a period of 0.3 second. What is its frequency?
5.
You want to describe the harmonic motion of a swing. You find out that it take 2 seconds for the swing to
complete one cycle. What is the swing’s period and frequency?
6.
An oscillator makes four vibrations in one second. What is its period and frequency?
7.
A pendulum takes 0.5 second to complete one cycle. What is the pendulum’s period and frequency?
8.
A pendulum takes 10 seconds to swing through 2 complete cycles.
9.
a.
How long does it take to complete one cycle?
b.
What is its period?
c.
What is its frequency?
An oscillator makes 360 vibrations in 3 minutes.
a.
How many vibrations does it make in one minute?
b.
How many vibrations does it make in one second?
c.
What is its period in seconds?
d.
What is its frequency in hertz?
Name:
Date:
Harmonic Motion Graphs
9.1
A graph can be used to show the amplitude and period of an object in harmonic motion. An example of a graph
of a pendulum’s motion is shown below.
The distance to which the pendulum moves away from this center point is call the amplitude. The amplitude of a
pendulum can be measured in units of length (centimeters or meters) or in degrees. On a graph, the amplitude is
the distance from the x-axis to the highest point of the graph. The pendulum shown above moves 20 centimeters
to each side of its center position, so its amplitude is 20 centimeters.
The period is the time for the pendulum to make one complete cycle. It is the time from one peak to the next on
the graph. On the graph above, one peak occurs at 1.5 seconds, and the next peak occurs at 3.0 seconds. The
period is 3.0 - 1.5 = 1.5 seconds.
1.
Use the graphs to answer the following questions
a.
What is the amplitude of each vibration?
b.
What is the period of each vibration?
Harmonic Motion Graphs
2.
Use the grids below to draw the following harmonic motion graphs. Be sure to label the y-axis to indicate the
measurement scale.
a.
A pendulum with an amplitude of 2 centimeters and a period of 1 second.
b.
A pendulum with an amplitude of 5 degrees and a period of 4 seconds.
Page 2 of 2
Name:
Date:
Waves
9.2
A wave is a traveling oscillator that carries energy from one place to another. A high point of a wave is called a
crest. A low point is called a trough. The amplitude of a wave is half the distance from a crest to a trough. The
distance from one crest to the next is called the wavelength. Wavelength can also be measured from trough to
trough or from any point on the wave to the next place where that point occurs.
•
The frequency of a wave is 40 Hz and its speed is 100 meters per second. What is the wavelength of this
wave?
Solution:
100 m/s
100 m/s
=
= 2.5 meters per cycle
40 Hz
40 cycles/s
The wavelength is 2.5 meters.
1.
On the graphic at right label the following
parts of a wave: one wavelength, half of a
wavelength, the amplitude, a crest, and a
trough.
a.
How many wavelengths are represented
in the wave above?
b.
What is the amplitude of the wave shown
above?
Waves
2.
Use the grids below to draw the following waves. Be sure to label the y-axis to indicate the measurement
scale.
a.
A wave with an amplitude of
1 cm and a wavelength of 2 cm
b.
A wave with an amplitude of
1.5 cm and a wavelength of
3 cm
3.
A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed.
4.
A wave has a speed of 50 m/s and a frequency of 10 Hz. Calculate its wavelength.
5.
A wave has a speed of 30 m/s and a wavelength of 3 meters. Calculate its frequency.
6.
A wave has a period of 2 seconds and a wavelength of 4 meters.Calculate its frequency and speed.
Note: Recall that the frequency of a wave equals 1/period and the period of a wave equals 1/frequency.
7.
A sound wave travels at 330 m/s and has a wavelength of 2 meters. Calculate its frequency and period.
8.
The frequency of wave A is 250 hertz and the wavelength is 30 centimeters. The frequency of wave B is
260 hertz and the wavelength is 25 centimeters. Which is the faster wave?
9.
The period of a wave is equal to the time it takes for one wavelength to pass by a fixed point. You stand on a
pier watching water waves and see 10 wavelengths pass by in a time of 40 seconds.
a.
What is the period of the water waves?
b.
What is the frequency of the water waves?
c.
If the wavelength is 3 meters, what is the wave speed?
Page 2 of 2
Name:
Date:
Wave Interference
9.2
Interference occurs when two or more waves are at the same location at the same time. For example, the wind
may create tiny ripples on top of larger waves in the ocean.The superposition principle states that the total
vibration at any point is the sum of the vibrations produced by the individual waves.
Constructive interference is when waves combine to make a larger wave. Destructive interference is when waves
combine to make a wave that is smaller than either of the individual waves. Noise cancelling headphones work
by producing a sound wave that perfectly cancels the sounds in the room.
This worksheet will allow you to find the sum of two waves with different wavelengths and amplitudes. The
table below (and continued on the next page) lists the coordinates of points on the two waves.
1.
Use coordinates on the table and the graph paper (see last page) to graph wave 1 and wave 2 individually.
Connect each set of points with a smooth curve that looks like a wave. Then, answer questions 2 – 9.
2.
What is the amplitude of wave 1?
3.
What is the amplitude of wave 2?
4.
What is the wavelength of wave 1?
5.
What is the wavelength of wave 2?
6.
How many wavelengths of wave 1 did you draw?
7.
How many wavelength of wave 2 did you draw?
8.
Use the superposition principle to find the wave that results from the interference of the two waves.
a. To do this, simply add the heights of wave 1 and wave 2 at each point and record the values in the last
column. The first four points are done for you.
b. Then use the points in last column to graph the new wave. Connect the points with a smooth curve. You
should see a pattern that combines the two original waves.
9.
Describe the wave created by adding the two original waves.
x-axis
Height of wave 1
Height of wave 2
Height of wave 1 + wave 2
(blocks)
(y-axis blocks)
(y-axis blocks)
(y-axis blocks)
0
0
0
0
1
0.8
2
2.8
2
1.5
0
1.5
3
2.2
-2
0.2
4
2.8
0
Wave Interference
x-axis
Height of wave 1
Height of wave 2
Height of wave 1 + wave 2
(blocks)
(y-axis blocks)
(y-axis blocks)
(y-axis blocks)
5
3.3
2
6
3.7
0
7
3.9
-2
8
4
0
9
3.9
2
10
3.7
0
11
3.3
-2
12
2.8
0
13
2.2
2
14
1.5
0
15
0.8
-2
16
0
0
17
-0.8
2
18
-1.5
0
19
-2.2
-2
20
-2.8
0
21
-3.3
2
22
-3.7
0
23
-3.9
-2
24
-4
0
25
-3.9
2
26
-3.7
0
27
-3.3
-2
28
-2.8
0
29
-2.2
2
30
-1.5
0
31
-0.8
-2
32
0
0
Page 2 of 3
Page 3 of 3
9.2
Name:
Date:
Decibel Scale
9.3
The loudness of sound is measured in decibels (dB). Most sounds fall between zero and 100 on the decibel scale
making it a very convenient scale to understand and use. Each increase of 20 decibels (dB) for a sound will be
about twice as loud to your ears. Use the following table to help you answer the questions.
10-15 dB
30-40 dB
65 dB
70 dB
90 dB
100 dB
110 dB
120 dB
•
A quiet whisper 3 feet away
Background noise in a house
Ordinary conversation 3 feet away
City traffic
A jackhammer cutting up the street 10 feet away
Listening to headphones at maximum volume
Front row at a rock concert
The threshold of physical pain from loudness
How many decibels would a sound have if its loudness was twice that of city traffic?
Solution:
City traffic = 70 dB
Adding 20 dB doubles the loudness.
70 dB + 20 dB = 90 dB
90 dB is twice as loud as city traffic.
1.
How many times louder than a jackhammer does the front row at a rock concert sound?
2.
How many decibels would you hear in a room that sounds twice as loud as an average (35 dB) house?
3.
You have your headphones turned all the way up (100 dB).
a.
If you want them to sound half as loud, to what decibel level must the music be set?
b.
If you want them to sound 1/4 as loud, to what decibel level must the music be set?
4.
How many times louder than city traffic does the front row at a rock concert sound?
5.
When you whisper, you produce a 10-dB sound.
a.
When you speak quietly, your voice sounds twice as loud as a whisper. How many decibels is this?
b.
When you speak normally, your voice sounds 4 times as loud as a whisper. How many decibels is this?
c.
When you yell, your voice sounds 8 times as loud as a whisper. How many decibels is this?
Name:
Date:
Palm Pipes Project
9.3
A palm pipe is a musical instrument made from a simple material—PVC pipe. To play a palm pipe, you hit an
open end of the pipe on the palm of your hand, causing the air molecules in the pipe to vibrate. These vibrations
create the sounds that you hear.
Materials:
•
•
•
•
•
•
1 standard 10-foot length of 1/2 inch PVC pipe for 180°F water.
Flexible meter stick
PVC pipe cutter or a hacksaw
Sandpaper
Seven different colors of permanent markers for labeling pipes
Simple calculator
Directions:
1.
Cut the PVC pipe into the lengths listed in the chart below. It works best if you measure one length, cut it,
then make the next measurement. You may want to cut each piece a little longer than the given measurement
so that you can sand out any rough spots and level the pipe without making it too short.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Note
F
G
A
B flat
C
D
E
F
G
A
B flat
C
D
E
F
Length of pipe (cm)
23.60
21.00
18.75
17.50
15.80
14.00
12.50
11.80
10.50
9.40
9.20
7.90
7.00
6.25
5.90
Frequency (Hertz)
349
392
440
446
523
587
659
698
748
880
892
1049
1174
1318
1397
2.
Lightly sand the cut ends to smooth any rough spots.
3.
Label each pipe with the number, note, and frequency using a different color permanent marker.
4.
Hit one open end of the pipe on the palm of your hand in order to make a sound.
Activities:
9.3
1.
Try blowing across the top of a pipe as if you were playing a flute. Does the pipe sound the same as when
you tap it on your palm? Why or why not?
Safety note: Wash the pipes with rubbing alcohol or a solution of 2 teaspoons household bleach per
gallon of water before and after blowing across them.
2.
Take one of the longer pipes and place it in a bottle of water so that the top of the pipe extends above the
top of the bottle. Blow across it like a flute. What happens to the tone as you raise or lower the pipe in the
bottle?
3.
Try making another set of palm pipes out of 1/2-inch copper tubing. What happens when you strike these
pipes against your palm? What happens when you blow across the top? How does the sound compare
with the plastic pipes?
4.
At a hardware store, purchase two rubber rings for each copper pipe. These rings should fit snugly
around the pipes. Place one ring on each end of each pipe, then lay them on a table. Try tapping the side
of each pipe with different objects—wooden and stainless steel serving spoons, for example. How does
this sound compare with the other sounds you have made with the pipes?
5.
Try playing some palm pipe music with your classmates. Here are two tunes to get you started:
Melody
Harmony
C
C
D
A
C
Melody
Harmony
C
C
C
F
A
Happy Birthday
F
E
A
Bb
F
C
E
Bb
D
C
C
D
Bb
C
G
Bb
F
A
Bb
Bb
A
C
F
G
F
A
Melody
Harmony
F
C
F
C
C
A
C
A
Twinkle Twinkle Little Star
D
D
C
Bb
Bb
Bb
A
G
Melody
Harmony
C
A
C
A
Bb
G
Bb
G
A
F
A
F
G
C
C
A
C
A
Bb
G
Bb
G
A
F
A
F
G
C
Melody
Harmony
F
C
F
C
C
A
C
A
D
Bb
D
Bb
C
A
Bb
G
Bb
G
A
F
A
F
G
E
G
E
F
C
Page
Projects
Bb
G
A
F
A
F
G
E
G
E
F
C
Page 3 of 3
6.
Challenge:
You can figure out the length of pipe needed to make other notes, too. All you need is a simple
formula and your understanding of the way sound travels in waves.
9.3
To figure out the length of the pipe needed to create sound of a certain frequency, we start with the formula
frequency = velocity of sound in air ÷ wavelength, or f = v /λ. Next, we solve the equation for λ: λ = v/f.
The fundamental frequency is the one that determines which note is heard. You can use the chart below to
find the fundamental frequency of a chromatic scale in two octaves. Notice that for each note, the frequency
doubles every time you go up an octave.
Once you choose the frequency of the note you want to play, you need to know what portion of the
fundamental frequency’s wavelength (S-shape) will fit inside the palm pipe.
To help you visualize the wave inside the palm pipe, hold the center of a flexible meter stick in front of you.
Wiggle the meter stick to create a standing wave. This mimics a column of vibrating air in a pipe with two
open ends. How much of a full wave do you see? If you answered one half, you are correct.
When a palm pipe is played, your hand closes one end of the pipe. Now use your meter stick to mimic this
situation. Place the meter stick on a table top and use one hand to hold down one end of the stick. This
represents the closed end of the pipe. Flick the other end of the meter stick to set it in motion. How much of
a full wavelength do you see? Now do you know what portion of the wavelength will fit into the palm pipe?
One-fourth of the wavelength of the fundamental frequency will fit inside the palm pipe. As a result the
length of the pipe should be equal to 1/4λ, which is equal to 1/4(v/f).
In practice, we find that the length of pipe needed to make a certain frequency is actually a bit shorter than
this. Subtracting a length equal to 1/4 of the pipe’s inner diameter is necessary. The final equation, therefore,
is: Length of pipe = ----v- – 1--4- D where D represents the inner diameter of the pipe.
4f
Given that the speed of sound in air (at 20°C) is 343 m/s and the inner diameter of the pipe is 0.0017 m, what
is the length of pipe you would need to make the note B, with a frequency of 494 hertz? How about the same
note one octave higher (frequency 988 hertz)? Make these two pipes so that you can play a C major scale.
Chromatic scale in two octaves (frequencies rounded to nearest whole number)
Note
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
Frequency 220 233 247 262 277 294 311 330 349 370 392 415
(Hertz)
Frequency 440 466 494 523 554 587 622 659 698 740 784 831
(Hertz)
7.
A
440
880
What is the lowest note you could make with a palm pipe? What is the highest? Explain these limits using
what you know about the human ear and the way sound is created by the palm pipe.
Name:
Date:
The Electromagnetic Spectrum
10.1
Radio waves, microwaves, visible light, and x-rays are familiar kinds of electromagnetic waves. All of these
waves have characteristic wavelengths and frequencies. Wavelength is measured in meters. It describes the length
of one complete oscillation. Frequency describes the number of complete oscillations per second. It is measured
in hertz, which is another way of saying “cycles per second.” The higher the wave’s frequency, the more energy
it carries.
Frequency, wavelength, and speed
In a vacuum, all electromagnetic waves travel at the same speed: 3.0 × 108 m/s. This quantity is often called “the
speed of light” but it really refers to the speed of all electromagnetic waves, not just visible light. It is such an
important quantity in physics that it has its own symbol, c.
The speed of light is related to
frequency f and wavelength λ
by the formula to the right.
The different colors of light
that we see correspond to
different frequencies. The
frequency of red light is lower
than the frequency of blue
light. Because the speed of both kinds of light is the same, a lower frequency wave has a longer wavelength. A
higher frequency wave has a shorter wavelength. Therefore, red light’s wavelength is longer than blue light’s.
c
When we know the frequency of light, the wavelength is given by: λ = -f
c
When we know the wavelength of light, the frequency is given by: f = --λ
The Electromagnetic Spectrum
Answer the following problems. Don’t forget to show your work.
1.
Yellow light has a longer wavelength than green light. Which color of light has the higher frequency?
2.
Green light has a lower frequency than blue light. Which color of light has a longer wavelength?
3.
Calculate the wavelength of violet light with a frequency of 750 × 1012 Hz.
4.
Calculate the frequency of yellow light with a wavelength of 580 × 10–9 m.
5.
Calculate the wavelength of red light with a frequency of 460 × 1012 Hz.
6.
Calculate the frequency of green light with a wavelength of 530 × 10–9 m.
7.
One light beam has wavelength, λ1, and frequency, f1. Another light beam has wavelength, λ2, and
frequency, f2. Write a proportion that shows how the ratio of the wavelengths of these two light beams is
related to the ratio of their frequencies.
8.
The waves used by a microwave oven to cook food have a frequency of 2.45 gigahertz (2.45 × 109 Hz).
Calculate the wavelength of this type of wave.
9.
A radio station has a frequency of 90.9 megahertz (9.09 × 107 Hz). What is the wavelength of the radio
waves the station emits from its radio tower?
10. An x-ray has a wavelength of 5 nanometers (5.0 × 10-9 m). What is the frequency of x-rays?
11. The ultraviolet rays that cause sunburn are called UV-B rays. They have a wavelength of approximately 300
nanometers (3.0 × 10-7 m). What is the frequency of a UV-B ray?
12. Infrared waves from the sun are what make our skin feel warm on a sunny day. If an infrared wave has a
frequency of 3.0 × 1012 Hz, what is its wavelength?
13. Electromagnetic waves with the highest amount of energy are called gamma rays. Gamma rays have
wavelengths of less than 10-trillionths of a meter (1.0 × 10-11 m).
a.
Determine the frequency that corresponds with this wavelength.
b.
Is this the minimum or maximum frequency of a gamma ray?
14. Use the information from this sheet to order the following types of waves from lowest to highest frequency:
visible light, gamma rays, x-rays, infrared waves, ultraviolet rays, microwaves, and radio waves.
15. Use the information from this sheet to order the following types of waves from shortest to longest
wavelength: visible light, gamma rays, x-rays, infrared waves, ultraviolet rays, microwaves, and radio
waves.
Page 2 of 2