Description

Physics 1103 Multimedia Project Description

These are worth 60 points EACH! That is the same weighting as a midterm! This is a serious

assignment and will require serious effort from all group members.

You must complete three projects. These are to be completed together as a team/table. If you are

unable to sync schedules and wish to complete a project individually, you must email your instructor

and get permission.

For each project you will design and implement an experiment to test some physical

phenomenon/behavior related to this class. For example, you might set up a lever and fulcrum to lift a

large weight using a small weight. Or you might film a falling object and use the frame rate to verify the

acceleration due to gravity on the surface of Earth.

Each project must have the following, and will be graded on these criteria:

•

•

•

•

•

•

•

•

(5 pts) A clear, short statement of the phenomenon you will test (one or two sentences).

(10 pts) An explanation of the physics behind this phenomenon (including relevant equations

and pictures/diagrams).

(5 pts) A clear statement of how you ensured the safety of everyone in your team during this

project. DO NOT DO ANYTHING UNSAFE! Do not use electricity irresponsibly or lean off of high

platforms to get good data! Your safety is more important than anything in this class!

(5 pts) A video or photograph of the experimental setup.

(5 pts) A clear statement of each group member’s contribution to the project. Falsifying this to

say that students contributed who did not could be considered academic misconduct.

(10 pts) A clear explanation of why you set up the experiment the way you did. These are NOT

free points! You need to think about potential problems with your setup (friction, forces you

forgot about, heat losses, imprecise measurements, etc.). You need to design your experiment

to avoid problems and get the best data possible.

(10 pts) Data collected (presented in a plot, table, or other suitable format).

(10 pts) Interpretation of the data. This means determining whether the data show the behavior

you expected. If so, explain how the data show that. If not, give possible explanations why not,

cite specific potential sources of error and describe how the experiment could be improved. DO

NOT SAY “human error”. You have to identify human errors and correct them in the project.

Citing specific sources of error here might mean explaining that results are skewed due to air

resistance and proposing that the experiment could be redone in an evacuated chamber (not

realistic for this project).

Timing and submission:

You may present the information you collect in any appropriate format, including video, as a written

report, as a PowerPoint presentation, etc. You will post the project in your chosen format and submit a

link to the project in Carmen. DO NOT UPLOAD THE PROJECT DIRECTLY TO CARMEN – space limitations

prevent us from storing all projects on Carmen; submit only a link to project.

Project due dates (due at 11:59 PM):

Project 1 – Monday, Oct. 18

Project 2 – Monday, Nov. 1

Project 3 – Monday, Nov. 15

You may complete these early, if you like, and turn them early. But they must be turned in NO LATER

than 11:59 PM on the days indicated above, and they may NOT be resubmitted, even if turned in early.

Chapter 17: Electric Circuits

Goals of Period 17

Section 17.1:

Section 17.2:

Section 17.3:

Section 17.4:

To define resistance in series circuits

To define resistance in parallel circuits

To measure human resistance

To illustrate combination circuits

17.1 Resistors in Series

As current flows through a resistor, the resistor reduces the electrical potential

energy of the circuit by transforming electrical energy into other forms of energy. For

example, a toaster’s resistor converts electrical energy into thermal energy, which is

then converted into radiant energy. Since a resistor reduces the electrical potential

energy per charge, the voltage across the resistor is reduced, producing a voltage drop.

Bulbs connected in series

When circuit elements are connected so that

the same current flows through each element, the

elements form a series circuit. Connecting resistors

in series gives a larger total resistance. A series

connection of resistors makes a single equivalent

resistor whose resistance is the sum of the individual

resistances. The batteries’ voltage in a series circuit is

divided across the circuit elements. Those elements with the greatest resistance receive

the most voltage. The sum of the voltage drops across the circuit elements equals the

voltage boost of the batteries.

For resistors connected in series:

RTot = R1 + R2 + R3 + ….

(Equation 17.1)

where

RTot = total resistance of the resistors connected in series (in ohms)

R1

= resistance of the first resistor (in ohms)

R2

= resistance of the second resistor (in ohms)

R3

= resistance of the third resistor (in ohms)

(Example 17.1)

Four resistors with resistances of 1.0 ohm, 0.5 ohm, 1.5 ohms, and 3.0 ohms are

connected in series in a circuit. What is the total resistance of these resistors when they

are connected in series?

RTot = R1 + R2 + R3 + R4 = 1.0 + 0.5 + 1.5 +3.0 = 6.0

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This principle follows from Ohm’s law: voltage = current x resistance. In a

series circuit, the same amount of current flows through each element. The load device

with the greatest resistance requires the largest voltage to push the current through it.

(Example 17.2)

A 0.1 amp current flows through two resistors in series. Resistor 1 has a

resistance of 10 ohms and Resistor 2 has 20 ohms. What is the voltage drop across

Resistor 1? (Assume that the connecting wires have no resistance.)

V = I R

=

(0.1 amps) x (10 ohms)

=

1 volt

Concept Check 17.1

a)

What is the voltage drop across Resistor 2 in example 17.2? ______________

b)

What is the voltage boost given by the battery in example 17.2? Assume that

the only load devices in the circuit are Resistors 1 and 2 and that the connecting

wires have no resistance.

____________________

17.2 Resistors in Parallel

When circuit elements are connected so that the

current has multiple paths to flow through, a parallel

circuit is formed. Current flows more easily through a

parallel circuit because the current has multiple paths

through the resisting material. A parallel connection of

resistors makes a single equivalent resistor that has less

total resistance than a circuit with just one resistor.

The more parallel paths for current to follow, the lower

the resistance. The total resistance of a parallel circuit

Bulbs connected in parallel

is always less than the resistance of the smallest

resistor in the circuit. Figure 17.1 illustrates the comparative total resistance of four

circuits consisting of identical resistors connected to identical batteries. In parallel

circuits, sum of the voltage drops in each independent parallel branch (path) equals the

voltage boost of the batteries.

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Fig. 17.1 Comparison of Total Resistance of Circuits with Identical Resistors

Most resistance

Less resistance

Even less resistance

Adding resistors in series increases

the total circuit resistance.

Least resistance

Adding resistors in parallel decreases

the total circuit resistance.

In series circuits, each added resistor increases the circuit resistance, and the total

circuit resistance is the sum of the individual resistances. In parallel circuits, each added

resistor decreases the circuit resistance, and the total circuit resistance is found by

summing the inverses of each individual resistance as shown in Equation 17.2.

1

RTot

1

R1

1

R2

1

R3

(Equation 17.2)

….

where

RTot = total resistance of the resistors connected in parallel (in ohms)

R1 = resistance of the first resistor (in ohms)

R2

= resistance of the second resistor (in ohms)

R3

= resistance of the third resistor (in ohms)

(Example 17.3)

Three resistors with resistances of 3 ohms, 4 ohms, and 6 ohms are connected in

parallel in a circuit. What is the total resistance of this parallel circuit?

1

RTot

1

R1

1

R2

1

R3

.

1

3

1

1

4

6

4

3

2

12

12

12

9

12

Summing fractions involves finding a denominator common to each fraction. In this

example, 12 is evenly divisible by the denominators of the fractions. Summing the

fractions gives 1/RTot. To find RTot divide the numerator by the denominator.

1

RTot

9

12

RTot

12

9

1.33

As expected, the total resistance of the three parallel resistors is less than the resistance

of the smallest resistor.

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Skills and Strategies #13: Summing Fractions

When adding fractions, each term must have the same denominator. The

common denominator must be divisible by the denominator of each of the fractions. In

some cases, a common denominator can be found by inspection. For example, when

adding the fractions 1/2, 1/3, and 1/5, we find that 30 is divisible by each denominator.

1/2 = 15/30; 1/3 = 10/30; and 1/5 = 6/30

The total of the fractions is found by summing their numerators and dividing their sum

by the common denominator.

15

10

6

30

30

30

31

30

1.03

If a common denominator cannot easily be found by inspection, one can be

found by multiplying together the denominators of each fraction. To add 1/3, 1/4, and

1/7, multiply 3 x 4 x 7 = 84. The numerator of each fraction is the number of times the

denominator can be divided into 84.

1/3 = 28/84; 1/4 = 21/84; and 1/7 = 12/84

The total of the fractions 1/3, 1/4, and 1/7, is

28

84

21

12

84

84

61

84

0.73

Concept Check 17.2

a)

One electric circuit consists of a 1.5 ohm resistor connected to a battery. A

second circuit consists of two resistors (1.5 ohms and 4.0 ohms) connected in

parallel and attached to a battery. Which circuit has less total resistance? Why?

______________________________________________________________

b)

What is the total resistance of a circuit connected in parallel that consists of a 2

ohm, a 3 ohm, and a 4 ohm resistor?

______________

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17.3 Resistance of Humans

In class, we will measure the resistance of your body when you and your

classmates are connected together in series and in parallel. The resistance of a human

body from one hand to another is typically 5,000 to 40,000 ohms. Your resistance

depends on how wet or sweaty your hands are and on how close your blood is to the

surface of your skin. Electrically, your body is like a sack of salty water. The fluids in

your body are good conductors of electric current, but the wall of the sack, your skin,

has a high resistance when it is dry. Sweaty or wet hands lower the resistance of your

skin, so that a better connection is made to the salty fluids inside. If you rub your

hands together briskly, blood is brought closer to the surface of your skin, lowering your

skin resistance. Some lie detectors work on the principle that people sweat under the

stress of lying. The lie detector measures changes in the resistance of the human skin.

17.4 Combination Series and Parallel Circuits

In class we will consider a circuit

consisting of two bulbs in parallel connected

in series to a third bulb. When all three bulbs

are lit, current flows from the batteries

through the single bulb (bulb 1). The current

then splits, with some current flowing

through the parallel bulb on the left (bulb 2)

and the remainder of the current flowing

through the bulb on the right (bulb 3). If the

resistances of the two parallel bulbs are

equal, the current splits evenly with one-half

flowing through each of the parallel bulbs.

1

2

3

The voltage boost of the batteries is divided across bulbs 1, 2, and 3. Since

bulbs in parallel have less resistance than a single bulb, bulbs 2 and 3 in parallel have

less resistance and, thus, less voltage than bulb 1. If bulbs 2 and 3 have equal

resistance, they will have equal voltages. As in any circuit, the sum of the voltage drops

across the elements in each path connected to the batteries is equal to the total voltage

boost from the batteries.

(Example 17.4)

In the combination circuit shown above, the bulbs have equal resistances and

the connecting wires have no resistance. The batteries have a total voltage boost of 5.5

volts and bulb 2 has a voltage drop of 1.3 volts. What is the voltage drop across bulb 3?

What is the voltage drop across bulb 1?

Since bulbs 2 and 3 are connected in parallel and have equal resistances, they

have equal voltages. Therefore, bulb 3 has a voltage drop of 1.3 V. The parallel path

from the batteries, through bulb 1 and through bulb 2 has a total voltage drop equal to

the voltage boost from the batteries, 5.5 volts. Since bulb 2 has a voltage drop of 1.3 V,

bulb 1 must have 5.5 V – 1.3 V = 4.2 V voltage drop.

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Period 17 Summary

17.1: The resistances of resistors in series add.

RTot = R1 + R2 + R3 + ….

The voltage drops across the resistors equals the voltage boosts across the

circuit’s energy sources.

The larger the resistance, the greater the voltage drop across the resistor.

17.2: Resistors in parallel provide additional paths for current flow and reduce the total

resistance of the circuit.

The more resistors in parallel, the lower the resistance of the circuit. The total

circuit resistance is less than the resistance of the smallest resistor.

For two resistors connected in parallel, the total circuit resistance is

1

RTot

1

R1

1

R2

1

R3

…

17.3: The resistance of the human body depends on factors such as moisture on the

skin. These differences in resistance have been used in some lie detectors.

17.4: Circuits that combine series and parallel elements follow the same principles as

described for simple series and simple parallel circuits.

1) The circuit elements with the greatest resistance have the largest voltage

drop.

2) The sum of the total voltage drops across the circuit elements in each

circuit path connected to the batteries equals the total voltage boost from

the batteries.

Solutions to Chapter 17 Concept Checks

17.1

a)

b)

V = I R

=

(0.1 amps) x (20 ohms)

=

2 volts

The battery’s voltage boost equals the sum of the voltage drops across the

circuit elements. 1 volt + 2 volts = 3 volts

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17.2

a)

The circuit with 2 parallel resistors has less total resistance than the circuit with

one resistor. Adding resistors in parallel provides more pathways for current to

flow. Each additional parallel pathway reduces the total circuit resistance.

b)

1

1

RTot

R1

1

R2

1

.

R3

1 1 1

2 3 4

6

4

3

12

12

12

13

12

To sum the fractions, find a denominator common to each fraction. In this

example, 12 is divisible by each of the denominators of the fractions. Summing

the fractions gives 1/RTot.

To find RTot divide the numerator by the

denominator.

1

RTot

13

12

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RTot

12

13

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Chapter 18: Electricity Use and Safety

Goals of Period 18

Section 18.1:

Section 18.2:

Section 18.3:

Section 18.4:

Section 18.5:

To define linear and exponential growth rates

To explore the growth of electricity use in the U.S.

To learn how to prevent electric fires

To learn how to prevent electric shocks

To examine the consequences of electric shocks

18.1 Linear and Exponential Growth

A growth rate is the ratio of the amount of increase to the time elapsed. We consider

two common models for growth rates – linear and exponential growth – using sample data for

the increase in the number of oil wells and hydroelectric dams in a hypothetical country. Figure

18.1 presents the data for dams.

Fig. 18.1: Linear Growth of Dams

10

Time

Periods

Dams

1998

0

5

1999

1

6

2000

2

7

2001

3

8

9

N (Number of Dams)

Years

8

7

6

2002

4

9

5

1998

1999

2000

2001

2002

t (Time in Years)

The growth rate of dams producing hydroelectric power is called linear because the

number of dams increases by a constant amount during each time period (1 dam/year). When

graphed, linear data form a straight line as shown in Figure 18.1.

The equation describing linear growth uses the symbol N for the number of dams at a

given time. This number depends on B, the initial number of dams (B = 5); t, the number of

one-year time periods elapsed; and A, the amount of increase per time period. The value of A

determines how steeply the straight graph line rises or falls and is known as the slope of the

line. The relationship between A, B, N, and t is

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N=Axt+B

Applying the equation to the data in Fig. 18.1 verifies that the equation is correct.

(A) (t)

(B)

In 2008,

N =

In 2009,

N =

1 x 1 + 5 = 6

In 2010,

N =

1 x 2 + 5 = 7

In 2011,

N =

1 x 3 + 5 = 8

In 2012,

N =

1 x 4 + 5 = 9

1 x 0 + 5 = 5

Next we consider a second type of growth rate called exponential growth. Figure 18.2

illustrates exponential growth using sample data for the increase in the number of oil wells in a

hypothetical country.

Fig. 18.2: Exponential Growth of Oil Wells

Oil

Wells

Number of

Wells as

exponentials

1998

0

1

1 = 20

1999

1

2

2 = 21

2000

2

4

4 = 22

2001

3

8

8 = 23

2002

4

16

16

N (Number of Oil Wells)

Time

Periods

Years

4

16 = 2

12

8

4

0

1998

1999

2000

2001

2002

t (Time in Years)

The graph of exponential growth is not a straight line because the amount of the increase per

time period is not constant. Exponential growth is characterized by a doubling of the amount of

the quantity during a fixed time period. Since the amount increases by a factor of two,

exponential growth is described by base 2 raised to an exponential power that is equal to the

number of time periods elapsed. The last column of Figure 18.2 illustrates this basis of

exponential growth.

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The equation for the exponential growth uses B for the initial amount of the quantity

(B = 1 oil well) and t for the number of one-year time periods elapsed. (We assume that

there is only one doubling per time period.) N is the number of wells.

In 2008,

In 2009,

In 2010,

In 2011,

In 2012,

N = Bx 2

t

N

N

N

N

N

0

=

1×2

=

1×2

=

1×2

=

1×2

=

1×2

1

2

3

4

0

= 2

= 1

= 2

= 2

= 2

= 4

= 2

= 8

= 2

= 16

1

2

3

4

Figure 18.3 uses the sample data on dams and oil well to compare the rates of linear and

exponential growth.

Figure 18.3 Increase in the Number of Dams and Oil Wells

When studying energy, we may be interested in the amount of a quantity at a particular

time, such as the amount of electrical energy used in 2010. More often we are interested in the

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increase or decrease in a quantity over a period of time, such as the increase in energy use

over the past 50 years. Table 18.1 presents sample data of the population of a town and

energy used by that town from 1940 to 2000. Figure 18.4 graphs these data.

Table 18.1 Sample Data on Population and Megajoules (MJ) of Energy Use

Year

Population

Energy Use (MJ)

Year

Population

Energy Use (MJ)

1940

500

50

1980

1,500

800

1950

750

100

1990

1,750

1,600

1960

1,000

200

2000

2,000

3,200

1970

1,250

400

2010

2,250

6,400

Population

or

Energy Use (in mega joules)

Fig. 18.4 Sample Data on Population and Energy Use

6750

6500

6250

6000

5750

5500

5250

5000

4750

4500

4250

4000

3750

3500

3250

3000

2750

2500

2250

2000

1750

1500

1250

1000

750

500

250

0

1940

Energy Use

Population

1950

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1960

1970

1980

Time (in years)

148

1990

2000

2010

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As discussed earlier, the slope of a graph is the ratio of the amount by which it rises or

falls to the elapsed period of time. In Figure 18.4, the graph of population is a straight line,

which has a constant slope. Graphs with a constant slope represent linear growth. Linear

growth is characterized by the addition of a constant amount during a fixed time period. In this

example, the population grows by 250 every 10 years. The constant linear growth is

independent of how long the population has been growing and is independent of the initial

number of people. For example, if the town had 750 people in 1960, there would be 750 + 250

= 1,000 people in 1970 and 1,250 in 1980. The population grows by 250 every 10 years,

regardless of the size of the initial population and how long the population has been growing.

The graph of energy use is an example of exponential growth because the use of

energy doubles during a fixed time period – in this example, every 10 years. In the case of

exponential growth, the amount added during each time period depends on the amount of the

quantity present at the beginning of that time period. Therefore, the amount to be added also

depends on the number of elapsed time periods. For example, the town used 50 megajoules

(MJ) of energy in 1940 and doubled its energy use to 100 MJ in 1950, an increase of 50 MJ in

10 years. But if the city had used 100 MJ in 1940 and doubled its energy use to 200 MJ by

1950, the increase would have been 100 MJ. The larger the initial amount, the greater the

increase per time period.

With exponential growth, an amount is added during each time period to double the

total quantity from the previous time period. The time between doublings is called the doubling

time. In this example, the doubling time of energy use is 10 years. Between 1940 and 1950,

energy use doubled from 50 MJ to 100 MJ – an increase of 50 MJ. Between 1950 and 1960,

energy use doubled again from 100 MJ to 200 MJ, but during this 10-year period the amount of

increase is 100 MJ. With exponential growth, the rate of change is not constant, but depends

on the amount to be doubled at any given time, as well as the initial amount.

Concept Check

18.1

a)

If the growth rate of a town’s population remains the same as shown in Table 18.1,

what will the population be in 2020?

___________________

b)

If the growth of energy use remains the same, what will be the energy use in 2020?

__________________

c)

In Figure 18.4, what is the slope of the straight line representing population growth?

__________________

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(Example 18.1)

A suburb had twenty gasoline station pumps in 2012. The number of gas pumps

increases at the rate of ten pumps per year. The number of vehicles driven by the suburb’s

residents was 5,000 in 2012. The number of vehicles grows exponentially with a doubling time

of one year. How many gas pumps and vehicles will there be in 2015?

A data table simplifies the solution. Since

the number of gas pumps grows linearly at the

rate of ten per year, add ten each year until 2015.

The number of vehicles grows exponentially,

beginning with 5,000 in 2012.

Double the

number of vehicles each year until 2015.

In

2015, there will be 50 gas pumps and 40,000

vehicles.

Years

Pumps

Vehicles

2012

20

5,000

2013

30

10,000

2014

40

20,000

2015

50

40,000

Exponential growth rates have many applications in business and finance and in physical

and biological systems. The length of time for a quantity to double, the doubling time, is

particularly important. Table 18.2 gives the doubling time in years for various growth rates

when compounded annually. As shown in the table, doubling times can vary substantially, but

still represent exponential growth.

Table 18.2: Growth Rates and Doubling Times

Annual Growth

Rate (in percent)

0

1

2

3

4

5

6

7

8

9

10

12

14

16

18

Doubling Time

(in years)

Infinite

69.7

35.0

23.4

17.7

14.2

11.9

10.2

9.0

8.0

7.3

6.1

5.3

4.7

4.2

Annual Growth

Rate (in percent)

20

30

40

50

60

70

80

90

100

200

300

400

900

9900

Doubling Time

(in years)

3.8

2.6

2.1

1.7

1.5

1.3

1.2

1.1

1.0

0.6

0.5

0.4

0.3

0.15

Concept Check 18.2

a)

If you invest $1,000 at 6% interest compounded annually, how long will it take for your

money to double to $2,000?

___________________

b)

If a stock doubles in value every 10.2 years, what is its rate of growth? ________

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18.2 Growth of Electricity Use

Our modern lifestyles would be impossible without inexpensive and easily available

electricity. Figure 18.5 illustrates the rapid increase in production of electricity during the past

century. Production is shown in units of billions of kilowatt-hours (kWh), which is the amount

of electricity in units of thousands of watts (kilowatts) multiplied by the hours of its use. 1

Figure

Growth in

in Electricity

Electricity Production

Production

Figure 18.5

9.1 Growth

3500

3250

2750

2500

2250

2000

1750

1500

1250

1000

750

500

250

2000

1995

1990

1985

1980

1975

1970

1965

1960

1955

1950

1945

1940

1935

1930

1925

1920

1915

0

1910

Kilowatt Hours (billions)

3000

Year

1

Data sources: U.S. Statistical Abstracts, 1920, 1933, and 1940, and 1950 for data through

1950. Data from 1950 – 1999 from U.S. Department of Energy

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In class we will examine the growth rates of a similar graph and identify time

periods when electricity production increased linearly or exponentially. In Figure 18.5, a

dashed curve showing exponential growth has been added to the graph. The electricity

production data closely resemble the exponential growth curve from 1910 through 1973.

After 1975, the exponential curve is sharply above the solid line showing the actual

production of electricity. The exponential curve rises sharply since, for an exponential

curve, the amount during each time period is larger than the amount added during the

previous time period.

Beginning in the mid 1970’s, increasing energy costs resulted in a slowing in the

rate of increase of electricity use in the U.S. The rate of electricity production after

1973 can be described as linear growth. Linear growth is characterized by a steady

amount of increase – the same amount of the quantity is added during each time

period. A dotted straight line representing linear growth has also been added to the

graph. Although not all of the data points fall on this line, the overall pattern of the data

fits the straight line of linear growth quite well. The ability to recognize overall patterns

in graphed data is an extremely useful skill.

Concept Check 18.3

a)

What type of growth does a straight line graph exhibit? ___________________

b)

If a region used 500 MW of electricity in 1995 and its use grew exponentially with a

doubling time of 5 years, how much electricity did it use in 2005?

_______________

c)

18.3

How much did it use in 2010?

______________

Electrical Safety: Devices that Prevent Electric Fires

The widespread use of electricity in developed countries over the past 100 years has

revolutionized our lives, making possible many technological advances. However, along with

the benefits of electricity come economic, environmental, and safety concerns. In this period

we discuss one of the most important topics of the course – how to reduce your risk of electric

fires and shock. Each year, electricity causes more than 160,000 home fires and 9,000 shock

injuries in the U.S. We will examine the causes of electrical accidents and discuss safety

devices that can help you avoid becoming one of these statistics.

Electric wires cause fires when their temperature reaches the combustion temperature

of materials they touch. Therefore, a major safety concern is joule heating, which causes

overheating in the wires that deliver electricity throughout your home. As we learned in Period

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16, the amount of joule heating in a wire is proportional to the resistance of the wire and the

square of the current in the wire: Pjoule = I2R. If current flowing through wires encounters

resistance, some electrical energy is transformed into thermal energy. The greater the

resistance of the wire and the larger the current, the greater the joule heating. Fires can occur

if joule heating brings wires to the combustion temperature of the materials touching them.

Such dangerous joule heating can occur due to localized “hot spots” of high resistance that can

develop if wiring in the walls or the wires in an electrical appliance, cord or plug are damaged.

Dangerous amounts of joule heating can also result from large currents in wires, which

can be caused by two types of problems: short circuits and overloaded circuits. A short

circuit occurs when metal, water, or other conducting material touches two points in the

circuit, giving the current a second parallel path to follow. We know from Ohm’s Law

(I = V/R) that if the shorting connection has less resistance than the devices it connects,

more current can flow through the circuit. When a short circuit occurs, the resistance R

becomes small and the voltage V remains unchanged, resulting in a large current I.

A circuit overloaded with many appliances connected in parallel requires additional

current for each device. The circuit voltage remains unchanged, and the increased current

causes more joule heating of the connecting wires. We next discuss fuses and circuit breakers,

which prevent fires by opening the circuit if the current becomes dangerously large due to an

overloaded or short circuit.

Fig 18.6

Fuses

Auto Fuse

If the current flowing through a circuit becomes large enough,

joule heating occurs even in the low resistance copper wires in the walls

of your home. Fuses contain a strip of metal that melts at a relatively

low temperature. The resistance of the fuse wire is greater than the

resistance of copper wires of the circuit. Under normal circumstances,

fuses conduct current and behave like the rest of the house wiring. But

if the current becomes too great, joule heating melts the fuse metal and

opens the circuit before a fire ignites. Once a fuse has melted, it must

be replaced to permit a closed circuit. Because this can be inconvenient,

most modern electric wiring is protected with circuit breakers rather than fuses.

Circuit Breakers

Circuit breakers perform the same function as fuses; they open, or “break,” the circuit

when the current becomes dangerously large. Unlike fuses, circuit breakers do not melt a wire.

Instead, circuit breakers use magnetism or a bimetallic strip to open the circuit.

In Period 2 your instructor heated a bimetallic strip in a flame. As the strip was heated

and then cooled, the metal was bent. A bimetallic strip consists of two layers of metal that

expand to different extents when the strip is heated. In a strip made of two metals, one layer

of metal expands more than the other layer, causing the strip to bend. If joule heating in a

circuit exceeds safe temperatures, a bimetallic strip in the circuit breaker bends, opening the

circuit. You can safely reset the circuit breaker after reducing the number of appliances

operating in parallel in the circuit or having a short circuit repaired.

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18.4 Electrical Safety: Devices that Prevent Electric Shocks

Electric shocks occur when a conducting path is created from an electric device through

a person and then to ground. We can decrease the probability of electric shock by using

ground wires, ground fault circuit interrupters, polarized plugs and three prong plugs.

Ground and Hot Wires

In Period 13 we studied the role of ground wires that remove excess charge from

objects by providing conducting pathways into the Earth. The enormous volume of the Earth

relative to the objects on it allows the Earth to easily absorb excess charge. Earth, or “ground,”

is taken as the reference level voltage for electric wiring.

In your home, metal plumbing fixtures and radiators are connected to a pipe driven into

the ground. This connection can be used to drain excess charge into the Earth. Each wall

outlet has at least two slots for inserting the prongs of an appliance cord. In a properly wired

home, the broad slot, the neutral or ground slot, is connected to the grounding system and has

near zero voltage relative to the Earth and your home’s metal fixtures. The narrow slot, the hot

slot, has a voltage of 110 or 120 volts (AC) relative to the Earth’s voltage. Current flows from

the narrow hot slot of the outlet, through the narrow prong of an appliance plug, through the

appliance, through the broad plug prong, and then back into the broad neutral outlet slot. To

prevent electric shocks, you must avoid touching a hot wire and a grounded object, thus

making your body part of a circuit and allowing current to flow through your body.

Polarized Plugs

Modern appliances have polarized plugs, which can be inserted only one way into an

outlet because one prong is broader than the other. With a polarized plug, an appliance

designer knows which direction the current flows and which wire is hot. To improve safety, a

lamp socket is designed with the conductor on the bottom of the light bulb connected to the hot

wire and the bulb’s screw base, which is easier to touch accidentally, connected to ground.

Older appliances with non-polarized plugs have two prongs of the same width. In these

appliances, either wire might be hot, depending on which way the plug is inserted into the

outlet. A defective appliance might not pose a shock hazard when the plug is inserted one way

into the outlet, but could become a shock hazard if the plug is reversed.

Three Prong Outlets and Plugs

If an appliance fails so that the hot side of its electric wiring is connected to its outer

metal case, someone touching the case can receive a severe shock. The shock hazard is

reduced if the appliance’s metal case is connected directly to ground. The round prong of a

three-prong outlet serves this purpose. The third or grounding prong of a three-prong plug is

connected to the appliance case by the manufacturer. When we insert a three-prong plug into

a three-prong outlet, the case of the appliance is directly connected to ground. If the hot side

of the wiring is accidentally connected to the case, appliances with three prong plugs allow

current to flow from the hot wire, through the case, and into the ground wire. This large

current might blow a fuse or trip a circuit breaker. However, someone touching the appliance

case might not be connected between the hot and ground wires and might not be shocked.

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When a three-prong outlet is not available, you can use an adapter that allows a three

prong plug to fit into a two prong outlet. However, to be safely grounded, the adapter’s ground

wire must be firmly attached to a grounded object. Often, the outlet screw plate is grounded,

providing a place to connect the adapter’s ground.

Figure 18.7: A Three-Prong Electrical Outlet and Plug

safety

ground or

neutral

ground

hot

outlet

plate screw

Double Insulated Appliance Cases

A double insulated case, often used in power tools, ensures that the inside of an

appliance cannot be connected to exposed metal on the outside. The inner appliance case is

made of an insulating material such as plastic, which isolates the outer metal case from the

inside wiring. However, double insulated appliances are not necessarily safe under all

circumstances. If the device becomes wet, the insulation is ineffective because water is a good

conductor of electricity.

Ground Fault Circuit Interrupters

A ground fault circuit interrupter (GFCI) is designed to prevent shocks by detecting a

leak of current to a grounded object. If a current as small as 0.005 amps leaks from the circuit

to ground, the GFCI quickly opens the circuit. In our plumbing analogy of circuits, if the

amount of water that leaves the pump is greater than the amount that returns to it, we know

that water must have leaked from the circuit. The GFCI detects leaking current by comparing

the amount of current flowing in the hot and ground wires. If the GFCI detects a difference in

the amounts of these currents, it opens the circuit, preventing or reducing the severity of

electric shock. GFCIs are particularly important for outlets near water sources and grounds –

such as bathroom, kitchen, and outdoor outlets – where the risk of shock is higher.

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How Physics Can Save Your Life: Preventing Electrical Accidents

To Prevent Fires

Don’t lay electric cords under carpeting. Keep cords away from water and heat.

Disconnect appliances by pulling on the plug, not on the cord. Replace worn cords.

Never break off the third safety prong on a plug. Use a properly connected adapter.

If a switch or an outlet becomes warm, replace it immediately

If an appliance catches on fire, unplug it immediately, if possible.

Never put water on an electrical fire.

To Prevent Shocks

Keep appliances away from water. If an appliance falls into water, unplug it before

reaching for it – even if the appliance is turned off. Don’t use a wet appliance.

Don’t touch an appliance with a metal object.

Unplug lamps before changing a bulb and unplug appliances before working on them.

If someone is being shocked, call 911 for help. Turn off the power at the circuit breaker or

fuse box if you can do so safely. Use great caution if you try to move a live wire from a

person. Do so only using a non-conducting object such as glass, plastic, or DRY wood.

Make sure you are standing on a dry surface.

18.5 The Consequences of Electric Shock

How Do Accidents Happen?

Most electric shocks occur when people inadvertently connect themselves between the

hot side of wiring and a grounded object. Such connections often involve a person in series

with some other resistor, such as the water in a bathtub or in a flooded basement. The hot

connection to the water could be exposed wiring or a faulty or wet appliance that creates a

connection from the inside of the appliance to the outside. The connection to ground might

occur when someone touches a faucet, wades in a flooded basement, or stands in a bathtub or

on a damp concrete floor. In these situations, your body, which is connected in series with

water, acts as a resistor in this series circuit. The amount of current is determined by the

resistance of your body and the other resistors in the circuit. Even if an appliance is not

operating but is plugged into an outlet, a deadly shock can result if the appliance gets wet or

has an internal short circuit.

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How Much Current Is Harmful?

The physiological effects of electric shock vary for each individual and situation.

Damage to the body depends in part on the resistance of your skin to current flow. Wet skin

has a much lower resistance (about 5,000 ohms) than dry skin (about 20,000 ohms). The

longer skin is in contact with an electric current, the greater the damage. Current decreases

the resistance of skin, drastically if burning occurs, which causes more current to flow. The

severity of a shock also depends on the path the current takes through the body. Current

flowing through the torso (heart and breathing muscles) is worse than through an arm or leg.

Table 18.3 gives the typical effects of electric shock.

Table 18.3: Effects of Electric Shock on the Human Body

Amount of Current

Effect on the Human Body

0.001 A

Barely detectable

0.005 A

Painful

0.01 A

Paralyzes some muscles making it hard to let go of conductor.

0.02 A

Paralyzes breathing muscles. Can be fatal if sustained.

0.1

A

Can cause ventricular fibrillation in the heart, which usually

continues after the current stops. Death is likely.

Since the danger of death or serious injury is greatly reduced if current flows for a very

short time, a ground fault interrupter is an extremely important safety device. A ground fault

interrupter is designed to open a circuit in 1/40 of a second when it detects even a very small

current leak. A GFCI can turn potentially fatal situations into merely painful ones.

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Period 18 Summary

18.1: Linear growth is expressed by N = A x t + B

Exponential growth is expressed by N = B x 2 t

where N = the amount of the quantity

A = the amount of increase per time period

B = the initial amount

t = the number of time periods elapsed

Linear growth rates add the same amount of a quantity during each time period.

The amount added is constant – it does not depend on the initial amount or on the

number of time periods.

Exponential growth doubles the amount of the quantity during each time period.

The doubling time for exponential growth is the length of time required for the

amount of a quantity to double.

The amount added varies for each time period – it depends on the initial amount

and on the number of elapsed time periods.

Growth rate tables (Table 18.2) provide an easy way to determine growth rates

and doubling times.

18.2: Electricity production in the U.S. has grown rapidly – at times linearly and at other times

exponentially.

18.3: Circuit breakers and fuses prevent fires by opening the circuit if the current becomes

so large that the wires might overheat. A larger current and more resistance

result in greater joule heating.

18.4: Ground wires, polarized and 3-prong plugs, and double insulated appliance cases

prevent electric shock by preventing current flow through your body.

Ground fault circuit interrupters open the circuit if current leaks from the circuit.

18.5: The severity of an electric shock depends on the amount of current flowing, the

length of time it flows, and the portion of a body it flows through. Since wet skin

has much lower resistance than dry skin, more current flows through wet skin.

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Solutions to Chapter 18 Concept Checks

18.1

a)

The population increases linearly by 250 every 10 years. In the year 2000, the

population was 2,000. In 2010, the population was 2,000 + 250 = 2,250. In 2020, the

population will be 2,250 + 250 = 2,500.

b)

Energy use increases exponentially with a doubling time of 10 years. In 2000, energy

use = 3,200 MJ. By 2010, it will had doubled to 3,200 MJ x 2 = 6,400 MJ. By 2020, it

will have doubled to 6,400 MJ x 2 = 12,800 MJ.

c)

Choose any two points on the line, for example, in 1960, population = 1,000, and in

1980, population = 1,500.

slope = vertical distance between points = 1,500 – 1,000 = 500 = 25 people

horizontal distance between points

1980 – 1960

20

year

The slope of the graph tells you that the population increases by 25 people per year.

18.2

a)

From the first two columns of Table 18.2, a 6% annual growth rate has a doubling time

of 11.9 years.

b)

From Table 18.2, a doubling time of 10.2 years equals a 7% annual growth rate.

18.3

a)

A straight line indicates linear growth.

b)

c)

In 1995

500 MW

In 2000

1,000 MW

In 2005

2,000 MW

In 2010

4,000 MW

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1

Impact of Weight on Electric Generation of Cycling

Name

Professor

Institute

Course

Date

1. Statement on Phenomena

We will test at what speed someone is likely to peddle a bicycle to start producing electricity that

can light a bulb. Specifically, I will determine that the weight of a person impacts how much

electricity is produced.

2

2. Explanation

The principle involved in the phenome is kinetic energy, or the energy of movement.

The bicycle converts around 90% of the energy produced by the body while cycling. It is based

on the conversation of energy concept that says that energy can only be generated by converting

it from one form to another. When a person is cycling, they are acting against air, or when they

are cycling uphill, they act against gravity. Also, in bumpy places, a person is forced to reduce

speed, producing some energy. Also, the process of making the wheels go round involves doing

work. However, in the resting state of a wheel on the ground, it is supporting the cyclist (Load).

Therefore, the tire wrapped around it is squeezed in some places as it bulges out in others. When

a person continues to cycle, the squeezing and bulging continue to happen in different tire

positions, making the rubber material they are made from being pulled and pushed in all

directions, producing energy and rolling resistance. The weight of the Load determines the

rolling resistance.

The formula that is utilized in calculating how power is generated is;

PFWT = Ɯ1 × RFW × L + IFW × Ɯ1 × (ƜI+1 – ƜI-1)/2

3

Where;

PFWT = Total power delivered to the ergometer flywheel

Ɯ1 = angular velocity of the flywheel

RFW = radius of the flywheel

L= Load (in Newton)

IFW= inertia moment of the flywheel (0.95 kg.m2)

i= time

I+1 and i-1= Conditions 1 second after and 1 second before the time (i)

3. Safety Measures

To ensure that the experiment did not result in any injuries related to cycling a bicycle, we

decided to place trainers in the bicycle and a stopper in the front so nobody could cycle. Also, the

devices used to generate electricity coming from the bicycle were coated with poor electricity

conductors to prevent anyone from being shocked. The persons responsible for cycling put on

protective gear in case the bike set up failed to minimize the chances of any injuries.

4. Picutre

4

5. Set-Up

The bicycle was the generator of the electricity needed. After it is set up, a person (the Load)

should sit and start to ride such that the back wheel starts to rotate. The back wheel is, in turn,

strapped with a D.C generator through a flat belt. A bulb is then connected to the generator. The

person cycling was supposed to start at a low speed and then continue to accelerate after one

minute up to three minutes before they slow down. After that, a person of a different weight was

placed and repeated the same process. Bulbs of different watts were used to measure each

category. There was a big problem in taking measurements of the different intervals as we had to

repeat as many cycling processes as possible to capture each cycling speed.

6. Data Collected

Person A (65kg)

Time (minutes)

5

10

15

20

25

30

35

40

45

50

Speed (Cycling per

15

20

40

50

60

50

40

30

20

15

10

10

10

20

40

40

35

25

20

15

5

10

15

20

25

30

35

40

45

50

min)

Power

Person B (84kg)

Time (minutes)

5

Speed (Cycling per

15

20

40

50

60

50

40

30

20

15

10

15

25

40

60

50

40

40

30

20

min)

Power (Watts)

7. Data Interpretation

It shows that the weight of the Load affects the quantity of electricity produced. The heavier the

Load, the higher the amount of electrical power generated. Also, the power is generated

depending on the speed. At lower speed, the power was small, but more power was likely to be

generated at higher speed.

Multimedia Projects

You will complete three (3) projects. For each project you will

design and implement an experiment to test some physical

phenomenon / behavior related to this class. You can be

creative and present this project in any format you like (video,

ppt, word document, etc.). Each project must have:

Clear statement of phenomenon you wish to test

Clear explanation why you chose to set up the experiment

as you did

Video or photograph of experimental setup

Data collected

Interpretation of the data

You will receive more specific instructions

Multimedia Projects

You will complete three (3) projects. For each project you will

design and implement an experiment to test some physical

phenomenon / behavior related to this class. You can be

creative and present this project in any format you like (video,

ppt, word document, etc.). Each project must have:

Clear statement of phenomenon you wish to test

Clear explanation why you chose to set up the experiment

as you did

Video or photograph of experimental setup

Data collected

Interpretation of the data

You will receive more specific instructions

1

1. Statement on Phenomena

We will test at what speed someone is likely to peddle a bicycle to start producing electricity that

can light a bulb. Specifically, I will determine that the weight of a person impacts how much

electricity is produced.

Comments

Files (1)

Rubric

Good job overall. I took 3 points off

because it was not clear how you obtained

the equation for P_FWT, as well as what

the physical meaning of angular velocity

and moment of inertia are, and how you

determined that the moment of inertia of

the wheel is 0.95 kg m^2. I also took 5

points off because there was no statement

for what each person did in this project.

Finally, I took 3 points off because it was

also not clear how bulbs of different

wattage were used to measure the power

generated; for example, if a bulb had a

wattage of 30 W and you only provided 25

W of power, the bulb would still light up,

right?

1

1. Statement on Phenomena

We will test at what speed someone is likely to peddle a bicycle to start producing electricity that

can light a bulb. Specifically, I will determine that the weight of a person impacts how much

electricity is produced.

Comments

Files (1)

Rubric

Good job overall. I took 3 points off

because it was not clear how you obtained

the equation for P_FWT, as well as what

the physical meaning of angular velocity

and moment of inertia are, and how you

determined that the moment of inertia of

the wheel is 0.95 kg m^2. I also took 5

points off because there was no statement

for what each person did in this project.

Finally, I took 3 points off because it was

also not clear how bulbs of different

wattage were used to measure the power

generated; for example, if a bulb had a

wattage of 30 W and you only provided 25

W of power, the bulb would still light up,

right?

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