Download energy transformations

AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
ENERGY
TRANSFORMATIONS
Team Leader:
Bob Holzer
Writer:
John Watson
Editor:
CHAOS Communications
Producer:
Michele Boniface
Content Reviewers:
Donna Matovinovic
Stella Shrum
Produced by ACCESS The Education Station
© 1997 Alberta Education
Published & Distributed by…
AGC/UNITED LEARNING
1560 Sherman Avenue
Suite 100
Evanston, IL 60201
1-800-323-9084
24-Hour Fax No. 847-328-6706
Website: http://www.agcunitedlearning.com
E-Mail: [email protected]
1
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
This video is the exclusive property of the copyright holder.
Copying, transmitting, or reproducing in any form, or by any
means, without prior written permission from the copyright
holder is prohibited (Title 17, U.S. Code Sections 501 and
506).
©MCMXCVII Alberta Education
2
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
ENERGY TRANSFORMATIONS
Teacher’s Guide
Table of Contents
Introduction ............................................................1
Program Summary ................................................1
Links to Curriculum Standards ...........................1
Pre-Test ....................................................................2
Teacher Preparation/Instructional Notes ..........2
Student Objectives .................................................3
Student Preparation...............................................3
Blackline Masters ...................................................4
Answer Key ............................................................5
Script of Video Narration .....................................9
This video is closed captioned
The purchase of this video program entitles the user to the
right to reproduce or duplicate, in whole or in part, this
teacher's guide and the blackline master handouts that accompany it for the purpose of teaching in conjunction with this
video, Energy Transformations. This right is restricted only
for use with this video program. Any reproduction or duplication in whole or in part of this guide and the blackline master handouts for any purpose other than for use with this video
program is prohibited.
3
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
CLASSROOM/LIBRARY
VIEWING CLEARANCE
This program is for instructional use. The cost of each program includes public performance rights as long as no admission charge is made. Public performance rights are defined as viewing of a video in the course of face-to-face
teaching activities in a classroom, library, or similar setting
devoted to instruction.
Closed Circuit Rights are included as a part of the public
performance rights as long as closed-circuit transmission
is restricted to a single campus. For multiple locations,
call your United Learning representative.
Television/Cable/Satellite Rights are available. Call your
United Learning representative for details.
Duplication Rights are available if requested in large quantities. Call your United Learning representative for details.
Quantity Discounts are available for large purchases. Call
your United Learning representative for information and
pricing. Discounts, and some special services, are not applicable outside the United States.
Your suggestions and recommendations are welcome. Feel
free at any time to call United Learning at 1-800-424-0362.
4
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
INTRODUCTION
This Teacher’s Guide accompanies Program Twenty-One,
“Energy Transformations,” from the Simply Science series.
Simply Science is a series of twenty-five science programs
for high school students. These instructional programs use
practical applications as context to the interdisciplinary concept development emphasizing the connections among science, technology, and society. This comprehensive
Teacher’s Guide and accompanying blackline master activity sheets provide extended practice and additional learning opportunities.
PROGRAM SUMMARY
“Energy Transformations” examines the conversion of energy from one form to another. Work is defined, and
changes from gravitational potential energy to kinetic energy, and the reverse, are calculated. Since graphing can
aid understanding of motion, a distance-versus-time graph
is produced and analyzed.
LINKS TO CURRICULUM STANDARDS
“Energy Transformations” correlates with the following National Science Education Standards for grades 9-12:
Physical Science: Motion and force
• Objects change their motion only when a net force is
applied. Laws of motion are used to calculate precisely the
effects of forces on the motion of objects. The magnitude
of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the
force. Whenever one object exerts force on another, a force
equal in magnitude and opposite in direction is exerted on
the first object.
Physical Science: Conservation of energy and the increase
5
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
in disorder
• The total energy of the universe is constant. Energy can
be transferred by collisions in chemical and nuclear reactions, by light waves and other radiations, and in many
other ways. However, it can never be destroyed. As these
transfers occur, the matter involved becomes steadily less
ordered.
• All energy can be considered to be either kinetic energy,
which is energy of motion; potential energy, which depends
on relative position; or energy contained by a field, such as
electromagnetic waves.
PRE-TEST
A Pre-Test is included with the Blackline Masters for this
program. It is meant to be administered before the video
and its ensuing activities are used. This assessment tool
allows you to gauge student comprehension of the Objectives before completing the lesson; its results may be contrasted with those of the Post-Test, also included herein, to
assess comprehension of the Objectives after completing
the lesson.
TEACHER PREPARATION/INSTRUCTIONAL NOTES
Before presenting this lesson to your students we suggest
that you preview the video and review this guide, and the
accompanying blackline master activities in order to familiarize yourself with their content.
As you review the materials presented in this guide, you
may find it necessary to make some changes, additions, or
deletions to meet the specific needs of your class. We encourage you to do so, for only by tailoring this program to
your class will they obtain the maximum instructional benefits afforded by the materials.
6
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
It is also suggested that the video presentation take place
before the entire group under your supervision. The lesson activities grow out of the context of the video, therefore, the presentation should be a common experience for
all students.
STUDENT OBJECTIVES
After viewing the video and participating in the follow-up
activities, students will be able to:
• Define energy as the ability to do work.
• Recognize potential energy is made useful when it is
converted.
• Show that energy transfer produces changes in motion.
• Prepare distance-versus-time graphs.
• Calculate the slope of the line on a distance-versustime graph to determine speed.
• Appreciate the need for math skills in solving problems dealing with energy transfers.
STUDENT PREPARATION
This video is one of a series. Before students view this program and complete the follow-up activities, they should
be able to:
1. Write the equation that is used to calculate the energy
an object possesses due to its height above a reference
position.
Ep = mgh
2. Define kinetic energy.
Kinetic energy is the energy an object has due to its motion.
3. Solve this equation for mass. (Rearrange the equation
so that mass is by itself on one side of the equation.)
1
Ek =
mv2
1
2
Ek =
mv2
2
2Ek= mv2
2E
m = 2k
v
7
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
If students have difficulty with any of the items, you should
review the concepts in reference materials before viewing
the video.
BLACKLINE MASTERS
The following blackline master activity sheets are included
with this guide. Duplicate and distribute those you wish to
use. An Answer Key appears on pages 5-7.
(1.) Blackline Master #1: Pre-Test is to be given to your
students prior to viewing the video to assess their prior
knowledge of the topic. It may be contrasted to Blackline
Master #8: Post-Test to gauge student comprehension of
the Objectives after the lesson has been completed.
(2.) Blackline Master #2: Glossary is a list of terms from
the video. Students may find this handout helpful when
completing the activities which accompany this lesson, as
well as for preparation for the Post-Test.
(3.) Blackline Master #3: Work examines the terms work
and force.
(4.) Blackline Master #4: Gravity Works explores the calculation of the amount of work done.
(5.) Blackline Master #5: Realizing Your Potential explains
the calculations needed to determine potential energy.
(6.) Blackline Master #6: Where Will It Stop? explores
resistance.
(7.) Blackline Masters #7a-7b: A Graphic Illustration uses
graphs to show the role of slope in determining speed.
(8.) Blackline Masters #8a-8d: Post-Test is an assessment
tool to be used after the video and follow-up activities have
been completed. The test is based directly on the Student
Objectives for this program and the National Science Education Standards for grades 9-12.
8
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
ANSWER KEY
Blackline Master #1: Pre-Test
1.T
2.F
3.T
4.F
5.T
6.T
7.T
8.F
9.F
10.T
Blackline Masters #3Note that some of these questions have more than one
possible answer.
1. Work is done because energy is transferred in:
a. as the ball is put in motion;
b. as the balloon moves upwards.
Work is not done in:
c. because the speed of the comet is not changing.
2. A force is a push or a pull.
3. Work is a transfer of energy from one object or system
to another.
4. F = 2.45 ×103 N
Note: At a constant speed, the force applied is equal
to the weight of the grain.
5. W = 7.1 × 104 J
6. W = 24 J
Note: The distance over which the force acts – 60 cm
– must be converted to 0.60 m to complete the calculation.
7. W = 7.8 × 102 J
9
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
8. Ep = Ek
1
divide by m
mgh = 2 mv2
v2
divide by g
gh = 2
v2
h = 2g
9. The egg would break. v = 5.4 m/s
10. h = 2.6 m
11. The shuttle’s kinetic energy is converted to thermal
energy and work done against the atmosphere. The
shuttle’s underbelly is covered in specially designed
ceramic tiles to dissipate the thermal energy created
during re-entry.
12.
Distance vs. Time
35
30
25
20
15
10
5
0
0
2
4
6
8
10
12
14
Time (s)
13. The speed of the object is 3.6 cm/s.
10
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
Blackline Masters #8a-8d: Post-Test
Multiple Choice
1.b.solar energy
2.d.gravitational potential energy
3.b. speed
Long Answer
1.
changed/transformed
2.
push; pull
3.
a transfer of energy when a force is applied over
distance
4.
reference level
5.
W = Fd
6.
W
= Fd
= (1000 N)(150 m)
W
= 1.50 x 105 J
7.
weight
8.
acceleration due to gravity
9.
energy; total energy decreases
10.
condition
11.
Ep
= mgh
= (65 kg)(9.81 m/s2)(10 m)
Ep
= 6.4 kJ
12.
It changes into kinetic energy.
13.
work done = gravitational energy gained
2.94 kJ
Ep
= Ek
mgh = 1/2 mv2
v
=
2gh
=
2(9.81m/s)(5.00m)
= 9.90 m/s
14.
Ep
= Ek
mgh = 1/2 mv2
h
= v2 / 2g
= (5.50 m/s)2/2(9.81 m/s2)
*
speed = slope of11the line
= rise ∏ run
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
18.
Distance vs Time
100
80
60
Distance
(m)
40
20
0
0
*
5
10
15
Time (s)
20
25
speed = slope of the line
= rise / run
v
= ∆d / ∆t
= (d2 - d1) / (t2 - t1)
= (100 m - 0 m) / (25 s - 0 s)
x
= 4.0 m/s
12
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
SCRIPT OF NARRATION
DANA: THIS MAY LOOK LIKE A SIMPLE BUILDING, BUT IN FACT
IT’S LIKE A GIANT ENGINE, CONVERTING ENERGY FROM ONE
FORM TO ANOTHER. USING SOME VERY SIMPLE TECHNIQUES,
THE ELEVATOR HARNESSES TWO OF THE MOST RELIABLE AND
EFFICIENT ENERGY SOURCES IN THE UNIVERSE. AND WHEN
IT’S FULL, A GRAIN ELEVATOR IS A GIANT EXAMPLE OF STORED
ENERGY. HOW DOES IT WORK? IT’S SIMPLY SCIENCE! POTENTIAL ENERGY. THERE’S A LOT OF IT IN HERE. BECAUSE OF GRAVITY AND MY POSITION RELATIVE TO THE FLOOR, I HAVE GRAVITATIONAL POTENTIAL ENERGY. SO DOES THE GRAIN IN THOSE
BINS UP THERE. THE GRAIN ALSO HAS CHEMICAL POTENTIAL
ENERGY. ALL SUMMER THE WHEAT PLANTS USED PHOTOSYNTHESIS TO STORE THE ENERGY OF THE SUN IN THESE KERNELS.
BUT POTENTIAL ENERGY IS ONLY CONSIDERED USEFUL WHEN
IT’S CONVERTED TO SOME OTHER FORM, LIKE KINETIC ENERGY.
THAT’S WHEN ENERGY GOES TO WORK. FORCE IS A PUSH OR A
PULL. IT CAN COME FROM A VARIETY OF SOURCES: A MOTOR,
GRAVITY, OR MY BODY. WHEN A FORCE ACTS OVER A DISTANCE, ENERGY IS TRANSFERRED FROM ONE OBJECT OR SYSTEM TO ANOTHER. THAT’S WORK. THE TRANSFER OF ENERGY
FROM ONE OBJECT OR SYSTEM TO ANOTHER.
TARA: WHEN WE DO WORK ON AN OBJECT, WE TRANSFER
ENERGY TO THE OBJECT. SO THE BALL GAINS ENERGY.
GRAEME LAUBER: SO THIS TRUCK IS TYPICAL OF THE TYPE
THAT WAS USED ON THE PRAIRIES TO HAUL GRAIN — AND
IT’S A TWO-TON TRUCK.
BRENDON: SO WHAT DOES A GRAIN ELEVATOR DO?
GRAEME LAUBER: GRAIN ELEVATORS ARE REALLY VITAL FOR
TRANSPORTING GRAIN FROM THE FARMS TO MARKET. THEY
GATHER THE GRAIN UP, AND THEN THEY’RE SHIPPED OFF TO
PLACES WHERE THE GRAIN CAN BE SOLD.
BRENDON: HMMM...SO I TAKE IT THE GRAIN IS DUMPED INTO
HERE.
GRAEME LAUBER: THAT’S RIGHT. SO THE GRAIN FALLS OUT
OF THE BACK OF THE TRUCK AND INTO A TANK BENEATH OUR
FEET THAT YOU CALL THE “PIT.” IN EARLIER DAYS, TRUCKS
13
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
WEREN’T ABLE TO DUMP THEIR OWN BOXES, SO THE ENTIRE
FLOOR HAD TO TILT SO THAT THE GRAIN COULD POUR OUT
THE BACK OF THE TRUCK.
BRENDON: SO IN RELATION TO THE PIT, THE GRAIN IN THE
TRUCK HAS GRAVITATIONAL POTENTIAL ENERGY?
GRAEME LAUBER: THAT’S RIGHT.
BRENDON: AND THE ELEVATOR TAKES ADVANTAGE OF THIS
AND CONVERTS ITS KINETIC ENERGY, PUTTING GRAVITY TO
WORK.
GRAEME LAUBER: ABSOLUTELY.
BRENDON: AH!
DARREN: WHEN A PERSON OR AN OBJECT PERFORMS WORK,
ENERGY IS TRANSFERRED FROM ONE SYSTEM TO ANOTHER.
MY ARM TRANSFERS ENERGY TO THE HAMMER, WHICH
TRANSFERS IT TO THE NAIL. BUT THE “FIRST LAW OF THERMODYNAMICS” STATES THAT ENERGY CAN NEVER BE CREATED
OR DESTROYED, ONLY CONVERTED FROM ONE FORM TO ANOTHER. THE HAMMER GIVES UP ENERGY TO THE NAIL. THAT’S
WORK.
BRENDON: SO WHAT HAPPENS TO THE GRAIN AFTER IT’S
DUMPED?
GRAEME LAUBER: WELL, THE GRAIN IS IN A PIT BENEATH OUR
FEET HERE, AND THEN IT TRAVELS UP THE LEG TO THE TOP OF
THE ELEVATOR. NOW, THE LOWER PART OF THE LEG IS CALLED
THE “BOOT.” SO THE GRAIN FLOWS FROM THE PIT, INTO THE
BOOT, AND THEN THIS BUCKET BELT TAKES IT TO THE TOP OF
THE ELEVATOR.
BRENDON: WHAT RUNS THIS BUCKET BELT?
GRAEME LAUBER: WE HAVE A MOTOR THAT GIVES THIS THE
ENERGY TO GET TO THE TOP.
BRENDON: SO THE MOTOR GIVES UP ENERGY TO THE BUCKET
BELT, WHICH IS WORK.
GRAEME LAUBER: THAT’S RIGHT.
BRENDON: AND NOW THAT THE GRAIN IS MOVING, IT HAS
KINETIC ENERGY, SO THE CONVEYOR GIVES UP ENERGY TO THE
GRAIN.
GRAEME LAUBER: THAT’S RIGHT. MORE WORK!
DANA: WORK IS THE TRANSFER OF ENERGY FROM ONE OB14
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
JECT OR SYSTEM TO ANOTHER. WHEN WORK IS DONE ON AN
OBJECT, THE OBJECT GAINS ENERGY. WHEN I PULL ON THIS
ROPE, I GAIN KINETIC ENERGY AND GRAVITATIONAL POTENTIAL ENERGY. AND WHEN AN OBJECT PERFORMS WORK, IT
GIVES UP ENERGY. PULLING ON THIS ROPE CONVERTS CHEMICAL ENERGY STORED IN MY BODY.
DARREN: HERE’S AN ENERGY CONVERSION FOR YOU. ON TOP
OF THE TOWER, CRYSTAL HAS GRAVITATIONAL POTENTIAL
ENERGY — ENERGY SHE CONVERTS TO KINETIC ENERGY. TO
CALCULATE GRAVITATIONAL POTENTIAL ENERGY IN JOULES,
WE USE THE EQUATION: EP EQUALS MGH.
LAUREEN: WHERE “M” IS THE MASS IN KILOGRAMS.
STEPHANIE: “G” IS THE ACCELERATION OF AN OBJECT FALLING TOWARD EARTH BECAUSE OF THE GRAVITATIONAL
FORCE.\E IT’S MEASURED IN METERS PER SECOND SQUARED.
LAUREEN: AND “H” IS THE OBJECT’S VERTICAL DISTANCE
FROM THE REFERENCE POSITION. WE MEASURE THAT IN
METERS.
DARREN: BOTH THESE SACKS OF GRAIN HAVE THE SAME MASS.
SO IN RELATION TO THE FLOOR, WHICH HAS GREATER GRAVITATIONAL POTENTIAL ENERGY?
STEPHANIE: THIS ONE, BECAUSE IT HAS MORE HEIGHT.
LAUREEN: WHAT IF I PUT THIS ONE INTO THE WHEELBARROW?
DARREN: IN TERMS OF ENERGY TRANSFER?
STEPHANIE: SHE TRANSFERS ENERGY FROM HER BODY TO THE
GRAIN.
DARREN: SO TO INCREASE THE GRAVITATIONAL POTENTIAL
ENERGY OF THIS SACK, LAUREEN HAD TO PERFORM WORK
AGAINST GRAVITY.
DANA: WE DESCRIBE THIS ENERGY TRANSFER WITH THE
EQUATION: W EQUALS FD. WHERE “W” REPRESENTS WORK IN
JOULES; “F” IS FORCE, MEASURED IN NEWTONS; AND “D” IS
DISTANCE, MEASURED IN METERS.
DARREN: IF CRYSTAL WANTS TO CLIMB HIGHER, SHE NEEDS
TO DO WORK AGAINST THE FORCE OF GRAVITY. HOW WOULD
YOU CALCULATE THAT?
STEPHANIE: USING W EQUALS F TIMES D.
LAUREEN: W IS WORK, AND D IS THE DISTANCE UP THE TOWER.
15
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
STEPHANIE: SO WHAT’S F?
DARREN: WELL, CRYSTAL’S WEIGHT IS REALLY AN EXPRESSION
OF THE FORCE OF GRAVITY ACTING ON HER MASS.
LAUREEN: SO THAT MEANS F IS HER WEIGHT IN NEWTONS.
STEPHANIE: SO USING W EQUALS F TIMES D, THE WORK CRYSTAL DOES IS HER WEIGHT TIMES HER CHANGE IN HEIGHT.
LAUREEN: WORK DONE IS:
DARREN: GREAT!
BRENDON: SO AFTER THE GRAIN REACHES THE TOP, WHAT
HAPPENS TO IT?
GRAEME LAUBER: WELL, THE GRAIN IS DUMPED INTO SOMETHING CALLED THE “HEAD,” WHICH IS JUST THE UPPER PART
OF THE ELEVATOR. THEN THE GRAIN ENDS UP IN SOMETHING
CALLED A “GERBER SPOUT.” AND I CAN USE THIS INDICATOR
WHEEL TO DECIDE HOW THE GERBER SPOUT IS GOING TO BE
POSITIONED. AND IF I LINE UP THE NUMBER 2 ON THE INDICATOR WHEEL WITH THE ARROW THERE, THAT MEANS THE
GERBER SPOUT IS POSITIONED TO DUMP THE GRAIN INTO BIN
NUMBER 2.
BRENDON: SO WHEN IT’S STORED IN BIN NUMBER 2, IT HAS
GRAVITATIONAL POTENTIAL ENERGY?
GRAEME LAUBER: THAT’S RIGHT. THE AVERAGE GRAIN ELEVATOR COULD HOLD MAYBE 3,000 TONS OF GRAIN.
BRENDON: OKAY. SO THAT’S: HOW HIGH IS AN AVERAGE
GRAIN ELEVATOR?
GRAEME LAUBER: A TYPICAL GRAIN ELEVATOR MIGHT BE 29
METERS HIGH.
BRENDON: SO TO FILL THE ELEVATOR TO CAPACITY, THE CONVEYOR WOULD HAVE TO APPLY A FORCE OF 2.94 TIMES 10 TO
THE 7 NEWTONS THROUGH A DISTANCE OF 29 METERS. THAT’S
8.5 TIMES 10 TO THE 8 NEWTON-METERS, OR 8.5 TIMES 10 TO
THE 8 JOULES OF WORK!
DARREN: CRYSTAL CONVERTS THE CHEMICAL POTENTIAL
ENERGY IN HER BODY TO KINETIC ENERGY AND PERFORMS
WORK AGAINST THE FORCE OF GRAVITY.
STEPHANIE: BUT THE “FIRST LAW OF THERMODYNAMICS”
SAYS ENERGY CAN’T BE CREATED OR DESTROYED, JUST CONVERTED TO ANOTHER FORM.
16
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
DARREN: THAT’S RIGHT.
STEPHANIE: SHE ISN’T MOVING NOW, SO WHERE’S THE ENERGY?
LAUREEN: I SUPPOSE A LITTLE BIT IS LOT AS HEAT, BUT MOST
OF IT’S STORED IN HER BODY.
STEPHANIE: NOW THAT CRYSTAL’S AT THE TOP OF THE TOWER,
SHE’S GOT A LOT MORE GRAVITATIONAL POTENTIAL ENERGY.
DARREN: IN OTHER WORDS, BY CLIMBING THE LADDER, CRYSTAL PERFORMED WORK TO INCREASE HER GRAVITATIONAL
POTENTIAL ENERGY.
DANA: SO ONE WAY TO INCREASE GRAVITATIONAL POTENTIAL ENERGY IS TO INCREASE THE HEIGHT OF AN OBJECT, WITH
RESPECT TO ITS REFERENCE POSITION. AND THAT REQUIRES
WORK DONE AGAINST THE FORCE OF GRAVITY. ENERGY CAN
BE CONVERTED FROM ONE FORM TO ANOTHER. GRAVITATIONAL POTENTIAL ENERGY BECOMES KINETIC ENERGY.
LAUREEN: CRYSTAL OWES HER GRAVITATIONAL POTENTIAL
ENERGY TO HER MASS AND HER HEIGHT ABOVE THE WATER.
STEPHANIE: AND HER GRAVITATIONAL POTENTIAL ENERGY
CAN BE CALCULATED USING THE EQUATION: EP EQUALS MGH.
LAUREEN: WHEN SHE LEAVES THE DIVING PLATFORM, GRAVITY GOES TO WORK, AND HER GRAVITATIONAL POTENTIAL
ENERGY IS CONVERTED TO KINETIC ENERGY.
STEPHANIE: WHICH WE CALCULATE WITH THE FORMULA: EK
EQUALS 1/2 MV SQUARED.
LAUREEN: BUT ENERGY CANNOT BE CREATED OR DESTROYED,
ONLY CONVERTED FROM ONE FORM TO ANOTHER.
STEPHANIE: SO CRYSTAL’S POTENTIAL ENERGY AT THE TOP
OF THE TOWER, EP, IS EQUAL TO HER KINETIC ENERGY, EK, JUST
AS SHE REACHES THE REFERENCE POINT, THE SURFACE OF THE
WATER.
LAUREEN: SO THAT MEANS MGH EQUALS 1/2 MV SQUARED.
STEPHANIE: RIGHT. IF WE WANT TO KNOW HOW FAST CRYSTAL IS GOING JUST BEFORE SHE ENTERS THE WATER, WE NEED
TO SOLVE THE EQUATION FOR V.
LAUREEN: THAT MEANS WE NEED TO ISOLATE THE TERM.
FIRST, DIVIDE BOTH SIDES BY M.
STEPHANIE: WHICH GIVES US:
17
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
LAUREEN: SO V IS THE SQUARE ROOT OF 2GH.
STEPHANIE: WHEN WE SUBSTITUTE IN THE VALUES, G IS EQUAL
TO 9.81 METERS PER SECOND SQUARED, AND H IS EQUAL TO
5.0 METERS.
LAUREEN: SO TO GET V, WE NEED TO MULTIPLY 2 TIMES 9.81
METERS PER SECOND SQUARED, TIMES 5.0 METERS, WHICH
GIVES US 98.1 METERS SQUARED OVER SECONDS SQUARED.
STEPHANIE: AND WHEN WE TAKE THE SQUARE ROOT OF ALL
THAT, WE GET 9.9 METERS PER SECOND.
LAUREEN: SO THAT’S CRYSTAL’S SPEED JUST BEFORE SHE ENTERS THE WATER.
BRENDON: SO HOW DOES ALL THE GRAVITATIONAL POTENTIAL ENERGY THAT’S STORED IN THE ELEVATOR GET TURNED
INTO KINETIC ENERGY TO LOAD THE RAIL CARS?
GRAEME LAUBER: WELL, ALL OF THE GRAIN BINS ARE STORED
JUST A LITTLE BIT ABOVE THE GROUND. SO WE CAN OPEN
DOORS IN THE BOTTOM
OF THE BINS, AND THE GRAIN WILL FLOW THROUGH TUBES
BACK INTO THE PIT. NOW, THE PIT IS WHERE THE GRAIN
STARTED OUT AFTER IT WAS
DUMPED FROM THE TRUCK. THEN THE GRAIN FLOWS INTO
THE BOOT, UP THE LEG TO THE TOP OF THE ELEVATOR, BY
WHICH TIME YOU’VE CHANGED THE POSITION OF THE GERBER
SPOUT USING THE INDICATOR WHEEL TO NUMBER 4, WHICH
IS THE TUBE OUT TO THE TRAIN. WE CALL IT “GRAVITY
FEED.”
TARA: KINETIC ENERGY CAN BE CONVERTED TO GRAVITATIONAL POTENTIAL ENERGY.
DARREN: REARRANGING THE EQUATION THAT STEPHANIE
AND LAUREEN USED, MGH EQUALS 1/2 MV SQUARED, WE CAN
USE THE INITIAL SPEED OF AN OBJECT TO PREDICT ITS CHANGE
IN HEIGHT. DIVIDING BOTH SIDES BY M, LEAVES GH EQUALS
1/2V SQUARED. THEN DIVIDING BOTH SIDES BY G, WE GET H
EQUALS V SQUARED OVER 2G. IF ITS INITIAL SPEED IS 6.0
METERS PER SECOND UP, THEN WE COULD EXPECT IT TO
REACH A HEIGHT OF 6.0 METERS PER SECOND ALL SQUARED,
DIVIDED BY 2 TIMES 9.81 METERS PER SECOND SQUARED. THAT
GIVES US A HEIGHT OF 1.8 METERS. SO POTENTIAL ENERGY IS
18
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
CONVERTED TO KINETIC ENERGY, AND KINETIC CONVERTED
TO POTENTIAL. WE CAN USE THE EQUATIONS THAT DESCRIBE
THESE CONVERSIONS TO MAKE PREDICTIONS ABOUT HOW OBJECTS WILL BEHAVE WHILE THEY’RE IN MOTION.
SARAH: OBJECTS INCREASE THEIR GRAVITATIONAL POTENTIAL ENERGY WHEN WORK IS PERFORMED AND THEIR POSITION CHANGES. BUT WE TALK ABOUT PLANTS HAVING
STORED ENERGY. HOW DOES THAT WORK? PLANT’S DON’T
MOVE. THE ANSWER, OF COURSE, IS PHOTOSYNTHESIS. IN
THEIR LEAVES, PLANTS HAVE WATER AND CARBON DIOXIDE
MOLECULES. THROUGH A COMPLEX SERIES OF REACTIONS,
ENERGY FROM THE SUN IS USED TO DO WORK ON THESE MOLECULES AND REARRANGE THEM. THE RESULT IS CHEMICAL
ENERGY STORED IN THE BONDS OF GLUCOSE MOLECULES. IT’S
CALLED “POTENTIAL ENERGY DUE TO CONDITION.” WHEN WE
EAT AND DIGEST PLANT MATERIAL, OUR BODIES BREAK THE
CHEMICAL BONDS, AND THE SIMPLE SUGAR MOLECULES ARE
CONVERTED BACK INTO CARBON DIOXIDE AND WATER DURING CELLULAR RESPIRATION.\E THE RELEASE OF THIS CHEMICAL POTENTIAL ENERGY GIVES OUR BODIES THE ABILITY TO
DO WORK.
DARREN: FOR AN OBJECT TO COME TO A STOP, ITS KINETIC
ENERGY MUST BE CONVERTED TO OTHER FORMS.
LAUREEN: CRYSTAL USES THE KINETIC ENERGY OF HER LEGS
AND ARMS TO INCREASE HER GRAVITATIONAL POTENTIAL
ENERGY, WHICH SHE THEN CONVERTS INTO KINETIC ENERGY.
WHEN SHE HITS THE WATER, CRYSTAL’S BODY SLOWS DOWN
AND HER KINETIC ENERGY IS CONVERTED TO A NUMBER OF
OTHER FORMS. A LOT OF IT IS ABSORBED BY THE WATER.
THAT’S THE ENTRY SPLASH AND THE WAVES THAT FOLLOW.
SOME OF IT IS CONVERTED TO SOUND ENERGY, WHICH IS WHY
WE HEAR THE SPLASH. AND A SMALL AMOUNT IS GIVEN OFF
AS HEAT. THAT’S ABSORBED BY THE WATER. YOU’LL HAVE TO
TRUST ME ON THAT ONE!
DARREN: FORCES THAT OPPOSE MOTION ARE CALLED “RESISTIVE FORCES.” SOME RESISTIVE FORCES ARE DESIRABLE.
STEPHANIE: IN HER DIVE, CRYSTAL IS CAREFUL TO KEEP HER
BODY COMPACT SO HER ENTRY IS CLEAN AND SMOOTH. BUT
19
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
ONCE SHE’S IN THE
WATER, CRYSTAL USES HER ARMS AND LEGS TO SPEED UP THE
ENERGY CONVERSION. THAT WAY, SHE COMES TO A COMPLETE
STOP BEFORE SHE HITS THE BOTTOM OF THE POOL. I’D SAY
THAT’S A DESIRABLE USE OF RESISTIVE FORCE.
DARREN: SOME RESISTIVE FORCES ARE UNDESIRABLE.
GRAEME LAUBER: ONE OF THE PROBLEMS IN A GRAIN ELEVATOR, ESPECIALLY THE OLDER ONES LIKE THIS, IS THE POSSIBILITY OF FIRE. NOW, ALL THE BEARINGS ON THE BELT HAVE
TO BE CLEAN AND WELL GREASED. IF ONE HAPPENS TO GO
DRY, WITH THE FRICTION OF THE MOTION, THEY COULD OVERHEAT. AND IN AN ELEVATOR LIKE THIS, WITH ALL THE GRAIN
AND DUST AROUND, IT DOESN’T JUST CATCH FIRE — IT EXPLODES.
BRENDON: WOW! I THINK WE CAN CONSIDER THAT AN UNDESIRABLE CONVERSION.
DANA: IT’S PRETTY EASY FOR ME TO RAISE MYSELF UP IN THIS
LIFT. THAT’S BECAUSE THE SYSTEM HAS A COUNTERBALANCE
EQUAL TO MY WEIGHT. THE COUNTERBALANCE HELPS TO
OVERCOME THE RESISTIVE FORCES THAT ACT AGAINST MOTION. IF THERE WERE LESS MASS IN THE COUNTERBALANCE,
I’D HAVE TO USE MORE FORCE TO OVERCOME THE RESISTIVE
FORCES. AND IF THE COUNTERBALANCE HAD TOO MUCH
MASS, ONE GOOD TUG ON THIS ROPE COULD SHOOT ME
THROUGH THE ROOF. WITH THE PROPER BALANCE, ALL I NEED
IS A LITTLE FRICTION TO CONVERT MY KINETIC ENERGY TO
THERMAL ENERGY, AND I COME TO A STOP.
BRENDON: TAKE A LOOK AT THIS. AN OBJECT WITH MOTION
HAS TO CHANGE ITS POSITION, RIGHT?
DANA: RIGHT.
BRENDON: SO MOTION INVOLVES DISTANCE AND TIME. WITH
TWO VARIABLES LIKE THAT, WE CAN USE A GRAPH TO DESCRIBE MOTION.
DANA: WE CAN ANALYZE THE MOTION OF THE BUCKET
BELT.\E I’VE MARKED OFF A SEGMENT OF THE LEG INTO 50
CENTIMETER SECTIONS. THAT’S 0.50 METERS.
BRENDON: OKAY. I’LL TIME A BUCKET AS IT PASSES EACH
MARKER.
20
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
DANA: AND I’LL RECORD YOUR TIMES ON THIS TABLE.
BRENDON: WHY DON’T WE START WITH THIS BUCKET...NOW!
15.5. 20.6. 25.7. 30.9. NOW WE HAVE A TABLE OF DISTANCE AND
THE ELAPSED TIME AS THE BUCKET MOVED UP THE LEG.
DANA: AND WE CAN USE THESE ORDERED PAIRS TO PLOT
POINTS ON A DISTANCE-TIME GRAPH. SO WHICH AXIS DOES
TIME GO ON?
BRENDON: WELL, YOU CHOSE YOUR DISTANCE INTERVAL. SO
DISTANCE IS THE INDEPENDENT VARIABLE, AND TIME IS THE
DEPENDENT VARIABLE.
DANA: AND TIME GOES?
BRENDON: ON THE VERTICAL AXIS.
DANA: GREAT! BUT FOR CONVENIENCE, LET’S PLOT TIME ON
THE HORIZONTAL AXIS. THE WHOLE POINT OF DRAWING A
GRAPH IS TO SHOW A PATTERN OR TREND IN THE DATA.\E SO
WE DRAW A “BEST-FIT” LINE ON OUR DISTANCE-TIME GRAPH.
THIS LINE AVERAGES THE EFFECTS OF ERRORS IN THE MEASURES OF DISTANCE AND TIME. IT GIVES US A MORE ACCURATE DEPICTION OF THE MOTION OF THE BUCKET THAN THE
PLOTTED POINTS THEMSELVES.
DARREN: THE SLOPE OF THE LINE ON A GRAPH REPRESENTS
THE RATE OF CHANGE IN ONE VARIABLE WITH RESPECT TO
THE OTHER. BY DEFINITION, THE SLOPE IS EQUAL TO THE
CHANGE IN THE VERTICAL VARIABLE, DIVIDED BY THE
CHANGE IN THE HORIZONTAL VARIABLE — OR SLOPE IS EQUAL
TO RISE OVER RUN. SO FOR THIS DISTANCE-TIME GRAPH, THE
SLOPE EQUALS DELTA D, DIVIDED BY DELTA T. AND WE CAN
CALCULATE THE CHANGE IN DISTANCE, DELTA D, USING THE
EQUATION: DELTA D EQUALS D2 MINUS D1. AND WE CAN
CALCULATE THE CHANGE IN TIME, DELTA T, USING THE EQUATION: DELTA T EQUALS T2 MINUS T1. SO IN OUR EXAMPLE, IF
WE TAKE D2 EQUALS 280 CENTIMETERS AND D1 EQUALS 40
CENTIMETERS, THEN D2 MINUS D1 EQUALS 240 CENTIMETERS.
AND T2 EQUALS 28 SECONDS AND T1 EQUALS 4.0 SECONDS. SO
DELTA T IS 28 MINUS 4.0, OR 24 SECONDS. WHICH MEANS THE
SLOPE IS 240 CENTIMETERS, DIVIDED BY 24 SECONDS, OR 10
CENTIMETERS PER SECOND.
BRENDON: SO THIS LINE DESCRIBES THE RELATIONSHIP BE21
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
TWEEN DISTANCE AND TIME, IN CENTIMETERS PER SECOND.
THAT’S SPEED!
DANA: RIGHT. THE SLOPE OF A DISTANCE-TIME GRAPH GIVES
US SPEED.
DARREN: SPEED, V, IS THE CHANGE IN DISTANCE, DELTA D,
OVER THE CHANGE IN TIME, DELTA T. IF WE USE A DISTANCETIME GRAPH, WE CAN SEE THAT THE SLOPE OF THE LINE ON
THE GRAPH IS ALSO SPEED.
BRENDON: SO A DISTANCE-TIME GRAPH GIVES A SORT OF
“SNAP SHOT” OF ENERGY IN ACTION. AND WHEN WE COMPARE THE SLOPES, WE CAN SEE IF ONE OBJECT IS MOVING
FASTER THAN ANOTHER.
DANA: SO A GRAIN ELEVATOR IS A GIANT ENGINE OF STORED
ENERGY. IT USES KINETIC ENERGY TO INCREASE THE GRAVITATIONAL POTENTIAL ENERGY OF GRAIN. THEN, GRAVITATIONAL POTENTIAL ENERGY IS CONVERTED TO KINETIC ENERGY WHEN THE GRAIN CARS ARE LOADED. IT’S A GREAT ILLUSTRATION OF THE FACT THAT ENERGY IS THE CAPACITY TO
DO WORK, AND THAT WORK IS THE TRANSFER OF ENERGY
FROM ONE SYSTEM TO ANOTHER. ENERGY AND WORK — IT’S
SIMPLY SCIENCE!
22
1
Name___________________________________
PRE-TEST
Directions: Circle the letter indicating whether the following statements are either true ("T") or false
("F").
T
F
1.
An object's energy due to its motion is kinetic energy.
T
F
2.
We can calculate an object's kinetic energy using the relationship: "energy is
equal to mass times the speed of the object squared."
T
F
3.
The energy due to position or condition of an object is its potential energy.
T
F
4.
Glucose and oxygen are products of cellular respiration.
T
F
5.
Work is the transfer of energy form one object or system to another when a force
is applied over a distance.
T
F
6.
Energy is defined as the ability to do work.
T
F
7.
The energy stored in grain, such as wheat, is chemical potential energy.
T
F
8.
The product of an object's mass times the acceleration of gravity is equal to the
gravitational potential energy of the object.
T
F
9.
Resistive forces, friction and air resistance for example, are always undesirable.
T
F
10.
The formula used to calculate the work done is W = Fd.
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
2
Name___________________________________
GLOSSARY
First law of thermodynamics – energy cannot be created or destroyed, only converted from one form to
another
Force – a push or a pull
Kinetic energy – the energy an object or system has due to its motion
Potential energy – the energy of an object or system due to its position or condition, e.g., gravitational
potential energy, chemical potential energy
Resistive force – a force which acts against the motion of an object; friction and air resistance are common examples of resistive forces
Slope – the ratio of the vertical change (rise) divided by the horizontal change (run) of a line on a graph
Work – the transfer of energy from one object or system to another when a force is applied over a
distance
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
3
Name___________________________________
WORK
Work is a transfer of energy from one object or system to another. This transfer occurs when a force is
applied over a distance. We can identify situations in which work has been done by looking for different energy forms at the beginning and at the end of an event. We also determine which object is doing
the work and which object is having work done on it.
Examples
1. What is the evidence that work is done when grain is lifted from the boot to the top of a grain
elevator?
There are two pieces of evidence. First, although the grain in the boot is not moving, the
elevator puts it in motion, and anything in
motion has kinetic energy. Second, the grain at
the top of the elevator has more gravitational
potential energy than it had in the boot. This
means the work done by the elevator on the
grain has increased the grain’s gravitational
potential energy. The change in energy indicates work was done.
bucket belt
boot
2. An ice skater on frictionless, horizontal ice glides at a constant speed across the ice.
There is no evidence of work here. While gliding, the ice skater has kinetic energy.
But because the speed remains constant the kinetic energy does not change. And, while moving
horizontally, there is no change in gravitational potential energy. If there is no change in energy, no
work is done.
Check your understanding of this segment by completing the following. Use the back of the sheet if
necessary.
1. In which of these situations is work done?
a. a pitcher throws a baseball towards home base
b. a hot air balloon rises from the ground
c. a comet travels at a constant speed through deep space
2. Define the term “force.”
3. Define the term “work.”
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
4
Name___________________________________
GRAVITY WORKS
We calculate the amount of work done by multiplying the force acting on the object by the distance the object moves in
the same direction as the force acts. The equation is W = Fd, where F is force in newtons and d is distance in meters. In
the special case where an object is moving vertically downward, the force required to cause the motion is the weight of
the object. This is the force of gravity acting. To find the force due to gravity we multiply mass by the acceleration due to
gravity (9.81 m/s2). The equation is Fg = mg, where m is mass in kilograms and g is the acceleration due to gravity in
meters per second squared.
Examples
1.
Crystal has a mass of 47.7 kg; how much work does she do climbing the 5.0 m dive tower?
given:
m = 47.7 kg
d = 5.0 m
Crystal is moving vertically up, so she is doing work against gravity. In order for Crystal to climb the tower at a
constant speed she must apply a force equal (and opposite) to the force of gravity acting on her. Crystal’s weight is
the force of gravity acting upon her, and we calculate it by multiplying her mass times the acceleration due to gravity.
solution:
Fg = mg
Fg = 47.7 kg (9.81 m/s2)
Fg = 467.937 N
Fg = 468 N
Now this value can be substituted into the work formula.
W = Fd
W = (467.9 N)(5.0 m)
W = 2340 N•m
W = 2.3 x 103 J
Note: The units newton•meter are identical to the joule – which is consistent with our description of work as a
transfer of energy. Work is measured in energy units.
2.
How much work is done to carry a 2.0 kg bowling ball horizontally at a constant 1.3 m/s?
While moving horizontally there is no change in gravitational potential energy. As the speed is constant, there is also no
change in kinetic energy. There is no work done in this case.
Note: Work is done when a force acts and an object moves in the same direction. In this case the force is applied vertically (to hold the ball up), but since the direction in which the ball moves is horizontal, no work is done.
Check your understanding of this segment by completing the following. Use the back of the sheet if
necessary.
4. Find the force required to raise 250 kg of grain against gravity at a constant speed.
5. Find the work done to raise 250 kg of grain 29 m to the top of a grain elevator.
6. A teenager applies an average force of 40 N on the pedals of her bicycle. If this force is applied over
a distance of 60 cm, how much work is done?
7. A 0.40 kg hawk dives vertically downward for a distance of 200 m. How much work does gravity do
on the hawk?
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
5
Name___________________________________
REALIZING YOUR POTENTIAL
Compare the amount of work done when a diver climbs from the swimming pool up to the five-metre
platform with the work done when he or she dives from the platform and returns to the pool. Identify
what does the work on the way up and on the way down.
The amount of work done on the climb up is equal to the work done on the dive down. While climbing up the diver
works against gravity. On the dive down, gravity works on the diver.
The law of conservation of energy states energy can never be created nor destroyed, only converted
from one form to another. When Crystal is on the platform she has gravitational potential energy. The
moment before she enters the water that potential energy has been converted to kinetic energy – Crystal
is moving. The law of conservation of energy tells us that Crystal’s initial gravitational potential energy
is equal to her final kinetic energy.
Example
Find Crystal’s speed the moment before she enters the water as she dives from the
five-metre platform.
From the law of conservation of energy we predict that gravitational potential energy is
converted to kinetic energy.
Ep = Ek
1
mgh = 2 mv2
1
gh = v2
2
2gh = v2
v =
divide both sides by m
multiply both sides by 2
take the square root of both sides
2gh
After isolating the variable, substitute the given values and calculate the answer. Measure from a reference level – in this
case from the pool surface, so the height, h, is 5.0 m, and the acceleration due to gravity, g, is 9.81 m .
s2
v =
2gh
v =
2(9.81 m )(5.0 m)
s2
v = 9.9
Note: This calculation assumes no energy loss due to air resistance.
Check your understanding of this segment by completing the following. Use the back of the sheet if
necessary.
8. Starting from Ep = Ek, find an expression for the height in terms of speed and the acceleration due to
gravity (h = ?).
9. If an egg were dropped from 1.5 m above the ground, would it survive the fall? How fast is it
travelling when it reaches the ground?
10. A volleyball is set at the net, travelling straight up at a speed of 7.2 m/s. How high above its original
position will it reach?
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
6
Name___________________________________
WHERE WILL IT STOP?
A car travelling down a level street at a constant speed does no apparent work.
There is no gain in gravitational
potential energy, and there is no change in kinetic energy. But with the engine running, obviously energy is
being converted. Where does it go?
The engine is doing work against two main resistive forces – the force of friction acting on all parts of the car,
where the tire meets the road, in the engine itself and in all the moving parts of the car; and the force necessary
to move the air out of the way (air resistance).
Resistive forces cause the car to use more fuel. That’s why car designers use wind tunnels and computer models to investigate methods of reducing these forces. But not all resistance forces are undesirable. The friction between the tire and the road, for instance, is essential to keeping the car on the road.
Turning and stopping would be very difficult if friction forces were not significant.
Check your understanding of this segment by completing the following. Use the back of the sheet if
necessary.
11. The space shuttle uses air resistance to slow its descent to earth. Describe the energy conversion
happening in this case and any design features the shuttle incorporates to deal with it.
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
7a
Name___________________________________
A GRAPHIC ILLUSTRATION
We draw graphs to aid our analysis of data we have collected. In general, graphs will have a title,
labelled axes, an appropriate scale and a best-fit line drawn through the data points.
The following graph is created from the bucket-belt data shown in this segment.
Calculating slope requires two points
from the best-fit line.
Choose two that are far apart.
This point is at 295 cm and 30 s.
Distance vs. Time of a Bucket
300
250
Distance (cm)
200
150
Points from the best-fit line
where it crosses a grid line of
the graph are easiest to use.
This point is at 50 cm and 5.0 s.
100
50
0
0
5
10
15
20
25
30
35
40
Time (s)
Graphing Guidelines
1. In general the manipulated, or independent, variable is plotted on the horizontal axis.
2. Axes should be labelled including the units of measure in brackets, e.g., Time (s).
3. Title should follow the standard form of the label of the vertical axis versus the label of the horizontal axis; if necessary it can be followed with some words of description.
4. Determine the scale you will use:
• make good use of the graph space; don’t crowd your data points in one corner
• the scale must be sufficient to include all data points
• the scales of the vertical and horizontal axis are not usually the same
5. Plot the points accurately.
6. Draw a best-fit line. Usually data points are not in a perfectly straight line. If they appear to be
close to a straight line, use a straight edge and draw a single straight line such that about equal
numbers of points lie above and below the line.
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
7b
Name___________________________________
A GRAPHIC ILLUSTRATION
Slope of a Line
The slope of the best-fit line on a distance-versus-time graph tells us information about the object.
Slope is defined as rise divided by run:
rise
slope = run = ∆ distance
Note: The symbol ∆ (called “delta”) means “change in.”
∆ time
As you can see, slope is change in distance divided by change in time – which is speed.
slope = speed
Example
From the graph on the previous page find the speed of the bucket.
We read two points from the best-fit line and substitute those values into the slope equation. When
possible, choose points that are far apart on the line and on one of the grid lines. This will reduce
error. The two points used in the calculation that follows are indicated on the graph: at 5.0 s and 50
cm, and at 30 s and 295 cm.
slope = ∆ distance = d2 - d1
∆ time
t2 - t1
slope = 295 cm - 50 cm
30 s - 5.0 s
slope =
245 cm
25 s
slope = 9.8
The speed of the bucket is 9.8 cm/s.
Check your understanding of this segment by completing the following. Use the back of the sheet if
necessary.
12. Graph the distance-versus-time data in the table below. Place time on them horizontal axis. Include
a title and labels, use appropriate scales and draw a best-fit line.
13. Calculate the speed of the object using the slope of the best-fit line.
© 1997 Alberta Education
Distance (cm)
Time (s)
0.0
0.0
7.1
2.0
14.3
4.0
21.6
6.0
28.9
8.0
36.0
10.0
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
Name___________________________________
8a
POST-TEST
MULTIPLE CHOICE
Directions: Decide which of the choices best completes the statement or answers the question,
then circle the letter that corresponds to your choice. (3 marks each)
1.
The chemical potential energy in grain is stored
a.
b.
c.
d.
2.
A person climbing a flight of stairs increases her
a.
b.
c.
d.
3.
carbon
solar energy
kinetic energy
gravitational energy
kinetic energy
potential energy
chemical potential energy
gravitational potential energy
The slope of a distance versus time graph is equal to
a.
b.
c.
d.
work
speed
acceleration
distance traveled
LONG ANSWER
Directions: Answer the following questions in the spaces provided. Use the back of the sheet if
necessary.
1.
In order for stored, potential, energy to be useful it first has to be _____________________. (3
marks)
2.
Scientists define a force as a ________________________ or ________________________. (3 marks)
3.
The scientific definition of work is _____________________________________________
__________________________________________________________. (4 marks)
4.
The gravitational potential energy of an object is always described relative to a
______________________________________________________. (3 marks)
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
8b
Name___________________________________
POST-TEST
5.
The formula used to calculate work done is _____________________________________. (4 marks)
6.
Having run out of fuel, a driver pushes his car with a constant force of 1000 N over 150 m toward
a service station. Calculate the amount of work done by the driver on the car. (8 marks)
7.
The force of gravity acting on an object is equal to the ___________________________ of that
object. (3 marks)
8.
To calculate your weight in newtons you multiply your mass in _____________________ by the
__________________________________________________________. (6 marks)
9.
Whenever work is done on an object its total ___________________________ increases, and when
an object or system does work its ______________________________________. (6 marks)
10.
A spring is used to close some screen doors automatically. When a spring is stretched we say it
has potential energy due to __________________________________. (3 marks)
11.
In preparation for a dive, a diver stands motionless on the edge of the 10-m platform. If the
diver's mass is 65 kg, what is his gravitational potential energy relative to the surface of the water? (8
marks)
12.
What happens to the diver's gravitational potential energy on the way toward the surface of the
water? (4 marks)
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
Name___________________________________
8c
POST-TEST
13.
A diver, with a mass of 60.0 kg, has 2.94 kJ of gravitational potential energy on top of the 5-m
platform. How much work did the diver do an her body to get up to the 5.00 m level? (3 marks)
Calculate her speed just before she enters the water. (Ignore air resistance.) (8 marks)
14.
Prior to serving, a tennis player tosses the ball vertically up. If the ball leaves the player's hand
with a speed of 5.50 m/s, calculate the maximum height above the player's hand the ball will reach
before coming back down. (Ignore air resistance.) (8 marks)
15.
The ratio change in distance to change in time defines __________________________. (3 marks)
16.
Drawing the best-fit line for data plotted on a graph averages ________________________. (3
marks)
17.
The ratio of the change in the vertical variable, the rise, to the change in the horizontal variable,
the run, of a graph is equal to the _______________________________________. (3 marks)
© 1997 Alberta Education
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084
8d
Name___________________________________
POST-TEST
18.
Use the following data to plot a distance versus time graph on the grid provided. Calculate the
speed of the object. (8 marks)
Time (s)
0
5
10
15
20
25
© 1997 Alberta Education
Distance (m)
0
20
40
60
80
100
Distributed by AGC/United Learning
AGC/United Learning • 1560 Sherman Ave., Suite 100 • Evanston, IL 60201 • 800-323-9084