FOR HIGH SCHOOL TEACHERS
TABLE OF CONTENTS
TABLE OF CONTENTS
MAP
THE EXHIBITS
RELATED NATIONAL SCIENCE AND MATH STANDARDS
CURRICULUM CONNECTIONS
GENERAL PROBLEM SOLVING
HEALTH / PHYSIOLOGY
PERSONAL HEALTH
MATHEMATICS
COORDINATE SYSTEMS: PITCH, ROLL AND YAW
GEOMETRY: ELLIPSES
PHYSICAL SCIENCE
ENERGY: POTENTIAL AND KINETIC
MOMENTUM CONSERVATION
TRAJECTORY
EXHIBITS BY SPORT / ACTIVITY
1
2
3
6
7
8
10
10
11
11
13
16
16
24
27
29
Elaine Catz
Education Division
Carnegie Science Center
© 2002, 2003 Carnegie Science Center. Educators and educational institutions may reproduce portions of
this document for nonprofit purposes, with proper attribution to Carnegie Science Center. No portion of the
document may be used for any commercial applications without express permission from Carnegie Science
Center. Please direct inquiries to Education Division, Carnegie Science Center, One Allegheny Avenue,
Pittsburgh, PA 15212.
The Carnegie Science Center Education Division welcomes
YOU to UPMC SportsWorks at Carnegie Science Center!!!
UPMC SportsWorks at Carnegie Science Center is located across the street from
our main building. Open since August 2001, UPMC SportsWorks features over
40 exhibits offering 70+ interactive experiences designed to test your skills in
virtual games and sporting events.
We believe that all educators can use our exhibits to further enhance their
students’ understanding of concepts studied in the classroom. We hope that the
information and activities included in this brochure will help you to do just that.
Please note:
1) Some exhibits have height requirements. See the exhibit descriptions on the
following pages.
2) While the Carnegie Science Center staff make every effort to keep all of the
exhibits in working order, exhibits are occasionally removed from the
building for maintenance. If you are especially interested in studying a
specific exhibit, please call ahead to verify that it will be fully functional.
MAP
UPMC SportsWorks at Carnegie Science Center
is made possible through the generous support of
UPMC Health System.
THE EXHIBITS
Note: (#s) refer to UPMC SportsWorks Map on previous page.
BALANCE BEAM (#9) A balance beam and a mirror allow you to test your balance and agility.
The BIG Idea: For an object to remain stabile and upright, its center of mass must be located
above its supporting base.
BASEBALL (#13) Test your speed and accuracy in a major league-sized pitching cage.
Exhibits containing baseball equipment and information regarding pitching, grips, batting and
reaction time surround the pitching cage.
The BIG Idea: Baseball players make use of aerodynamics, leverage and physical conditioning
every time they throw or hit a ball.
BE THE JUDGE (#16) Watch an Olympic event play, then ‘make the call.’
The BIG Idea: A person judging a sport needs to pay attention to detail, to observe carefully and
maintain concentration, and must have in-depth knowledge regarding the activity.
BOUNCE (#5) Get fastened into a bungee harness, then bounce up to 20 feet on a trampoline.
The BIG Idea: When a bungee cord is stretched, it gains potential energy. This energy can then
be converted into kinetic energy.
BROADCAST TRUCK (#11) Give directing a try, and switch back and forth from live images
around the exhibit.
The BIG Idea: In order to broadcast a sporting event, the broadcast team must pay attention to
detail, observe carefully, maintain concentration, and must be able to communicate effectively.
CLIMBING WALL (#1) Get strapped into a climbing harness and try a 25-foot vertical climb,
or try an equipment-free horizontal climb.
The BIG Idea: In order to safely climb a rock wall, a climber must be a good problem solver, be
properly trained to use specialized gear, and be in good physical condition.
DESIGN A COASTER (#3) You program the coaster, then enter a 2-seat, full-motion ride
simulator with 360-degree motion! Or ride Kennywood’s legendary “Steel Phantom.”
The BIG Idea: The human brain may interpret sensory input incorrectly.
HEIGHT REQUIREMENT: In order to ride the virtual coaster, the visitor must be at least 48” tall.
DRUGS IN SPORTS (#32) Learn how drugs allow injured athletes to recover faster.
The BIG Idea: Maintaining balanced diets and staying away from “performance-enhancing”
drugs keeps athletes healthy.
ENERGY RACE (#34) Pedal your bike, generating the energy to power your car around a
miniature racetrack.
The BIG Idea: Energy can be converted from one form to another.
FOOTWORK (#30) Observe your gait from a unique, ground level rear angle.
The BIG Idea: Walking is good exercise. Each person’s gait is unique.
FORE! (#15) Take a swing from our tee and see where on the ‘virtual’ green you would land.
The BIG Idea: The trajectory of a moving object can be calculated based on its initial conditions.
HANG GLIDING (#36) Coordinate your movement with the image of the Grand Canyon as you
pilot your craft.
The BIG Idea: The position of an object in space can be determined by controlling its pitch, roll
and yaw.
HANG TIME (#23) Do a chin-up as the length of your endurance is counted.
The BIG Idea: Strength and endurance are not the same.
3
THE EXHIBITS
HIGH CYCLE (#6) Pedal a unicycle on a one-inch steel beam 15 feet overhead, kept upright by a
counterweight.
The BIG Idea: If the center of mass of an object is located below its base of support, the object
cannot tip over.
HOCKEY (#10) This oversized hockey table allows 12 visitors to play together. GOAL!
The BIG Idea: In order to be successful, teammates must be able to accurately communicate and
work together.
HOOPS VISION (#27) Three mini-basketball hoops have goggles that distort your vision. Can
your brain compensate?
The BIG Idea: The human brain has the ability to compensate and readjust to new circumstances.
IMPACT! (#26) Leap onto a sensor pad while a computer shows the impact pattern of your jump.
The BIG Idea: Bones bear weight and distribute stress over a framework of supports.
INJURIES (#31) Be a sports medicine surgeon!
The BIG Idea: Many injuries in sports can be prevented when athletes are well conditioned, learn
proper techniques and use safety equipment correctly. For those who do become injured, newer,
less-invasive surgical techniques may help correct problems while requiring shorter recovery
times than ever before.
MINI-GOLF MATH (#41)
ELLIPSE GREEN Putt the ball in any direction and in most cases, you get a hole in one.
The BIG Idea: The sum of the distances from the edge of an ellipse to each of its focal points is
a constant.
GEAR RATIO / PROBABILITY GREEN Putting through gear powered doors takes your
ball to the top of a ‘bell curve’ demonstration.
The BIG Ideas: Gears are simple machines that can transmit motion and force. A Bell Curve
often arises as the result of a series of many independent random events.
GRAVITY WELL GREEN The ball enters a gravity well to the center hole, then comes out a
tube on the lower green.
The BIG Idea: An object maintains an elliptical orbit when it balances the gravitational pull
arising from another object with its own momentum.
OPTICAL ILLUSION GREEN A seemingly straight putt misses the mark.
The BIG Idea: The human brain may interpret sensory input incorrectly.
OLYMPIC SPRINT (#17) Step into a 40-foot, 4-lane Olympic track to race against a world class
‘virtual sprinter.’
The BIG Idea: Running is an excellent way to achieve and maintain fitness.
ORBITRON (#2) You are strapped into the center of a gyroscope-like contraption, where you
control your spin on three axes.
The BIG Idea: The position of an object in space can be determined by controlling its roll, pitch
and yaw.
HEIGHT REQUIREMENT: In order to ride the Orbitron, the visitor must be at least 48” tall.
PARACHUTE DROP (#19) Engineer your own parachute, then drop it from 20 feet to test your
design.
The BIG Idea: Air resistance slows a parachute and results in drift.
REACTION TIME (#22) Two different exhibits test your ‘reaction time.’
4
THE EXHIBITS
The BIG Idea: Signals cannot travel from the brain to other body parts instantaneously.
ROTATION (#21) Step on the disk and spin. Lean in or out to control the speed, like an Olympic
skater.
The BIG Idea: The rate at which a spinning object rotates about an axis depends not only on its
mass, but also on the distribution of that mass. Angular momentum is conserved.
SIMULATOR XTREME (#40) This full motion simulator sends you down ski slopes, around a
racetrack, and more.
The BIG Idea: The human brain may interpret sensory input incorrectly.
SKATEBOARDING (#25) Balance on a skateboard while an LED display counts every second.
The BIG Idea: Lowering the center of mass of an object helps it to become more stabile.
SNOW SPORTS (#8) A collection of sports equipment and exhibitry depicts ways that athletes
attempt to reduce air drag while competing.
The BIG Ideas: The human brain may interpret sensory input incorrectly (Bobsled simulator).
Skiers, ski jumpers, lugers and speed skaters use physical technique, bodysuits and equipment to
minimize air drag while competing in their sports. Gravitational potential energy is position
dependent (Sledding).
SNOWBOARDING (#35) Try your skills at snowboarding down a ‘virtual’ mountain.
The BIG Idea: Lowering the center of mass of an object helps it to become more stabile.
SPORTS GEAR (#28) This exhibit is a collection of equipment used in numerous sports.
The BIG Idea: Advances in materials and design have greatly improved the performance of
athletes in many sports including cycling, golf, hockey and tennis.
SPORTS GEAR (#29) This exhibit is a collection of equipment and protective safety devices
used in numerous sports.
The BIG Idea: Advances in materials and in the design of uniforms and equipment have helped to
better protect athletes in many sports.
TARGET (#14) Test your skill as you shoot hockey pucks at a ‘virtual goalie’ or play quarterback
in a live pro football game.
The BIG Idea: The trajectory of a moving object can be calculated based on its initial conditions.
TRAJECTORY (#18) Change the tilt and change the arc pattern of a pinball’s path.
The BIG Idea: The trajectory of a moving object depends on its initial conditions.
TRICK SHOT (#20) Line your pool cue up and make a perfectly executed trick shot!
The BIG Idea: The angle of incidence equals the angle of reflection.
VERTICAL JUMP (#24) Touch the highest button while standing, then jump and touch the
highest button to hear your vertical jump distance.
The BIG Idea: When you bend your knees, you gain potential energy. When you jump, this
energy is converted into kinetic energy.
VIRTUAL SPORTS (#37) Block a variety of ‘virtual’ soccer balls as they come in, or pick up
and shoot a ‘virtual’ basketball.
The BIG Idea: The trajectory of a moving object can be calculated based on its initial conditions.
VOLLEYBALL (#38) Your group competes in a 5-point ‘virtual’ volleyball match.
The BIG Idea: The trajectory of a moving object can be calculated based on its initial conditions.
5
THE EXHIBITS
WHEELCHAIR RACE (#12) You and another visitor race each other around a one-mile track,
shown on an LED panel.
The BIG Idea: Spinal cord injuries may result in impaired movement of the body. Athletes in
wheelchairs are as competitive, strong and well trained as able-bodied athletes.
WOMEN IN SPORTS (#33) Follow the experiences of a record-breaking female Olympic high
jumper.
The BIG Idea: Women’s athletic opportunities have greatly increased over the past century.
RELATED NATIONAL SCIENCE AND MATH
STANDARDS
National Science Content Standards
Grades 9-12
Baseball
Bounce
Drugs in Sports
Energy Race
Fore!
Injuries
Mini Golf Math: Ellipse
Green
Mini Golf Math: Gravity
Well Green
Orbitron
Parachute Drop
Snow Sports
Trajectory
Vertical Jump
Volleyball
Wheelchair Race
Women in Sports
F: Science in Personal and
Social Perspectives
Personal and community
health
B: Physical Science
Motions and
forces
Conservation of
energy
x
x
x
Principles and Standards for
School Mathematics
NM.9-12.8
NM.9-12.7 Geometry – An
Geometry
Algebraic
Perspective
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
6
CURRICULUM CONNECTIONS
TOPIC
GENERAL PROBLEM SOLVING
HEALTH / PHYSIOLOGY
•
Personal Health (Exercise,
Nutrition, Risks)
•
Physiology (Structure and
Function)
•
Perception and Illusion
MATHEMATICS
•
Coordinates: Pitch, roll and yaw
Geometry: Ellipses
PHYSICAL SCIENCE
•
Angular Momentum
•
Center of Mass
•
•
Drag Forces
•
Energy: Potential and Kinetic
•
•
Gears
Material Properties
Momentum Conservation
Trajectory
•
•
RELATED EXHIBITS
Be the Judge
Broadcast Truck
Climbing Wall
Hockey
Drugs in Sports
Hang Time
Impact!
Injuries
Olympic Sprint
Women in Sports
Footwork
Impact!
Reaction Time
Wheelchair Race
Design a Coaster
Hoops Vision
Mini-Golf Math: Optical Illusion Green
Simulator Xtreme
Snow Sports (Bobsled simulator)
Hang Gliding
Orbitron
Trajectory
Mini-Golf Math: Ellipse Green
Rotation
Balance Beam
High Cycle
Orbitron
Skateboarding
Snowboarding
Baseball
Parachute Drop
Snow Sports
Bounce
Vertical Jump
Mini-Golf Math: Gear Ratio /Probability Green
Sports Gear
Trick Shot
Fore!
Target
Trajectory
Virtual Sports
Volleyball
7
GENERAL PROBLEM SOLVING
Topic Focus:
•
Problem solving is a skill that encompasses the following abilities: to ask
relevant questions, to observe, to strategize, to make decisions based on
available information and to effectively communicate.
Background Information:
According to the National Science Education Standards, students need to develop
abilities and understanding of all aspects of the inquiry process.
From Kindergarten on, students should develop questioning, observation, problem
solving and communication skills. In order to develop these abilities, students
need opportunities to practice applying these skills in everyday life.
Try these at school:
Observation / Communication Practice: Change your Appearance
Objective: Students will discover how observant they really are.
Materials: watch or clock
Procedure:
• Have all of the students stand up.
• Pair each student with a partner.
• Ask the students to carefully observe their partners for one minute (do not give the
students any other instructions or hints as to what comes next).
• Have the partners turn back-to-back.
• Give the students one minute to make three (or more) changes in their appearance
(e.g. move watch to opposite arm, tuck or untuck shirt, remove jewelry, untie a
shoelace, etc.).
• Have the partners face each other.
• Give the students thirty seconds to identify the changes that their partners have made.
Questions:
How observant were the students? What changes were the most obvious? What
changes were the least obvious? How many students thought to add something to their
appearance (e.g. pick up an object)? Was it easier to identify something that was moved
or something that was missing?
Observation / Communication Practice: What do you hear?
Objective: Students will learn that listening is another way to “observe.”
Materials: pencils, paper, watch or clock
Procedure:
• If possible, take the students outside or open the classroom windows.
• Have the students take a piece of paper and a pencil and find a space to sit down as
far apart from one another as possible.
• Give the students five minutes to write down a list of all of the sounds that they can
hear. During this time, they are not allowed to speak.
Questions:
What kinds of sounds did the students hear? How many of these sounds have they
really noticed before? Did they learn anything from the sounds that they heard? What
sounds could give them clues about their location? (e.g. Could they tell that they were
near an airport, railroad track, or construction site? If they were able to identify birdcalls,
what might this tell them about their geographic location?) Why is being able to listen
carefully an important “observation” skill?
8
GENERAL PROBLEM SOLVING
Problem Solving Practice: Build a Paper Tower
Objective: Students attempt to build the tallest freestanding structure possible with the
materials provided.
Materials: paper (8.5” x 11”), cellophane tape, watch or clock, yard or meter-stick/
measuring tape
Procedure:
• Divide the class up into teams of four students each.
• Give each team ONE sheet of 8.5” x 11” paper and ONE piece of tape that is 25 cm
long.
• The paper may be torn, rolled or folded, but only one piece will be given to each team.
• The students have 20 minutes to create a freestanding tower using their materials.
• The tower is freestanding if it remains self-supporting for at least 10 seconds.
• Height is measured from the floor to the highest point on the tower above the floor.
• Once 20 minutes have passed, the students may no longer have any physical contact
with the towers.
• Measure and record the height of each tower.
Questions:
Did the teams discuss the problem before beginning or did they jump right in? What
were the best strategies employed by the students? What roles did communication and
teamwork play in this activity? If the students could try this activity again, what would
they do differently?
Visit Suggestions:
•
•
•
•
•
Pay close attention to details and develop your observation skills at the BE THE
JUDGE exhibit (#16).
Hone your concentration, observation and decision-making skills, as you scan the
UPMC SportsWorks for the most interesting action in the BROADCAST TRUCK
exhibit (#11).
Climbing and conquering a rock wall requires strategic planning and good decisionmaking skills. Test your skills at the CLIMBING WALL (#1).
Teamwork is just as important in science as it is in sports. The ability to accurately
communicate can make or break a team. Work together to win as you play a game of
HOCKEY (#10).
Observe people at the HOCKEY exhibit (#10). What kinds of strategies are the
teams using? Are the players working together? Are they communicating effectively?
Sources:
“National Science Education Standards.” [4th printing]. Washington D.C.: National Academy
Press. 1996 National Academy of Sciences.
http://books.nap.edu/html/nses/html/index.html
9
PERSONAL HEALTH
HEALTH / PHYSIOLOGY
Topic Focus:
•
Each person must take some responsibility for his / her own health and safety.
It is important to understand the benefits of exercising regularly and eating
properly and the negative effects of abusing substances and engaging in risky
behavior.
Background Information:
The National Science Education Standards include Section F: Science in Personal
and Social Perspectives for all grades K-12. Each grade range includes a
subdivision of this standard entitled “Personal Health.” Personal Health topics
that are addressed by UPMC SportsWorks activities are listed below:
•
•
•
•
•
Injury and accident reduction
Disease transmission
Personal health practices
Risks and benefits of using chemical substances
Nutritional balance
Visit Suggestions:
•
•
•
•
•
•
•
•
Stretch as you follow the warm up instructions before trying out the activities at these
exhibits: BOUNCE (#5), BASEBALL (#13) and OLYMPIC SPRINT (#17).
At the DRUGS IN SPORTS exhibit (#32) learn how to improve your athletic
performance with good nutritional practices rather than via supplements or steroids.
Take a hike on the FOOTWORK exhibit (#30) treadmill and learn about the
exercise benefits that can be derived from walking.
Learn about muscle strength and endurance as you hold yourself up at the HANG
TIME exhibit (#23). How long can you hang out?
Jump off the platform at the IMPACT! exhibit (#26) and land as softly as you can.
When playing games that require a lot of jumping, what can you do to minimize stress
on your joints?
At the INJURIES exhibit (#31) learn about common sports injuries and what you
can do to lessen the likelihood that you’ll suffer one.
Calculate your resting heart rate and compare it with your pulse after you race
against Jackie Joyner Kersee at the OLYMPIC SPRINT (#17). Read about how
running helps to strengthen your heart.
At the WOMEN IN SPORTS exhibit (#33) read about the importance of proper
nutrition for women athletes, and about injuries more likely to affect women than men.
Sources:
“National Science Education Standards.” [4th printing]. Washington D.C.: National Academy
Press. 1996 National Academy of Sciences. http://books.nap.edu/html/nses/html/index.html
Topic Focus:
•
The orientation of an object in space can be determined by controlling its
pitch, roll and yaw.
10
COORDINATE SYSTEMS
MATH
Background Information:
The location of any object can be defined by its coordinates with respect to three
principal axes x, y and z. These axes are mutually perpendicular (at right angles
to each other). The orientation of the object can
z
be defined by its angles of rotation with respect
yaw
to the three principal axes.
•
•
•
The object’s roll is defined to be its rotation
φ, about the x-axis.
The object’s pitch is defined to be its
rotation θ, about the y-axis.
The object’s yaw is defined to be its rotation
ϕ, about the z-axis.
roll
pitch
x
Try this at school:
THE ROLL, PITCH AND YAW GAME
(Source: http://www.sln.org/pieces/cych/apollo%2010/students/activities/offline/roll.html)
Note: to view animated instructions, see the web site listed above.
This activity is only for brave teachers! But if you can carry it off - it's great fun. It's also
useful for lessons on flight!
Stand in front of the class with your arms out
like an aeroplane.
Explain that you are going to show the children
how to "Roll, Pitch and Yaw"!
Get the whole class to mirror you - first you are
going to teach them how to PITCH.
Put your head down to your knees without
bending them, still keeping your arms out like an
aeroplane...
Tell them Pitch is easy to remember because of being "pitched forwards" or "pitchfork"
etc...
Do the same in the opposite direction.
Next, show them how to ROLL.
To ROLL just lower your right hand down to your thigh following it with your head and
lifting your (straight) left arm in the air.
Lastly - you've guessed it, you are going to
show them how to YAW!
11
y
COORDINATE SYSTEMS
MATH
To YAW - keep your hands out and turn you whole upper
body from the waist.
Once you have practiced all three a couple of times –
get them to do it.
The position you are in is called "attitude" – if someone gets it
wrong - you could tell them they've got a bad "attitude.”
This page uses Flash 5 – please download the current player.
Visit Suggestions:
•
Control your own roll, pitch and yaw, as you spin about all three axes at the
ORBITRON exhibit (#2).
•
•
For a less dizzying experience, experiment with the effects of changing pitch and roll
at the TRAJECTORY table (#18). How does tilting the table affect the path of the
pinball?
Try varying your roll, pitch and yaw as you steer your craft at the HANG GLIDING
simulator (#36).
Sources:
Doser, Andrew, et al. Exploring Aeronautics. CD-ROM. National Aeronautics and Space
Administration, 1998 (NASA EC-1998-03-002-ARC).
Friedland, Bernard. Control System Design. NY, NY: McGraw-Hill, Inc., 1986.
Hewitt, Paul G. Conceptual Physics, A High School Physics Program. Menlo Park, CA: Addison
Wesley Publishing Co., Inc., 1987.
12
GEOMETRY: ELLIPSES
MATH
Topic Focus:
•
The sum of the distances from the edge of an ellipse to each of its focal points
is a constant.
Y
Background Information:
An ellipse is a conic section containing 2 focal
points, F1 and F2.
•
r1 is the distance from the
F1
edge of the ellipse at point
(-a, 0)
(-c, 0)
(x,y) to its focal point F1.
•
r2 is the distance from the edge of the
ellipse at the same point (x,y) to its focal point
F2.
(0,b)
(x,y)
r1
r2
F2
(0,0)
(c, 0)
(0, -b)
An ellipse is defined such that the sum of r1 and r2 is always
a constant: r1 + r2 = 2a.
The defining equation of an ellipse in Cartesian Coordinates can be derived from
the information above:
(x,y)
r1
(x, 0)
(-c, 0)
The distance r1 is calculated using the Pythagorean
Theorem*
r12 = (x-(-c))2 + y2
So, r1 = ((x+c)2 + y2)1/2
* Note: Pythagorean Theorem: The square of the hypotenuse of a right triangle is equal to the
sum of the square of the legs.
A
c
a
B
ABC is a right triangle with sides of length a and b and a hypotenuse of
length c.
C
b
Similarly, the distance r2 is calculated using the Pythagorean
Theorem:
(x,y)
r2
(x, 0)
c2 = a2 + b2
r22 = (c-x)2 + y2
So, r2 = ((x-c)2 + y2)1/2
(c, 0)
Since, r1 + r2 = 2a, we can substitute in the equations above to
get: ((x+c)2 + y2)1/2 + ((x-c)2 + y2)1/2 = 2a
or ((x-c)2 + y2)1/2 = 2a - ((x+c)2 + y2)1/2
13
(a, 0)
x
GEOMETRY: ELLIPSES
Squaring both sides we get:
MATH
(x-c)2 + y2 = 4a2 – 2a((x+c)2 + y2)1/2 + (x+c)2 + y2
By subtracting y2 from both sides and expanding the squares this becomes:
x2 – 2cx + c2 = 4a2 + x2 + 2cx + c2 – 4a((x+c)2 + y2)1/2
Subtracting x2 + c2 from both sides of the equation and rearranging we have:
4a2 + 4cx = 4a((x+c)2 + y2)1/2
We then divide by 4 and square both sides: a4 + 2a2cx + c2x2 = a2(x+c)2 + y2
Expanding the terms and rearranging we have: a2(a2 - c2) = (a2- c2)x2 + a2y2
2
2
2
and finally, dividing through by a (a - c ) we are left with:
x2
y2
+
=1
a2 a2-c2
Try this at school:
Draw an ellipse
http://chickscope.beckman.uiuc.edu/explore/eggmath/shape/ellipse_eq.html
(Adapted from “Explore: EggMath: The Shape of an Egg.” Chickscope 1.5. (12/27/2001))
Description: Students will use a pin and string construction to create an ellipse.
Materials
• Paper
• Straight pins
• String
• Cardboard
• Pencil
Procedure
• Place a piece of paper on top of the cardboard.
• Stick two straight pins into the paper / cardboard so that they are perpendicular to the
paper.
• Tie the string into a loop.
• Place the string loop over the two pins.
• Have someone hold the pins so that they don’t move.
• Use the pencil point to pull the string horizontally across the paper until it is tight.
• Pulling the pencil around the pins and keeping the string tight, trace out an ellipse on
the paper.
Conclusions
Notice that at all times, the loop of string is pulled into the shape of a triangle, with the
two pins and the pencil at the three corners. The sum of the lengths of the sides of the
triangle is equal to the total length of the string.
The length of string between the two pins is always the same. This means that the sum
of the length of string between the pencil and the first pin and the length of string between
the pencil and the second pin must also be constant.
In other words, the sum of the distances from the edge of the ellipse to each of its focal
points is a constant.
14
GEOMETRY: ELLIPSES
MATH
Visit Suggestions:
•
•
Starting at the focus tee at the MINI-GOLF MATH: ELLIPSE GREEN (#41),
ricochet a golf ball off the perimeter of the ellipse. Watch the path that the ball traces
as it moves toward the second focus. Did you get a hole-in-one? Why (Why not)?
What are the differences between theory and reality? What additional variables are
there in the real world?
For more information, check out the central Mini-Golf kiosk and trace an ellipse using
a piece of chain. What is the connection between the path of the ball on the green and
the shape of the chain as you trace?
Sources:
Banks, John. “Ellipse Game.” (12/27/2001).
http://johnbanks_maths.latrobe.edu.au/Games/Ellipse/
“Explore: EggMath: The Shape of an Egg.” Chickscope 1.5. (12/27/2001).
http://chickscope.beckman.uiuc.edu/explore/eggmath/shape/ellipse_eq.html
“Conic Sections – Math Tables, Facts and Formulas.” Hoxie High School Mathematics
Department. (12/28/2001).
http://www.hoxie.org/math/algebra/conics.htm
“Solving Linear Systems of Equations: Conic Sections. Ellipse: Definition and Equations.”
(12/28/2001).
http://www.frcc.cccoes.edu/~aland/col_alg/col_alg_files/ellipse_def.pps
15
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
Topic Focus:
•
Potential energy is the energy that is stored in an object by virtue of its
position.
•
Kinetic energy is energy of motion.
•
The potential and kinetic energy of an object (in an ideal mechanical system)
are proportional: when one increases the other decreases.
Background Information:
Energy is the ability to do work. Energy is always conserved. This means that it
may change from one form to another, but the total energy of a closed system is
always the same.
There are two different basic forms of mechanical energy: kinetic and potential.
•
Kinetic energy, KE, is the energy of motion. KE = ½ mv2 where m is the
mass of the object and v is the object’s velocity.
•
Potential energy, PE, is the energy stored in an object by virtue of its position.
An object with potential energy is in its current state because work has already
been applied to it. This energy may be changed into kinetic energy.
Gravitational potential energy, PEg, is the potential energy stored in an object
because it is at some height above the earth’s surface. PEg = mgh where m is the
mass of the object, g is the acceleration of gravity, and h is the height of the
object above the earth’s surface. Note that mg is equal to the weight of the object.
Elastic Potential Energy is the energy that is stored in a
compressed spring. This potential energy, PEs = ½ kx2
where k is the spring force constant and x is the distance
that the spring has been compressed.
Hooke’s Law says that if a spring attached to an object is
compressed or stretched a small amount, the force of the
spring Fs, acting on the object will be Fs = -kx
where x is the distance that the spring has been compressed
or stretched, and k is the force constant of the spring. The
spring’s force constant, k, can be determined
experimentally.
x=0
x
To do so, the spring is suspended vertically, as shown.Æ
The spring is in equilibrium, neither stretched nor
compressed.
x=0
x=d
An object of mass m is hung from the spring, causing
the spring to stretch a distance d, from its equilibrium
position.
16
M
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
The only force acting downward on the spring is the weight of the object,
W = mg.
When the object is at rest, the spring force, Fs, balances the weight, so while they
may be acting in opposite directions, they are equal in magnitude.
W = -Fs
Fs = kd
Because the mass m of the object and the distance d that it has
displaced the spring are known numbers, k can be calculated:
k = mg / d
W = mg
Try these at school:
Gravitational Potential Energy: Teacher’s toybox
http://www.nsta.org/main/news/stories/science_scope.php?category_ID=87&news_story_ID=45779
(Source: Herald, Christine. “Toys that Teach.” Science Scope. October 2001, p. 30.)
Toys are a great way to teach physical science—the simpler, the better. I have used
everything from rubber balls to wind-up toys to teach students about potential and kinetic
energy, speed and acceleration, and many other concepts. Rubber band-powered
airplanes and simple machines made from plastic building blocks are also student
favorites. I like to use toys because they engage students and provide a hands-on
experience that stays with them a lot longer than simple paper-and-pencil exercises.
The following are a few of my favorite activities that I use with my eighth grade students
as part of an intensive year-long physical science unit.
As a culminating activity in the motions unit, a guest speaker from Kansas State
University’s biomechanics laboratory stops by with a radar gun. The speaker reviews the
concept of speed, and then we take the class to the gym and let students see how fast
they can throw baseballs or softballs.
If you want to add some fun to your physics unit, consider adding toys to your equipment
list. With a little imagination, you can teach just about any physics concept with a toy,
and your students (literally) will have a ball.
Bouncing balls
Purpose: To determine which ball will bounce the highest
Hypothesis
Which ball will bounce the highest? Write your hypothesis as an “If, then” statement
Materials
• meter stick
• tennis ball, ping-pong ball, sponge ball, kickball, and racquetball
Procedure
1. Decide who in your group of four will act as the measurer, dropper, spotter, and
recorder.
2. Complete the following paragraph before beginning the activity:
When an object such as a ball falls, it accelerates and acquires energy of motion or
______________. If it does not reach terminal velocity, it acquires its maximum velocity
17
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
and therefore its maximum kinetic energy just as it hits the ground. At that point, its
motion is stopped and it is compressed. The kinetic energy is momentarily converted to
stored energy or ______________, which is then converted back to kinetic energy as the
ball bounces back. No ball will return to the exact height from which it was dropped
because some of the kinetic energy is converted to other forms of energy, such as heat,
when the ball strikes the ground. According to an important principle known as
the______________________, however, the total amount of energy does not change.
In this investigation, you will describe the motion of a bouncing ball and examine how the
ball demonstrates the law of conservation of energy. By plotting graphs, you will also
examine how well different substances retain their original energy. What are some
variables that would affect the height of the bounce?
1. Have the measurer hold the meter stick upright with the zero mark on the floor.
2. Have the dropper release the tennis ball from the top of the meter stick (100-cm mark).
Make sure the ball does not touch the stick on the way down.
3. Have the spotter note the height of the first bounce and call it out.
4. The recorder should note the height of the bounce in a data table.
5. The spotter should continue to call out the height of each consecutive bounce until the
heights become too difficult to judge accurately.
6. Repeat steps 1 through 5 with the ping-pong ball, the sponge ball, the kickball, and the
racquetball.
7. Graph your data and draw a curved line that best fits the data points for each ball.
Questions
1. Which ball retained the greatest percentage of its kinetic energy on each bounce?
2. Explain the shape of each line on the graph. Why are they similar?
3. What type of ball seems to bounce the least? Why?
4. What is the independent variable? What is the dependent variable?
5. Why didn’t any ball bounce higher than the height from which it was dropped?
6. How would the results be different if you carried out this experiment on a carpet?
7. Explain the conversion of energy when the ball is dropped.
8. What would happen to the kinetic energy if a ping-pong ball collided with a sponge
ball?
Extra credit: Determine the kinetic energy for each ball using the formula
KE = mass(speed)2
Christine Herald teaches physical science at Eisenhower Middle School in Manhattan, Kansas.
18
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
Energy Conversion: Conversion Contraption
(Source: Chahrour, Janet. “Conversion Contraption.” Science Scope September 2000. pp. 26-29.)
http://www.nsta.org/main/news/pdf/ss0009_26.pdf
A candle flame burns through a string holding up a gate. The gate, pulled down by
stretched rubber bands, releases a dozen marbles. The marbles roll down a ramp and
bump into a snake-like series of dominoes that each fall in turn with the last one closing a
circuit to light a bulb and trigger a buzzer. Wow! The audience of visiting kindergartners
is amazed. “Do it again!” they call out. It’s show time for eighth grade physical science
students after a week of designing, building and refining Conversion Contraptions. The
contraptions are fun combinations of moving parts that use many forms of energy and
many conversions of energy. It’s the culminating project for a unit on energy and energy
conversions. As preparation for this project, students do labs during a unit that applies
their knowledge of energy to toys. For example, in caps (from cap guns), chemical
potential energy of the caps is converted into heat, light, and sound when triggered by the
mechanical kinetic energy of the hammer. In a wind-up car, mechanical energy of the
person is converted into elastic potential energy of the wind-up mechanism, which in turn
is converted into the mechanical energy of the car. Students also analyze a top, slinky, a
light ball that plays music when the circuit is completed, and any other toys I have that
demonstrate energy conversions.
Getting started
At the outset of this project, the students and I read through the instruction sheet
together. Teams of three to four students then form to discuss the project.
“What do we have to do?” someone calls out to me.
“Check the instructions.” I answer.
“Do we have to use potential energy?” asks another.
“Check the instructions.”
“Does it have to work?” inquires a third student.
“Check the instructions.”
“This is way too hard!” complains a fourth.
“You can do it!”
Soon the groups are generating ideas—once the ideas start flowing the creative pace
accelerates. Some students have wild ideas that others dismiss but I encourage the
groups not to rule out possibilities too quickly. If they don’t know how to accomplish a
certain idea, they may ask me for suggestions. If they have an idea that has safety
issues I try to figure out a way to make it acceptable.
Contraption construction
I provide each group with a sheet of standard-size
(50 cm x 75 cm) foam core poster board
(preferably used, but available at office supply and art and craft stores).
I also supply scissors, tape, glue, wires, light bulbs and miscellaneous junk, but students
bring in most of their materials from home. They raid their child-hood toy boxes to locate
balls, marbles, cars, and game parts along with paper towel tubes, batteries, mousetraps
(safety alert!), blocks of wood, and so on. To give students ideas of what to bring in we
have a class brainstorming session. What can have elastic potential energy? What has
chemical potential energy? How about gravitational potential energy? In what interesting
ways can moving objects make other objects move?
All construction is done in the classroom, which has advantages and disadvantages. The
disadvantage is space—finding room for all the projects for four or five classes is a
19
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
challenge! But what is a teacher if not innovative? The advantage of having the work
done at school is the playing field is level. No overly eager parents are building these
projects. Students may consult anyone, but I am the on-site consultant for all. The
students have great ideas that I help steer toward practical implementation.
I approve teams’ designs and supervise the building of the contraptions so if something
unsafe is in the works I can intervene. For example, I have approved some projects that
use fire if the available fuel was small, all nearby parts were covered with foil, and the
burning part was stationary. I have nixed designs that included less predictable fire
dangers such as firecrackers and require students to wear goggles if any projectiles are
being used. While the students work together on the physical contraption, each student
must diagram and analyze the group’s contraption. Figure 1 illustrates how the
contraption described in the opening of this article would be diagrammed and analyzed.
In the analysis, an arrow means “is converted into.” No arrow connects the dominoes to
the light or buzzer since the energy for those two events came from the batteries, not
from the movement of the dominoes.
The introduction and planning of this project takes about two days (of 40-minute class
periods). The actual building of the contraptions generally takes students four or five
classes. Those who finish early can work on their analysis and diagram in class. I allow
two class periods for students to show off their contraptions.
The benefits of building
What’s the value of this work? It’s motivating, it solidifies concept understanding, it
exercises problem-solving skills, and it addresses curriculum standards. Creativity and
practical sense, as well as analytical talent, are tapped and stirred. Some students who
score poorly on tests are wonderful at implementing ideas to demonstrate their
understanding of these physical science concepts. To help assess students’ work, I use
an evaluation form (see Figure 2). Assuming all the requirements are met, I use the
checkmarks at the bottom to formulate a grade (i.e., mostly “excellents” earn an A, mostly
“goods” earn a B, and so on). I point out the project’s strengths and weaknesses in the
Comments section and assign a numeric grade. Exceeding the requirements usually
adds to Level of Challenge. If requirements are not met, points are subtracted from the
grade. In a team where members shared work equally, each person receives the same
grade. If from the self-evaluations and my own observations, I can see that work was not
shared equally, I assign different grades.
20
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
FIGURE 2: Teacher Evaluation Form
Requirements
Meets base
requirements
Yes
No
Comments
Numeric Grade
Elastic potential
energy
Gravitational
potential energy
Chemical
potential energy
Mechanical
kinetic energy
Light
Sound
Electrical energy
Quality
Excellent
Good
Fair
Poor
Creativity / interest
Quality of construction (works reliably)
Level of challenge
Energy exposition
To add to the excitement of completing the project we invite elementary students, usually
kindergartners, to view the action of the final contraptions. The wide-eyed youngsters
gather around each project in turn for a demonstration. Comments like “Awesome!”
“Ooooh!” and “Cool!” are heard around the room as each contraption is set into action. I
take pictures to put on display later. After seeing all the projects in action, our visitors
return to their own classrooms brimming with enthusiasm for hands-on science. One
contraption ended with a baking soda packet falling into red vinegar for a quasi-volcanic
eruption. Another used a catapult to shoot a Lego figure through a hoop. Another was
set up as Santa’s workshop where falling weights triggered an electric train engine to
transport mini packages. When we complete this final stage, students take apart their
didn’t-think-we-could-do-it-but-we- did contraptions and I collect the foam core. My
students have expanded their experience and confidence in managing their physical
world. And the unclaimed junk provides me with more treasure to share with next year’s
students.
This activity meets the following National Science Education Standards
Physical Science Content Standard —Transfer of Energy
- energy takes many forms and can be converted from form to form
- circuits transfer electrical energy from heat, light, sound, and chemical changes
Science as Inquiry Standard
- develop descriptions, explanations, predictions, and models using evidence
- think critically and logically to make the relationships between evidence and
explanations
Janet Chahrour is a middle school science teacher at Cincinnati Country Day School in Cincinnati, Ohio and
author of Flash! Bang! Pop! Fizz! Exciting Science for Curious Minds (Barron’s).
21
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
INSTRUCTION SHEET
Conversion contraption
Enough with all this theory and analysis! Build already! Design and construct a
contraption using as many different forms of energy and as many energy conversions as
possible.
Minimum requirements
- The base of the contraption must be the size of a standard foam core board.
- Three forms of potential energy must be converted to kinetic energy.
- At least five different objects must pick up mechanical kinetic energy.
- Heat, sound, light and electrical energy must be included.
- Any form of energy may begin the process and new forms may be introduced along
the way.
- Once the action begins, the contraption should be designed to run to the finish without
assistance. (If needed, however, each group is allowed one “assist” along the way.)
Along with the actual contraption, each group member will turn in a diagram of the
sequence of events and an energy conversion analysis (Figure 2). The diagram shows
the parts of your contraption while the analysis shows the forms of energy involved.
These may be done on the computer or by hand. The diagram is best done as a linear
version of your contraption—it probably won’t look like the contraption itself. Finally, each
group member will complete a self and group evaluation form (below).
How to get started
- Write down each of the energy forms you want to show.
- For each energy form, brainstorm interesting, creative ways to bring that form about
and to connect it with another form in a series.
- What junk from around the house can you use? Collect stuff and bring it in. You can
use parts from toys and kits but originality is expected in how you use them.
- Sketch a step-by-step plan.
- Start building!
Self and group evaluation
1. What were the strengths of your contraption?
2. What were the weaknesses of your contraption?
3. List each member of your group and check the appropriate category.
yourself.
Name
Did clearly less than
his / her share
Did about his /
her share
Include
Did clearly more
than his / her share
4. Explain further how your group operated. Did you have a leader? Were some people
especially good at certain tasks? What were the strengths?
22
ENERGY: POTENTIAL AND KINETIC
PHYSICAL SCIENCE
Visit Suggestions:
•
•
•
Why can’t you ride a sled uphill? Find out at the SNOW SPORTS exhibit (#8).
Bungee cords have spring constants too. Investigate elastic potential energy at the
BOUNCE exhibit (#5). Would calculations using Hooke’s Law give you accurate
results (or would the stretch vary in a nonlinear way with force)?
Bent knees store energy. Convert your own potential into kinetic energy at the
VERTICAL JUMP exhibit (#24). How similar are knees and springs?
Sources:
Eby, Denise, and Robert B. Horton. Physical Science. New York: Macmillan Publishing
Company, 1986.
Hewitt, Paul G. Conceptual Physics, A High School Physics Program. Menlo Park, CA: Addison
Wesley Publishing Co., Inc., 1987.
Hewitt, Paul G. Conceptual Physics. 3rd ed. Boston: Little, Brown and Co., Inc., 1977.
Macaulay, David. The Way Things Work. Boston: Houghton Mifflin Co., 1988.
Serway, Raymond, A. Physics for Scientists and Engineers with Modern Physics. 2nd ed.
Philadelphia: Saunders College Publishing, 1986.
Worden, Gregory P., Byron G. Murphy and David Stevens. “Bungee Basics.” The Science
Teacher. October 1994, pp. 50- 53.
23
MOMENTUM CONSERVATION
PHYSICAL SCIENCE
Topic Focus:
•
In any collision, momentum is always conserved.
•
Some collisions are elastic and some are inelastic.
Background Information:
The linear momentum, p, of an object of mass m, moving at velocity v, is defined
to be p = mv
•
The momentum in a closed system is ALWAYS conserved. This means that
the total momentum before a collision between two objects is the same as the
total momentum after the collision. After the collision, each object does not
necessarily continue to move in its initial direction or with its initial velocity,
but the total momentum of the system is the same -- only redistributed.
There are several different types of collisions. In ALL of the following cases, the
initial momentum of object #1 added to that of the object #2 equals the final
momentum of the object #1 added to the final momentum of object #2.
mv#1 initial + mv#2 initial = mv#1 final + mv#2 final
•
An elastic collision is one in which the colliding objects’ total momentum
AND total kinetic energy are conserved.
T IME
2 objects of equal mass
collide head on
m2
m1
2 objects of equal mass,
1 object at rest
m1
m2
Elastic collision
Elastic collision
•
•
2 objects of equal mass,
both objects are moving in the same
direction at different velocities
m1
m2
Elastic collision
An inelastic collision is one in which the colliding objects’ total momentum is
conserved, but the total kinetic energy of the system is not. In this type of
collision, the kinetic energy of the colliding objects may be “lost” to the
creation of heat, object deformation or noise.
A perfectly inelastic collision is one in which the colliding objects stick
together at impact. This implies that the two objects have the same final
velocity.
2 objects of equal mass
collide head on
m2
m1
T IME
Perfectly inelastic
collision
2 objects of equal mass,
1 object at rest
m1
m2
Perfectly inelastic
collision
24
2 objects of equal mass,
both objects are moving in the same
direction at different velocities
m1
m2
Perfectly inelastic collision
MOMENTUM CONSERVATION
PHYSICAL SCIENCE
Try these at school:
3. The Pool Table Physics Lab Rap
Copyright 1996 Robert A. Morse
http://physics.dickinson.edu/PhysicsPages/Physics_Pholk_Songs/Pooltable
1. One day when I was chillin' in the physics laboratory,
The professor started tellin' a momentum story.
With two balls of equal mass, prof was telling us a fable
About how they collide on an ideal pool table.
Now the energy's conserved when you add up the sum
Of kinetic and potential, so you know that ain't so dumb.
Prof said you take the cue ball and hit it with the cue,
And smash it at the 8-ball just to see what they will do.
You don't use no english; you gotta hit it straight,
And watch it do a number on that ball number eight.
But how fast and which direction will the 8-ball go,
If it’s hit head-on by the cue ball, do ya know?
What speed does the 8-ball have rollin' on the slate,
Compared to the cue ball in its pre-collision state?
Chorus: In this pool game no energy is lost.
The kinetic gets passed when the balls' paths cross .
2. The principle here is that momentum stays the same
As the cue ball had when it entered the game.
If the 8-ball goes right when it's hit real deft,
The cue ball's gotta move off to the left.
If the cue ball and the 8-ball roll at just the same speed,
What's the angle between `em? What indeed?
And after this collision where does each ball head
(In a frictionless world, just like the prof said)?
Whatever, whichever way the billiard balls go,
Momentum and energy are all ya gotta know.
Chorus: When the ball's go bang, their momenta can change
But the total of their vectors has to stay the same
3. To try this out for real you gotta find a pool table;
Put the 8-ball on the spot just as neatly as you're able.
Now the cue ball hits the eight and gives that ball a thumper,
And you mark where the two balls collide with a bumper.
You take a protractor, find the angle of each path,
Then you can do some real vector math.
When you've marked down the vector, spot the 8-ball again,
And do some more collisions until you got ten.
Collect a bunch of data and draw the vectors too
On a neat sheet of paper for the prof to review.
With a list of the angles, which you can then compare
To see how off they are from being square.
You write up your results based on the world that's real,
And tell how close they come to Newton’s ideal.
With timers and cameras we could make this real cool,
But to heck with that, let's just go play some pool!
25
MOMENTUM CONSERVATION
PHYSICAL SCIENCE
Home Demo #17 Marble Madness
http://nyelabs.kcts.org/openNyeLabs.html
(Source: “Marble Madness.” Home Demos. BillNye.com)
Description: This simple experiment will give you a chance to prove to yourself that when
it comes to physics, "Every action has an equal but opposite reaction." It will also give
you the opportunity to lose your marbles, so try to keep track of them.
Materials
• Ruler with a center groove
• Seven marbles, each the same size
Procedure
• Tape the ruler to a level surface.
• Place five marbles in a row touching each other in the center groove of the ruler.
• Roll a sixth marble down the groove into the marbles standing still.
• Repeat the experiment, but this time roll two marbles into the row of five.
What's Happening?
When a moving marble hits the row of motionless marbles, an exchange of energy takes
place. The rolling marbles have momentum, which is transferred from one marble to the
next, until the marble (or marbles) at the other end gets sent into motion.
Visit Suggestions:
•
Shoot some pool at the TRICK SHOT exhibit (#20) and experiment with
conservation of momentum. Reality and theory are not the same. Is the momentum
conserved 100%? How might energy be “lost”?
Sources:
Eby, Denise, and Robert B. Horton. Physical Science. New York: Macmillan Publishing
Company, 1986.
Hewitt, Paul G. Conceptual Physics, A High School Physics Program. Menlo Park, CA: Addison
Wesley Publishing Co., Inc., 1987.
Hewitt, Paul G. Conceptual Physics. 3rd ed. Boston: Little, Brown and Co., Inc., 1977.
Serway, Raymond, A. Physics for Scientists and Engineers with Modern Physics. 2nd ed.
Philadelphia: Saunders College Publishing, 1986.
26
TRAJECTORY
PHYSICAL SCIENCE
Topic Focus:
•
Given the initial velocity of a projectile and its take-off angle with respect to the
horizontal axis, the trajectory of the projectile can be calculated.
Background Information:
Kinematic equations (equations of motion) can be used to mathematically represent the
motion of projectiles. Given a projectile launched with a velocity vi at an initial angle of
θi, the initial horizontal and vertical components of the velocity vector can be calculated
as vector projections:
y
viy = visin(θ)
vi
θi
vix = vicos(θ)
vi
θi
x
Using this information, and the following equations, the path of the projectile can be
calculated for any time, t.
x = vixt + ½axt2
vfx = vix + axt
vfx2 = vix2 + 2axx
where:
t = time
θi = initial projected angle
vi = initial velocity
x = horizontal displacement
ax = horizontal acceleration
vix = initial horizontal velocity
vfx = final horizontal velocity
y = viyt + ½ayt2
vfy = viy + ayt
vfy2 = viy2 + 2ayy
y = vertical displacement
ay = vertical acceleration
= acceleration of gravity
viy = initial vertical velocity
vfy = final vertical velocity
Try this at school:
Many computer programs exist on the Internet that illustrate / animate projectile motion. These
programs use kinematic equations to calculate the path of a projectile once the user has chosen
27
TRAJECTORY
PHYSICAL SCIENCE
the launch angle and velocity. Some programs also allow the user to change the acceleration of
gravity and to add in other variables (e.g. air drag). Check out the following web sites:
1) Cannon, Energy, Drag and Gravity: Using this Applet, see the results as you vary the initial
angle and velocity of a projectile shot from a cannon. This site includes instructions for
experiments that you can do with the computer program.
http://zebu.uoregon.edu/nsf/cannon.html
2) Activity: Golf Range! Change the launch velocity and launch angle as you drive a few balls.
http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=19
3) View the mechanics animations, particularly the motion of a body in the presence of a
gravitational field.
http://www.infoline.ru/g23/5495/Physics/English/mech.htm
Visit Suggestions:
•
How do computer programs like FORE! (#15), TARGET (#14), VIRTUAL SPORTS
(#37), or VOLLEYBALL (#38) really work? How does the computer predict where your real
projectile will end up in a virtual world? What are the initial conditions that the computer has to
work with? Do all of these programs work in a similar way?
•
Try tracking the path of a pinball at the TRAJECTORY table (#18). What happens when
you change the initial conditions?
Sources:
“Projectile Motion.” The Physics Classroom. The Physics Classroom and Mathsoft Education and
Engineering, Inc. 2001.
http://www.physicsclassroom.com/Class/vectors/vectoc.html
Serway, Raymond, A. Physics for Scientists and Engineers with Modern Physics. 2nd ed. Philadelphia:
Saunders College Publishing, 1986.
28
EXHIBITS BY SPORT / ACTIVITY
Note: (#) refers to UPMC SportsWorks Map
SPORT /
ACTIVITY
Baseball
Basketball
Bobsledding
Bowling
Car Racing
Cycling
Figure Skating
Football
General Fitness
Golf
SPORT / ACTIVITY
Gymnastics
EXHIBIT
Baseball (#13)
Jr. Pitching Cage (#43)
Hoops Vision (#27)
Vertical Jump (#24)
Virtual Sports (#37)
Snow Sports (#8)
Sports Gear (#28,29)
Energy Race (#34)
Jr. Big Wheel Racers (#44)
Energy Race (#34)
High Cycle (#6)
Sports Gear (#28,29)
Be the Judge (#16)
Rotation (#21)
Snow Sports (#8)
Target (#14)
Footwork (#30)
Hang Time (#23)
Jr. Exercise Equipment
(#45)
Jr. Obstacle Course (#42)
Reaction Time (#22)
Fore! (#15)
Mini-Golf Math greens
(#41)
Sports Gear (#28,29)
Hang Gliding
Hockey
Ice Climbing
Pool
Rock Climbing
Skateboarding
Ski Jumping
Skiing
Skydiving
Sledding
Snowboarding
Soccer
Synchronized Swimming
Tennis
Track and Field
Volleyball
Walking
Wheelchair Racing
29
EXHIBIT
Balance Beam (#9)
Be the Judge (#16)
Bounce (#5)
Rotation (#21)
Hang Gliding (#36)
Hockey (#10)
Sports Gear (#28,29)
Target (#14)
Snow Sports (#8)
Trick Shot (#20)
Climbing Wall (#1)
Skateboarding (#25)
Snow Sports (#8)
Snow Sports (#8)
Parachute Drop (#19)
Snow Sports (#8)
Snowboarding (#35)
Virtual Sports (#37)
Be the Judge (#16)
Sports Gear (#28,29)
Olympic Sprint (#17)
Women in Sports (#33)
Vertical Jump (#24)
Volleyball (#38)
Footwork (#30)
Wheelchair Race (#12)