for elementary school teachers table of contents

FOR ELEMENTARY SCHOOL TEACHERS
TABLE OF CONTENTS
TABLE OF CONTENTS
MAP
THE EXHIBITS
RELATED NATIONAL SCIENCE EDUCATION CONTENT STANDARDS
CURRICULUM CONNECTIONS
GENERAL PROBLEM SOLVING
HEALTH / PHYSIOLOGY
PERCEPTION AND ILLUSION
PERSONAL HEALTH
MATHEMATICS
COORDINATE SYSTEMS: PITCH, ROLL AND YAW
PHYSICAL SCIENCE
ANGULAR MOMENTUM
GEARS
MATERIAL PROPERTIES
EXHIBITS BY SPORT / ACTIVITY
1
2
3
6
7
8
9
9
10
11
11
12
12
13
17
19
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, and 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 360degree 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.
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.
3
THE EXHIBITS
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.’
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.
4
THE EXHIBITS
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.
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 CONTENT STANDARDS
5
THE EXHIBITS
Grades K-4
B: Physical Science
National Science
Content Standards
Balance Beam
Baseball
Bounce
Climbing Wall
Drugs in Sports
Energy Race
Footwork
Hang Time
High Cycle
Hoops Vision
Impact!
Injuries
Mini Golf Math:
Gravity Well Green
Olympic Sprint
Orbitron
Parachute Drop
Reaction Time
Skateboarding
Snow Sports
Snowboarding
Sports Gear
Sports Gear
Vertical Jump
Wheelchair Race
Women in Sports
Grades 5-8
F: Science in
B: Physical Science
Personal and Social
Perspectives
Properties Position Light, heat, Personal Science Motions Transfer
of objects
and
electricity, health
and
and
of energy
and
motion of
and
technology forces
materials objects magnetism
in local
challenges
C: Life D: Earth
F: Science in
Science and Space Personal and Social
Science
Perspectives
Structure Earth in Personal Risks and
and
the solar
health
Benefits
function system
in living
systems
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
6
x
x
x
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.
Try this 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?
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?
8
PERCEPTION AND ILLUSION
PHYSIOLOGY
HEALTH /
Topic Focus:
•
The human brain may interpret sensory input incorrectly.
Background Information:
People who design virtual reality motion simulators need to know how the brain
collects and interprets sensory input in order to give the players a threedimensional virtual experience.
•
Visual Effects: our eyes perceive objects that are close by as moving more
than objects in the distance. This phenomenon, called motion parallax, helps us
to sense how far away things are from us as we move. Ride designers use this
principle when creating virtual reality programs to fool our visual senses.
•
Sound: stereo sound (coming from more than one location) inside the
simulator helps create an immersive experience for the riders.
•
Motion: many virtual reality rides use hydraulic lifts to move the seats in time
with the images projected around the riders. The motion is closely
synchronized with the visual images. Consequently, the fluid in the riders’
inner ears moves in a way that is consistent with the information that they
receive visually. Consistency of sensory signals is important for preventing
motion sickness.
Optical illusions are false
perceptions. The brain interprets
visual information in a way that is
incorrect. The Mini-Golf Math
Optical Illusion Green is an example of the “Café Wall Illusion.” View this page
from arm’s length. The gray lines in between the rows of squares are parallel.
First described in 1979 by Dr. Richard Gregory of Bristol England, this illusion
relies on the position of the squares with relation to each other, their contrasting
colors and the color of the lines in between the rows.
Try this at school:
Learn more about Optical Illusions at the Exploratorium Online Exhibits:
http://www.exploratorium.edu/exhibits/f_exhibits.html
Visit Suggestions:
•
•
•
See how realistic motion simulators can be. Try out the DESIGN A COASTER
simulator (#3), SIMULATOR XTREME(#40) or the SNOW SPORTS
BOBSLED SIMULATOR (#8).
Does the Café Illusion confuse your brain? Try putting at the MINI-GOLF MATH:
OPTICAL ILLUSION GREEN (#41).
Sometimes your brain is able to learn to compensate when it receives confusing
sensory input. Try shooting a few baskets while looking through distorting lenses at
the HOOPS VISION exhibit (#27). Are you able to make your shots after a few
tries?
9
PERSONAL HEALTH
PHYSIOLOGY
HEALTH
/
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:
K-4
•
•
•
5-8
Responsibility for one’s own health
Importance of good nutrition
Bodily harm caused by some substances
•
•
•
•
•
Importance of regular exercise
Injury and accident prevention
Risks of tobacco use
Alcohol and other substance abuse
Nutritional requirements
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.
10
COORDINATE SYSTEMS
MATH
Topic Focus:
•
The orientation of an object in space can be determined by controlling its
pitch, roll and yaw.
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 see animated instructions, log onto the website, 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."
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!
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).
11
ANGULAR MOMENTUM
PHYSICAL SCIENCE
Topic Focus:
•
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.
Try this at school:
Momentum Machine
http://www.exploratorium.edu/snacks/momentum_machine.html
Description: How ice-skaters, divers and gymnasts get themselves spinning and twisting
faster. You've probably seen an ice skater spinning on the tip of one skate suddenly start
to spin dramatically faster. A diver or gymnast may also suddenly flip or twist much
faster. This speeded-up rotation results from a sudden redistribution of mass. You can
make yourself suddenly spin faster while sitting in a rotating chair.
materials
• A rotating stool or chair from a scientific supply house,
an office supply store, or a classroom.
• 2 heavy masses. Use the heaviest weights that you can
support at arm's length.
• A partner.
• Adult help.
to do and notice
• Sit in a chair with one of the masses in each hand and with arms outstretched.
• Have your partner start rotating you slowly, then let go and move away.
• Quickly pull the masses inward and notice that you rotate faster. Be careful! A very
rapid spin may cause the chair to tip over! Also, you may be dizzy when you get up.
what’s going on?
A rotating object tends to remain rotating with a constant angular momentum unless it is
acted upon by an outside twisting force. The definition of angular momentum is slightly
more complex than that of linear momentum. Angular momentum is the product of two
quantities known as angular velocity and moment of inertia. Angular velocity is merely
velocity measured in degrees, or radians-per-second, rather than meters-per-second.
A person sitting on a rotating chair or stool approximates a system in which angular
momentum is conserved. The friction of the bearings on the chair stem serves as an
outside twisting force, but this force is usually fairly low for such chairs. Since angular
momentum is conserved, the product of angular velocity and moment of inertia must
remain constant. This means that if one of these factors is increased, the other must
decrease, and vice versa. If you're initially rotating with your arms outstretched, then
when you draw your arms inward, your moment of inertia decreases. This means that
your angular velocity must increase, and you spin faster.
etcetera
The conservation of angular momentum explains why an ice skater
starts to spin faster when he suddenly draws his arms inward, or
why a diver or gymnast who decreases her moment of inertia by
going into the "tuck" position starts to flip or twist at a faster rate.
©1997 The Exploratorium, 3601 Lyon Street, San Francisco, CA 94123.
Visit Suggestions:
•
•
Visit the ROTATION exhibit (#21) and experience conservation of angular
momentum first hand! How does changing the distribution of your own mass affect
your spinning speed?
For more hands-on activities regarding rotational inertia, try spinning the disks at
“The Turning Point” panel and compare the rates of speed of the tops at “The Art of
Rotation.”
12
GEARS
PHYSICAL SCIENCE
Topic Focus:
•
Gears transmit motion and force in machines.
Background Information:
A gear is a toothed wheel mounted on a rotating shaft. Gears are simple machines
that are used in combination in order to:
•
reverse the direction of rotation of a spinning object.
•
change the angular velocity (speed of rotation in a particular direction) of a
spinning object.
•
move rotational motion from one shaft to another.
•
maintain synchronous rotation of two shafts.
Torque-Multiplying Machines
Simple machines may be used to create mechanical advantage, meaning they
decrease the amount of applied force necessary to produce a desired effect.
The mechanical advantage of a system of gears is quantified by calculating the
gear ratio of the system. Gear ratios are dependent on the gears’ circumferences
(the distances around the edge of each gear).
The circumference of a gear is equal to πD where π ≈ 3.14 and D
is the gear’s diameter.
D
In a given gear assembly the teeth on meshing gears must fit
together. Each gear’s number of teeth is proportional to its diameter. Therefore,
gear ratio calculations are greatly facilitated when the numbers of gear teeth are
known.
For example:
The gear ratio of the gear system to the right is:
driven gear yellow gear 16 teeth
=
=
= 2:1
blue gear
8 teeth
driver gear
•
This 2:1 (“two-to-one”) mechanical advantage
means that every time the blue gear rotates about its
axis twice, the yellow gear rotates about its axis
once. Therefore, the blue gear has twice the angular
velocity of the yellow gear.
Blue gear: 8 teeth
radius = rb
rb
ry
Yellow gear: 16 teeth
radius = ry
Newton’s Third Law states that if two bodies interact, the action force is equal to
and opposite to the reaction force.
•
Here, the force that a blue gear tooth applies to a yellow gear tooth, Fb, must
13
GEARS
PHYSICAL SCIENCE
be equal to and in the opposite direction of the force that the
yellow gear tooth applies to the blue gear tooth, Fy. Therefore,
Fb = -Fy where the minus sign indicates that the forces are
applied in opposite directions.
Blue gear
tooth
Fb
When dealing with rotating objects, torque is more commonly
discussed than force. Torque, τ, is the tendency of a force to
rotate an object about a defined axis.
For a gear (which is symmetrical) τ = Fr, where F is the force
applied at a distance, r, from the center of rotation of the gear.
•
Fy
Yellow
gear tooth
F
Substituting for the forces in the equation Fb = -Fy yields:
τb -τy
=
rb ry
where, rb < ry.
Thus, (
r
ry
)τ = -τy.
rb b
16 teeth
Because the ratio of the yellow and blue gear teeth (
= 2:1) is
8 teeth
proportional to the ratio of the gears’ diameters (and hence to the ratio of their
ry
radii),
= 2. Therefore, 2τb= -τy.
rb
The torque that is supplied by the yellow gear is twice the amount applied to
the blue gear, in the opposite direction.
Blue gear: 8 teeth
Speed-Multiplying Machines
•
If the gears were reversed such that the yellow gear
were driving the blue gear, the mechanical advantage of
the gear assembly would be:
driven gear
blue gear
8 teeth
=
=
= 1:2
driver gear yellow gear 16 teeth
When the mechanical advantage is equal to a fraction less
than 1:1, the machine magnifies the angular velocity of the
driven gear’s shaft rather than magnifying its applied force.
•
radius = rb
ry
rb
Yellow gear: 16 teeth
radius = ry
While the torque that must be supplied to the yellow gear is equal to twice the
blue gear’s torque output, rotating the yellow gear one turn will result in two
rotations (in the opposite direction) of the blue gear. Thus, the blue gear rotates
at twice the angular velocity of the yellow gear.
Note: In both cases above, the blue and yellow gears rotate
in opposite directions relative to each other. If the two
gears’ diameters (and number of teeth) were equal, the mechanical advantage
would be 1:1. The gear assembly would do nothing more than change the
direction of the shaft rotation between its beginning and end.
14
GEARS
PHYSICAL SCIENCE
A gear train is created when many gears are connected together. By connecting
many gears, gear ratios between input and output may be significantly changed,
either increasing the supplied torque or the supplied shaft angular velocity.
Try this at school:
Student Gears
http://www.colby.edu/cpse/equipmet2/simple/simple.html
(Source: Cook, Debbie, et al. “Simple Machines with Lego Dacta Kits.” (9/18/2000))
(Adapted from Human Gears, the Boston Museum of Science teaching ideas)
Description
This activity will involve the full class. Use 10 children at a time for this activity. Each of
the ten participants will extend his or her arms to be the teeth of a gear. The gears will
combine to create a gear pattern.
Grade Level: 2-3
Duration: 15-35 minutes, depending on how many variations are used
Materials
• Four slips of paper labeled “4”, three slips labeled “3”, two slips labeled “2” one slip
labeled “1”.
• Open space
• Cord lengths or large loops of 1” sewing elastic
Procedure
• Have children draw a gear number out of a jar. (Note: Gear #1 will spin the fastest
and have the greatest needed for self-control. You may want to assign this role, rather
than leave it to chance.)
• Gear #1 is only one person. S/he stands alone with arms stretching out straight from
his or her body.
• Gear #2 is two people standing back to back with shoulders touching. To make four
teeth, they hold their arms out straight, but at an angle of 90 degrees, as if they are
holding a big, imaginary box. A piece of cord or elastic around their waists will help
them stay together.
• Have the two “gears” stand so that a Gear #1 arm is in between the arms of a Gear #2
person. Explain that you are the force of this machine and you are going to send this
force along. Start Gear #2 turning slowly, keeping their feet in place.
• Have the children watch what happens to Gear #1. Does it move faster or slower
than Gear #2? What direction does each Gear turn in?
• Stop before the children get dizzy and lose their footing.
• Create Gear #3 with three people, shoulders touching and arms out at about 60
degrees. Tie their waists together as before.
• Connect Gear #3 to your pattern by having the smaller gears move in to connect. (It
will always be easier to move the smaller groups.)
• Start the gear pattern moving by gently helping Gear #3 to start spinning. Have the
children report again on which gear moved fastest. Slowest? In which direction did
each gear move?
• Create Gear #4 with four children, shoulders touching and arms out at about 45
degrees. Tie their waists together.
• Before adding them to the pattern, ask the children to predict: Which gear will move
most slowly? Most quickly? In which direction will each gear turn if the teacher starts
Gear #4 going clockwise?
• Have the smaller gears move in to connect which Gear #4 and start Gear #4 moving
slowly clockwise. Run the “machine” until the watchers have been able to check their
15
GEARS
•
PHYSICAL SCIENCE
predictions against the actual gear movements. Discuss the observations the children
have made about gear movements and speed.
Repeat the experiment using children who have been observers. Setting up the gears
will go much more quickly, since the children have clear expectations about the
procedures and outcomes. Run the experiment in the same way, letting the children
predict the direction of every new gear as it’s added. Now before Gear #1 is a total
dizzy wreck, reverse the action and let Gear#1 start turning so that his/her motion
controls the turning of the other gears.
Extensions
• Try mixing and matching gear sizes in a machine that uses everyone in your room.
How will the force be transferred? Can you still predict which direction a gear will turn
in? Can you make predictions about the relative speeds of each gear? If your group
has managed this activity without mishap, consider combining with another class to
make a “super machine.” Gear # 5 would have 10 teeth, Gear #6 would have 12 teeth,
etc.
This curriculum project was funded by the Colby Partnership for Science Education, the
Howard Hughes Medical Institute, and the Bell Atlantic Foundation.
Visit Suggestions:
•
Calculate the gear ratios at the MINI-GOLF MATH: GEAR RATIO /
PROBABILITY GREEN (#41). What are the mathematical relationships between
the three gears?
Sources:
Brain, Marshall. “How Gears Work.” How Stuff Works. (8/04/2000).
http://www.howstuffworks.com/gears.html
Eby, Denise, and Robert B. Horton. Physical Science. New York: Macmillan Publishing
Company, 1986.
“Gears.” Teacher support materials, St. Agnes Workshop LEGO Design and Programming
System, Engineering and Science: A curriculum for K-12, 1998.
http://ldaps.ivv.nasa.gov/Workshop/StAgnes/support/gears.html
“Loose Gears.” Tool Box Science: Square Wheels…Driving Science Home. Ohio’s Center of
Science and Industry, 1994.
Macaulay, David. The Way Things Work. Boston: Houghton Mifflin Co., 1988.
“Machine.” abstracted from the Grolier Encyclopedia.
http://students.pratt.edu/~arch543p/help/machine.html
Serway, Raymond, A. Physics for Scientists and Engineers with Modern Physics. 2nd ed.
Philadelphia: Saunders College Publishing, 1986.
16
MATERIAL PROPERTIES
SCIENCE
PHYSICAL
Topic Focus:
•
Advances in materials and in the design of uniforms and equipment have helped to
better protect and improve the performance of athletes in many sports.
Background Information:
While athletic equipment was once predominantly constructed from natural materials
(wood, leather, etc.), the development of metal alloys, fiberglass, plastics and ceramics
has revolutionized many sports. Each material has innate benefits and drawbacks. Many
factors come into play when designing and constructing equipment including a potential
material’s strength, weight, density, malleability (flexibility) and cost.
Try this at school:
Classroom Activity: Shoe Friction Challenge
(Source: Jordan, Jeff, Classroom Activities, UPMC SportsWorks at Carnegie Science Center, 2001.)
Objectives: Students will compare various types of sports shoes to make inferences about the
design of footwear as it relates to the sport in which it is used.
Messages:
- Objects at rest on a flat surface are held in place by a gravitational force as well as a frictional
force between the object and the surface.
- If the surface slants, gravity can overcome the frictional force, and the object moves.
- Different types of footwear are engineered to provide a specific amount of friction between an
athlete and their performing surface.
Materials:
- various sports shoes / footwear
- smooth-surfaced tilting board
- shims
- turf-surfaced tilting board
Preparation:
- Create a tilting board by placing a brick or other small, heavy object against one edge of a 12”
x 24” piece of ¼ inch plywood or stiff cardboard. The brick will act as a hinge/stop when the
other end of the board is tilted upward.
- If using wood, sand the surface of the plywood very smooth on one side.
- Optional: paint with a high gloss spray paint or wax; let surface dry totally. Self-adhesive
smooth floor tile with no large grooves can also be used to cover the smooth side.
- Cover the other side of the board with a rough surface such as indoor-outdoor carpeting.
- Shims can be made of foamcore or wood in uniform pieces, the thinner, the better.
Interaction:
- Students inspect the tilting board device and make hypotheses about how high the slant will
have to be before each piece of footwear loses its grip on the slanting surface.
- The shoes do not need to be limited to the “appropriate” surface for this experiment; for
example, the ballet slippers could easily be used on the turf-like slant simply for the purposes
of experiment.
- Students place a piece of sports footwear on the tilting board (smooth or turf, depending on
sport).
- By slowly adding shims beneath the back of the board, they increase the angle at which the
shoe rests.
- Students record the number of shims required to make the shoe initially lose its position, and
the number of shims required to make the shoe slide off the board entirely.
17
MATERIAL PROPERTIES
SCIENCE
brick
PHYSICAL
shims
smooth
Results:
- Footwear is engineered to perform optimally for each individual sport. Obviously, it would be
difficult to use cleats on a smooth, hard surface, and ballet might be more of a challenge on
Astroturf.
- What kind of shoes would be appropriate for a football game on a smooth surface?
- What kind of shoes would permit ballet on turf?
- While neither scenario is particularly practical, considering questions like these leads to the
engineering of new products that perform specialized jobs.
References:
nd
- Physics, 2 Ed., Tipler, Worth Publishing, Rochester, MI 1982. 5-3.
- Hands-on Physics, Cunningham, CARIE Publishing,  1994. 3.3.
- Active Physics Sports, It’s About Time Publishing,  1998. S86-91.
- http://www.exploratorium.edu/hockey/skating1.html
Visit Suggestions:
•
Investigate how Material Science has helped to improve the performance of athletes at the
SPORTS GEAR exhibit (#28). Can you find examples of how changing the material from
•
which sports equipment is constructed helps to improve an athlete’s race times?
Visit the “Gear Family” at the SPORTS GEAR exhibit (#29). Can you name all of the
athletic equipment that the family is modeling? Do you know which sport each piece of
equipment is used for?
18
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
19
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)