Download The University of Kalahari Presents: High School

The University of Kalahari Presents:
High School Physics and Math
Wisconsin Dells, Wisconsin
Karibu! It is with great pleasure that we welcome you to the Kalahari Resorts’ version of a classroom. At
the University of Kalahari, we traditionally spend our time molding and shaping our associates – but today
we share that same passion with you and your high school class.
To successfully complete this class, you’ll need some help. Just as we expect our associates to do, you’ll
have to: have an open mind, be willing to work, and ask good questions when you run into some speed
bumps.
Our job is to serve our guests – and to give them Beyond Expectations moments. Your job is to use your
tools from this mini-course to increase your skills in the classroom. You’ll need to complete some of the
activities while in our indoor waterpark. The Kalahari is proud to present the largest and wettest indoor
waterpark in Wisconsin to you and your classmates. Make sure to stand-up surf or boogie board on
the FlowRider! Experience the thrill of the Master Blaster. Brave the Sahara Sidewinders and
the Screaming Hyena. Don’t forget to the huge indoor wave pool, lazy river, and so much more!
With 125,000 square feet of wet and wild indoor fun, no matter what the weather is like outside, you can
splish-splash all day long at Kalahari.
The University of Kalahari strives to be a win-win. We hope that you take this amazing opportunity and
have fun while you are on our campus. We also demand that you work diligently with your teachers to
apply what you have learned in the classroom in completing the activities in our park. We have an old
motto around here – “work hard, play hard”. There will be plenty of time for both.
Thank you for selecting Kalahari Resorts and welcome to A World Away!
Learn everyday,
Professor Kenya
University of Kalahari Educational Team Lead
We PROMISE to Deliver Products and Services Beyond Expectations
Physics Defined with Basic Terms
Let’s begin our class by looking what physics consists of, and some basic definitions.
Physics is the study of matter and energy in space and time and how they are related to each
other. Physicists assume (take as given) the existence of mass, length, time and electric
current and then define (give the meaning of) all other physical quantities in terms of these
basic units. Mass, length, time, and electric current are never defined but the standard units
used to measure them are always defined.
In addition to these four units, there are three other ones: the mole, which is the unit of the
quantity of matter, the candela which measures the luminous intensity (the power of lighting)
and the Kelvin, the unit of temperature.
Physics studies how things move, and the forces that make them move. For example: velocity
and acceleration are used by physics to show how things move. Also, physicists study the
forces of gravity, electricity, magnetism and the forces that hold things together.
Physics studies very large and very small things. For instance, physicists can study stars, planets
and galaxies. But they can also study a waterpark or the movement of water in the park. They
may also study sound, light or other “waves”. Additionally, they may examine energy, heat and
radioactivity, space or time.
Physics not only helps people understand how objects move, but how they change form, how
they make noise, how hot or cold they will be, and what they are made of at the smallest level.
Physics is a quantitative science because it is based on measuring with numbers. Math is used in
physics to make models that try to guess what will happen in nature. The guesses are compared
to the way the real world works. Physicists are always working to make their models of the world
better.
To make some sense out of it all, here are some basic terms used in physics.
Acceleration: The change in velocity (speed or direction or both) per unit of time.
Accelerometer: a Transducer that senses acceleration.
Air Resistance: The force of air pushing against a moving object.
Buoyant Force: The upward force exerted on an immersed body by the water beneath.
Centrifugal Force: the force directed radially outward that is exerted by a rotating body on a
structure or mass that exerts a center-directed (centripetal) force on that body.
Centripetal Force: The force directed radially toward the center of rotation that is exerted by a
mass on a rotating body and that causes that body to travel in a circular path.
Circumference: The distance around the outside of a circle.
Deceleration: Negative acceleration.
Doppler Effect: Sound is louder when the source is approached than when going away from it.
Force: That which causes or tends to cause a change in a body's motion or shape.
Friction: The force that resists the sliding of one surface upon another.
Gravity: The acceleration due to gravity is 9.8 meters/second squared.
G Force: A force, acting on a body, as a result of acceleration or gravity. One "g" equals the
gravitational pull at the surface of the earth.
Heart Rate: The number of times a heart beats in a minute.
Inertia: The resistance of a body to a change in its state of motion.
Kinetic Energy: The ability of a body to do work by virtue of its motion.
Mass: the measure of a body's inertia; the amount of matter in a body.
Momentum: A system's resistance to change in its state of motion (inertia) multiplied by its
velocity.
Period: Motion that exactly repeats itself in regular time intervals
Potential Energy: The ability of a body to do work by virtue of its position above an object
(gravitational potential energy) or by virtue of its deformation (elastic potential energy)
Speed: The magnitude of a body's displacement per unit of time without regard to direction
Velocity: The Speed and direction of a body.
Wave Drag: A force caused by and acting against a body moving through water, forming waves
at the surface of the water.
An Interesting Read
Standing over six stories above the waterpark floor, looking down the Kalahari’s newest extreme
slides at Tufani Falls, some riders have been known to have second thoughts. Mysterious music
pumps into the loading area at the top of the three slides, muffling the sound of park goers
below. “Just go for it!” the ride operator urges, and another human torpedo surrenders,
accelerating to a velocity of about 40 feet-per-second while zooming through the slide’s super
loops.
“Yup, that’s a crazy one,” engineer Marvin Hlynka says, chuckling when asked to comment on
the intensity of the attraction. Hlynka works for WhiteWater West Industries, a maker of extreme
waterslides. It’s his job to use science to find new ways to scare riders out of their minds, but
there’s a limit to how much his equations and computer programs can help him. In the alternate
universe of waterslide design, Newtonian models don’t always work, and chaos lurks in every
hairpin turn. “In terms of actually predicting where a particular drop of water or a particular
body is going to be in the slide at any given time, you can’t do it,” Hlynka says. “It’s just not
possible.”
The path that water takes through a channel is primarily a function of its volume and the
channel’s shape, slope, and the roughness of its surface. As the water picks up speed, however, it
starts to develop eddies—zigzagging, swirling currents—that make the flow less predictable.
The velocity at which a smoothly flowing stream produces eddies depends on the water’s
viscosity, the diameter of the channel, and other factors, but no one fully understands what
triggers all the turbulence.
Turbulent water, like thunderstorms and other chaotic systems, is extremely sensitive to minor
disturbances. The tiniest contaminant—a speck of dust, a blade of grass—can disrupt a
waterslide’s flow, touching off larger irregularities that in turn create swirling eddies, and so on.
Newtonian principles predict that minute initial variations in a system lead to similarly minute
final ones. Not so in chaotic systems. “There are tiny perturbations to start out with, and they get
bigger and bigger in unpredictable ways,” says Parviz Moin, director of the Center for
Turbulence Research at Stanford University. “You’ve heard how a butterfly flapping its wings in
China can change the weather in California. In a sense, that kind of thing is what’s happening
inside a waterslide.”
Because no equation can predict these changes in a straightforward way, waterslide designers
can’t know for certain how the frothy water will behave when they switch on the jets. Yet they
rely on water flow and gravity to safely convey riders to the splash pool. “If you’re building a
roller coaster or a similar ‘hard’ amusement-type ride, you strap the riders in so they can’t
move,” Hlynka says. “With a waterslide, there’s none of that control.”
Other variables further complicate the equation. Different bathing suits, for instance, generate
differing amounts of friction as they rub against a slide, and that affects the character of the
turbulence as well as the speed of the rider. Go down the Screaming Hyena in a pair of cotton
shorts and you might find the ride ho hum. Go down it in a pair of Spandex trunks and you
might need some time to recuperate.
Hlynka’s only safeguard against such uncertainty is real-world testing. He creates detailed
designs based on past experience, and then uses an army of eager volunteers to act as guinea
pigs to verify the slides’ safety. “Experience helps,” Hlynka adds. “After 20-odd years, you know
that if a typical person with a typical bathing suit rides a fiberglass slide at a 9 to 10 percent
slope, there aren’t going to be any problems.”
Just to be sure, Hlynka and his team tend to over engineer the safety features on their slides.
Their non-enclosed flumes have inward-curving sides that are anywhere from 2 1/2 to 5 feet
high. These ensure that even riders who encounter powerful turbulence won’t be catapulted off
the slide.
Slide designers also have a few predictable physical principles in their favor. In WhiteWater
West’s new High Speed 32 slide, for instance, riders veer through a succession of gentle curves
at more than 30 feet per second. Each body’s speed and subtle rotation creates a force of about
3 g’s that pins the riders against the fiberglass chute as they slide. “The faster you go, the more
the g-force holds you against the wall and locks you in position,” Hlynka says. “It’s almost like a
restraint.”
Still, even the best-laid slide can sometimes throw a wrench in engineers’ plans. A few years ago,
a WhiteWater slide was installed in Sandusky, Ohio, and the new slide was almost an exact copy
of the original which debuted in Minneapolis. Its measurements were identical within a quarter
of an inch. Hlynka and his fellow engineers figured the design would be a no-brainer. They were
wrong. “We had it all set up, and we saw water pouring out of one particular place. We said,
‘What the heck is that?’ ” Hlynka remembers. “The water went down a completely different path
than it had in the Minneapolis slide—it zigged where it should have zagged.” In the end, the
team had to design a new set of plastic splash guards to take care of the unexpected spillovers.
Hlynka still isn’t sure what chaotic inconsistencies were at fault. “It could be something as
prosaic as one city being dustier than another,” he says.
New computer models may help minimize such mishaps. Parviz Moin and his Stanford team are
tackling turbulence by breaking it down into manageable chunks, using a computer program to
determine a fluid’s velocity and pressure at closely spaced points. This approximates the overall
flow, much as a pixelated image approximates an actual scene. Yet each “flow event” depends
on the one before it, so simulating the entire sequence in detail might take even the speediest
supercomputer hundreds of years.
In the meantime, Hlynka will continue to revel in the inexactitude of his science. “I like to think of
waterslide designers as similar to cathedral builders,” he says. “In the Middle Ages, they created
these beautiful buildings basically because they knew how. They couldn’t express their designs
in calculations or formulas, but they got it right anyway. They were guided by visual proportion
and a sense of the way the materials behaved.” It takes more than a slide rule, you might say, to
build a waterslide.
Safety Information
Individual Ride Restrictions for the Indoor Waterpark
FlowRider - Must be 42" tall to ride.
Tanzanian Twister - Must be 48" tall to ride.
Elephant's Trunk - Must be 48" tall to ride.
Zig Zag Zebra - Must be 42" tall to ride.
Master Blaster - Must be 42" tall to ride.
Victoria Falls - Must have at least 2 riders.
Sahara Sidewinders - Must be 54" tall to ride.
Screaming Hyena - Must be 54" tall to ride.
There is also no eating or drinking while on rides or while waiting in lines. Please follow
the directions of lifeguards at all times.
Safety Notice
Students are not required to ride any ride that makes them uncomfortable. If you do not
want to ride a particular ride, you may excuse yourself from that ride. Each student will
be responsible for getting the missing data from other students. Please wait in the
assigned area for the group to complete the ride.
Safety Warning
Pregnant women and individuals who have experienced the following medical
conditions are advised not to ride: Seizures, back injuries, neck injuries, arthritis,
dizziness, motion sickness, claustrophobia, high blood pressure, heart conditions, pace
maker, stroke, or other serious medical conditions. Individuals are prohibited from riding
if they are intoxicated or under the influence of drugs that impair their mental or
physical abilities. You assume risk of injury when you ride. Not responsible for lost or
broken property
Formulas
Distance, Speed, Velocity, Acceleration
Speed = Distance/Time
S=d/t
Velocity = Distance/Time in a given direction
V = d / t + direction
Acceleration = (Final velocity - Beginning velocity)/(Final time - Beginning time)
a = ∆v/∆t = (vfinal - vinitial) / (tfinal - tinitial)
Potential and Kinetic Energy
Potential Energy = Mass x Gravity constant X height (above the earth)
Kinetic Energy = (Mass x Velocity squared) / 2
PE = mgh
KE = (m )/2
Force, Momentum, Weight, Gravity
Force = Mass x Acceleration
Gravity = 9.8 meters/second squared
Weight = Mass x Gravity
Momentum = Mass x Velocity
F = ma
G = 9.8m/
W = mg
M = mv
Metrics
1000mm = 100cm = 10dcm = 1m = .1dkm = .01hm = .001km
Centripetal Force
Centripital Force needed = Mass x speed squared / radius of circle
Fc = m
/r
Buoyancy
Weight Density = weight/volume.
Converting Pounds (lbs) to Newtons (N) = weight in lbs x 4.44822162
Fresh Water Weight Density = 9.8 Newtons per Liter
Normal Resting Heart Rates
Adults = 60 - 100 beats per minute
Children = 70 - 150 beats per minute
WF = W/V
“Gut Feelings” at the Waterpark
Use the best measuring device of all, your body. Your body is equipped with highly
sensitive measuring devices used to measure acceleration. You are a “natural
accelerometer.” Below is a data table to help you read your “natural accelerometer.”
Direction of
Acceleration
Physics Term
Gut Feeling
Upward
Vertical
- You feel pressed
downward. (The greater the
acceleration, the more
squished you feel)
Downward
Vertical
Forward
Longitudinal
- You feel like you are
rising.
- Your stomach feels like it's
in -your throat.
- You may feel queasy.
- You feel pushed
backwards.
- Your head and shoulders
may swing backwards.
Backward
Longitudinal
- You feel pushed forward.
- Your head and shoulders
may roll forward.
Left or Right
Lateral
- You slide Sideways
- Your shoulders may be
pressed against the ride
wall or your riding partner.
Heart Rate Reactions
Heart rates should be takes as soon as possible after exiting the ride for most accurate
results.
Activity
FlowRider
Elephant's Trunk
Zig Zag Zebra
Victoria Falls
Master Blaster
Tanzanian Twister
Rippling Rhino
Sahara
Sidewinders
Screaming Hyena
Pre-Activity
Heart Rate
(beats/min)
Post-Activity
Heart Rate
(beats/min)
Buoyancy in the Activity Pool
Based on Archimedes' Principle that states; a solid body immersed in a fluid is buoyed
up by the force equal to the weight of the liquid it displaces.
Degree of buoyancy depends on body density. There are three different types of
"floaters" - True Floater, True Sinker, and Conditional Floater.
True Floater: (positively buoyant) apply to those whose body density remains less than
that of water after exhalation.
True Sinker: (negatively buoyant) Even with lungs fully expanded with air, body density
is too great to float.
Conditional Floater: (neutrally buoyant) Body density is equal to that of buoyancy, able
to float with lungs full, and sink with lungs empty.
Go to the Activity Pool to find out what type of floater you are. To test your buoyancy
properly, use the “jellyfish position” portrayed in the examples.
1. What type of floater are you?
2. When wearing a life jacket, does it increase or decrease your buoyancy?
3. Convert your weight from pounds (lbs) to Newtons (N).
3. Who is more likely to float, A 668 N (150 lbs) person, or an 801 N (180 lbs) person?
Why?
FlowRider Hydrodynamic Lift Force
In swimming activities, relative water flow past the moving body can provide not only
drag force, but also a second kind of force. This force is called Hydrodynamic Lift Force.
As a body or surf board moves over the flowing water, an upward lift force acts on the
board because of the difference in water/air pressure the board creates.
1. What was your “gut feeling” during this ride?
2. Draw a picture of water as it moves around a board on FlowRider.
Centripetal & Centrifugal Force on
Tanzanian Twister
As an object goes in a circle around a point there are two forces that act upon that
object. Centripetal Force is responsible for continually forcing a rotating object on a
circular path around a central axis. Centrifugal Force is the equal and opposite reaction
and is the force the object exerts along the radius on the central axis.
1. What was your “gut feeling” during this ride?
2. How many times did you travel around the bowl?
3. The radius of Tanzanian Twister is 20 meters and the max speed a person enters the
bowl is 15 mph. How much centripetal force did you generate to travel around in one
circuit? (Use your own body mass and assume max speed.)
Gravity on Screaming Hyena
Newton's law of universal gravitation declares that the force attraction between two
masses is directly proportional to the masses of the two bodies. This means that the
greater the masses of the bodies, the greater the force of attraction between them.
1. What was your “gut feeling” during this ride?
2. For the first few moments on Screaming Hyena, you are in free fall. Calculate your
Potential Energy if you were 1000ft above the earth. (Use your own body mass.)
Kalahari Indoor Waterpark Basic Math
1. How many lights are there in the Indoor Waterpark?
_________________________ lights. What is the quickest way to come up with the
solution?
2. How many steps are there in all three slide towers?
__________________________Steps
3. Price Calculation: A group of four decides to go to Zulu Grille for lunch. Their order
consists of:
ZULU GRILLE
1 Hamburger
2 Cheeseburgers
1 Vienna Hot Dog
2 French Fries
1 Fruit Bowl
3 Large Sodas
1 Smoothie
What is the total of their order without tax?
4. Discount Calculation: The previous group had a coupon for 20% off their total
purchase. What is their new total before tax?
5. Possible Combinations: How many possible combinations can be made from the
Slushies using 10 different flavors?
6. What is the Maximum load a tube can hold on Elephant's Trunk?
7. How many turns are on Victoria Falls?
8. *EXTRA CREDIT* - Write the equation below and solve, rounding to the nearest tenth.
Multiply the lights (L) by the possible combinations of Slushies (S) and divide it by the turns in
Victoria Falls (T). Take the answer and find the square root.
Notes or Work Page