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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