TEACHERS RESOURCE Theme Park Physics EDUCATION The following information will help to brings physics out of the classroom and in to a fun atmosphere, with real time examples and applications. It is designed as a guide to what we can offer, a base from which to launch your own lesson plans & projects to fit within your existing syllabus. You will find activities to suit students from Year 3 to Year 12. These will encourage students to interact with each other as well as develop their own ideas and opinions using basic physics principles. We encourage you to adapt the suggested activities to suit your group’s age and abilities. As we strive to provide the best possible service to the education sector we welcome & encourage any suggestions. Thanks to the ThinkQuest website, physics students & theme park enthusiasts around the world for their input. CONTENTS Info & Activities for Year 11 and under Questions & Answers Year 12/13 Basic Physics Build Your Own Force Meter Please note the following pages are not numbered so your own workbooks can be compiled as you like. INTRODUCTION Theme Parks around the world use physics laws to simulate danger, while the rides themselves are typically very safe. Ride designers must fully understand these laws to work out how far the envelope can be pushed. Designers and theme park enthusiasts alike want to feel like they’re in danger but be absolutely safe at all times. There is only one thing that really limits how far, how fast and how high when it comes to theme park rides … what our bodies can take without breaking! SUGGESTED ACTIVITY - GENERAL Isaac Newton's laws can be applied to every ride at Rainbow’s End and other theme parks around the world … make a list of our rides & how many laws of motion they each involve. Explain your choices. A SCARY CAROUSEL? Our Carousel ride in the Cadbury Land Castle is not classed as a “thrill” ride. Yet, it relies on the laws of motion as much as our Corkscrew Coaster. It’s theoretically possible that a carousel could throw its passengers off if it gained enough speed! With all of its simplicity, the carousel has a delicate balance of motion and forces. Every horse moves around one complete circle in the same amount of time. The horses on the outside have to cover more distance than the inside horses in this amount of time; therefore, the horses on the outside have a faster linear speed than those close to the centre. SUGGESTED ACTIVITY - CAROUSEL In pairs, take turns riding the Carousel, one of you on an outside horse and the other on an inside horse. Which felt faster? Which did you prefer? Did you get dizzy? Explain what that felt like. SHAPES & COLOURS & STUFF If you look really closely you will find heaps of different geometric shapes at a theme park. Triangles are a strong shape. The shape of a triangle cannot be changed when pressure is applied to it. This makes it good for building. Quadrilaterals are also common … squares and rectangles and a sort of a squashy square called a parallelogram. Theme parks are colourful places. Bright colours make people smile and feel happy. Dark colours can be a bit scary or make people feel sad. You’ll find lots of different colours at Rainbow’s End. We hope they make you feel happy. Some of our rides have got lights on them. This makes them sparkle on cloudy days and when we are open at night. SUGGESTED ACTIVITIES – SHAPES & COLOURS & STUFF Some rides aren’t made up of circles but they do go round and round. What rides are like that? How many different shapes can you see on each ride you go on? What is the shape that you see most often at Rainbow’s End? Why do you think this is? The Rainbow’s End logo has shapes and colours in it. What are the colours used? Do you know the names of these colours in any other languages? Make a list of all the colours you can find in the park. How many did you get? How many rides use your favourite colour? Which ride at Rainbow’s End has the most lights? Did you count them all? WEIGHTLESSNESS & PENDULUM RIDES Our Pirate Ship is a pendulum ride. Riders experience a sensation of weightlessness when they approach the top of the arc of travel. What passengers feel is the force of the seat pushing on their body with a force to counteract gravity’s downward pulling force. A 60 kilo person at rest in a chair experiences the seat pushing upwards on his or her body with a force of 60 kilos. At the top of the Pirate Ship this same 60 kilo person will feel less than this normal sensation of weight. In fact at the very top of the Pirate Ship, riders begin to fall out of their seat, that’s why we have lap bars. Since the 60 kilo person is no longer in full contact with the seat, it is no longer pushing on them with the same amount of force. And that’s why riders get the sensation of weighing less than their actual weight. MOTION SICKNESS Motion sickness is caused when the information from a person’s eyes does not coincide with the apparatus in a person’s inner ear that senses motion. The sensation of motion sickness can also be caused by sensory overload. Medical research has determined that the two most likely places to produce motion sickness are on a ship in the middle of a stormy sea and on a pendulum ride like the Pirate Ship! SUGGESTED ACTIVITY – PIRATE SHIP Close your eyes while you are sitting in the very back of the Pirate Ship. Does this make the ride more or less fun? Why? Raise your legs and arms as your side of the Pirate Ship swings down towards the middle. What does it feel like? Does where you sit on the Pirate Ship make a difference? Why do you think that is? THE THIRD LAW OF MOTION: THE LAW OF INTERACTION “Every action produces an equal and opposite reaction” We’ve all heard this one repeated at some time or another, but not everyone realises that this is Newton’s third law of motion, The Law of Interaction. At Rainbow’s End, two of the best real world examples of The Law of Interaction are the Dodgems and the Bumper Boats. These two rides are designed so riders can crash into each other without causing danger to themselves or others. The Dodgems have a large rubber bumper, the bumper boats are each housed within a large inflatable tube. When the vehicles collide, the drivers feel a change in their motion and become aware of their own movement (inertia). Though the vehicles may stop or change direction, the drivers continue in the direction they were moving before the collision. Collisions are also affected by the mass of the driver. The driver with the lesser mass has the greater change in motion, a larger jolt. Of course the kind of collision, velocity of the involved cars and the mass of the drivers also plays a role in bumper car collisions. SUGGESTED ACTIVITY – DODGEMS & BUMPER BOATS Get a group of friends together of all different sizes, maybe ask your teacher as well. Observe how different types of collisions affect the movement of the drivers. Did the smaller drivers get more or less of a jolt? How did different types of crashes affect the jolts received? Does the water affect the velocity of the boats and the resulting jolt in a collision? How? Why? THE FIRST & SECOND LAWS OF MOTION: INERTIA & ACCELERATION Isaac Newton's first two laws relate to force and acceleration, which are key concepts in roller coaster physics. The Law of Inertia states that bodies in motion will stay in motion unless they are acted on by an external force. Bodies at rest will stay at rest unless they are acted upon by an external force. Initial resistance to that force is called inertia. The degree of inertia is dependent on the mass of the body. Newton’s second law, The Law of Acceleration, explains how the mass of an object and the amount of force applied to it are related to the acceleration of an object. The greater the mass, the more it resists being moved, the smaller its acceleration will be. The greater the force … well I’m sure you get the picture! SUGGESTED ACTIVITY - COASTER Watch the Corkscrew Coaster go through a couple of circuits. What are some of the external forces acting on the coaster cars? Explain. THE ENERGY AND FORCES OF A COASTER There are two main types of energy at work on the Corkscrew Coaster, Potential & Kinetic. The forces we will look at are ‘G’ forces, centripetal force & centrifugal force. Potential Energy is the same as stored energy. When you lift a heavy object you exert energy (which later will become kinetic energy when the object is dropped.) The lift motor from the Rainbow’s End coaster exerts potential energy when lifting the cars to the top of the hill. The higher the hill, the more potential energy that is produced and the greater the amount of kinetic energy when the cars are dropped. At the top of the hills the train has a huge amount of potential energy, but it has very little kinetic energy. At the bottom of the hill there is very little potential energy but a great amount of kinetic energy. Think of Kinetic Energy as the energy of motion, the ability to do work. The greater the mass and speed of an object the more kinetic energy there will be. As the coaster cars accelerate down the hill potential energy is converted into kinetic energy. As you change direction on the coaster you feel "G forces". When the amount of force exerted by the seat to keep you up, equals the amount of gravitational force pulling you down, you experience "1G". That’s the normal gravitational pull. If it takes more than that amount, (typically because you are moving upward) you can experience greater G forces. So there’ll be a time on the coaster when, for a brief period of time, you weigh two and three times what you weigh normally! If you are not being pushed upward by the seat, (typically because you are moving downward) you can experience less than "1G." "Pulling negative g's" is what happens when you go over a hill and the coaster cars begin to descend. (You’ll pull negative ‘g’s as you descend on the FearFall as well.) For a brief period, you are not sitting on the seat. Eventually, you are stopped from your parabolic course by the lap bar and are pulled along with train. To complete a vertical loop, a coaster train must enter with sufficient kinetic energy to reach the top and still be moving. It then has converted kinetic energy into potential energy and starts down the other side of the loop, and accelerates out. As the coaster train starts towards the loop, gravity and momentum are pulling the train out of the loop, the force that moves the train through the loop is called the centripetal force. On its upward climb, the train reaches a point where gravity is no longer pulling it out of the loop and thereafter it is acting as part of the centripetal force pulling the train toward the centre of the circle. It is from this point until the top of the loop that it is important that the train has enough momentum to counteract the forces pulling it toward the centre of the loop. SUGGESTED ACTIVITY - COASTER Ride the Corkscrew Coaster and identify four distinct stages of the ride. What forces are at work in each of these stages? What effect did they have on the coaster train? What effect did they have on the riders? Ride the coaster a few times but sit in a different position. Try the front car, the rear car and a middle car. Is the experience different each time? Explain how & why. CENTRIFUGAL FORCES & THE CORKSCREW COASTER Have you ever noticed that the loops on modern-day steel track roller coasters aren’t circles? When coaster builders first started turning riders upside down, they built 360° loops. They were repeatedly unsuccessful. The centrifugal force generated as the cars moved up towards the top of the loop pushed riders into their seats with too much energy. And because the cars decelerated sharply at the top of the circle, sometimes riders fell out! Modern coasters, including the Corkscrew Coaster, have a clothoid loop which smoothes out the acceleration so riders speed safely along the interior of the loop. The secret is the loop’s changing radius, which controls the speed of the cars. When the circle is elongated into an ellipse the radius at the top of the loop is much smaller. The coaster cars move faster than they would in a 360° circular loop, creating a greater centrifugal force to counteract gravity and keeping riders safely in their seats. SUGGESTED ACTIVITY - COASTER Tie a small pebble to a piece of string and whirl it in a circle. Observe how fast the weight moves. What happens if you lengthen the string? What happens if you shorten it? Now imagine the weight is a roller coaster car on a track … would you rather ride the short string ride or the long string one? Why? FREE FALLING ON THE FEAR FALL A man called Galileo first introduced the concept known as free fall. According to legend, Galileo dropped balls of different weights from the Leaning Tower of Pisa to help support his ideas. These classic experiments formed the basis of the work of Isaac Newton who reiterated to the world that all objects free fall at the same rate, regardless of their mass. An object in the state of free fall is influenced only by the force of gravity. The object has a downward acceleration toward the centre of the earth, the source of gravity. On earth the rate of acceleration caused by gravity is 9.8m/s2. FearFall gives riders the sensation of free fall. There are three distinct parts to this ride: 1. Ascending to the top 2. Momentary suspension 3. The quick downward plunge. In the first part of the ride, force applied to the car lifts it to the top of the tower. The amount of force depends on the mass of the car and the passengers within the car. Motors create this upward force. There are built-in safety allowances for variables concerning the mass of the riders. Once the car reaches the top of the tower, it suspends for a short moment in time. Dramatically the car plunges down toward the ground, influenced by the earth’s gravitational pull. "Pulling negative g's" is what happens when the FearFall cars begin their descent. For a brief period, you are not sitting on the seat. Eventually, you are stopped by the restraints and your bottom makes contact with the seat once again. According to Galileo’s and Isaac Newton’s theories of free fall, the least massive, and also the most massive, riders free fall with the same rate of acceleration. Our FearFall ride has a special patented magnetic braking system that produces a controlled stop at the bottom. SUGGESTED ACTIVITY - FEARFALL What was the scariest part of the ride for you? Why? Did you lose contact with the seat as the car came down? Why do you think that was? Would you have come down faster if you weighed less? If you weighed more? Why? FEELING THE POWER OF THE POWER SURGE Power Surge is the latest ride at Rainbow’s End. Twenty-four riders in six clusters of four begin their journey seated with their feet dangling below them. There are four main stages to the ride. 1. The main arm rises. 2. The main arm spins vertically and the sweep arms rotate horizontally. These are motor driven rotations. 4. The seats rotate independently. 3. The main arm spins vertically and This is a gravity-driven rotation the sweep arms rotate horizontally. and differs depending on how the These are motor driven rotations. four seats in your cluster are loaded. SUGGESTED ACTIVITY – POWER SURGE Ride Power Surge with people who weigh more than you in your cluster and then again with people who weigh less than you. Is the ride experience different? Why? What about if you were the only person sitting in the cluster? What would happen then? What are the forces at work on this ride?? QUESTIONS OF ENERGY 1. On FearFall we have two carriages which each weigh the same. If one carriage is empty and the other has four adults each weighing 100 kilos and both carriages are released from the top of the 54m tower at the same time, which will travel faster? a) The car with four people b) The empty car c) The cars will travel the same time. 2. When the Corkscrew Coaster is taken to the top of the hill by the chain, what increases? a) The potential energy of the train. b) The gravity of the train. c) The mass of the train. 3. When the train goes through the loop on the Corkscrew Coaster, what is the force that keeps it going? a) Centrifugal force b) Centripetal force c) Gravity 4. How fast will your FearFall carriage be falling after 2 seconds? a) 19.6m/sec b) 29.4m/sec c) 96.04m/sec 5. Why are tear drop shaped loops used on roller coasters instead of circular loops? a) Clothoid loops are more pleasing to the eye. b) Circular loops are difficult to build c) Circular loops put too much force on passengers. 6. When the train goes through the loop on the Corkscrew Coaster, what is the force that presses riders into their seats? a) Centrifugal force. b) Centripetal force. c) Gravity. 7. The Corkscrew Coaster takes approximately two minutes from start to finish when empty. Ignoring friction, with all seven cars loaded to maximum capacity, how long will the journey take? a) Approximately two minutes. b) Approximately four minutes. c) Approximately three and a half minutes. 8. What force is used to brake a roller coaster? a) Small nuclear force. b) Friction. c) Centrifugal force. 9. If you dropped a small parachute off the top of FearFall just prior to the carriage being released, why would it reach the bottom after you? a) Because Newton proved weight does affect the rate of descent. b) Because you were pulled down by the restraints in the carriage. c) Because the force created by the gravity pulling the parachute down is reduced by the amount of friction the parachute will generate during its drop. YEAR 12/13 BASIC PHYSICS The following Rainbow’s End Physics worksheets are designed for Year 13 but some sections are suitable for Year 12. Please familiarise yourself with the contents prior to handing out to students. This module has been put together by Physics teachers in the Auckland region. We would encourage teachers to present the pages to students with a tailor-made cover sheet. It should include the following:- Designated assembly area & time of departure from the park Equipment needed Equipment provided (horizontal accelerometers) & time of return. Please note that in response to feedback from teachers, Rainbow’s End no longer provides force meters for students use, rather we have included a stepby-step guide for students to make their own equipment in the classroom prior to their visit. Rainbow’s End opens at 10am and students will need at least four hours to get the necessary measurements and make calculations. DODGEMS 1. Describe what happens to the motion of the cars in a nose to tail collision involving 2 cars. Sketch a vector diagram to show the forces acting during the collision. Description: 2. In this collision the passenger should measure the acceleration during the collision using the horizontal accelerometer. Ө = a = 3. Write down the mass of each person in the car. 4. Observe what happens to the heads of the people in the cars when a collision occurs. Write down a description of why this occurs. 5. The cars each have a mass of 175kg. Find the total mass of car and passengers and hence calculate the force acting on the car during the collision. 6. Calculate the force on one of the people in the car. Compare in with the force on the car. Explain why these forces are different. 7. Explain using momentum, why in real-life collisions people suffer from whiplash. MEASUREMENTS MEASURING TIME When measuring the period of a ride that rotates or swings, measure the time for several repetitions of the motion and calculate an average. When measuring a single event ride, like a train passing a given point, measure the times for several trains to pass the point and calculate an average. MEASURING DISTANCE 1. Pacing – a reasonable method is to pace out a distance given the known distance of your pace. Ideally count your paces over ten meters then work out the average length of your pace. 2. Ride Structure – some rides, such as the roller coaster, have regularly spaced cross supports. Estimate the size of one and then determine the length or height of the track. 3. Triangulation – use the horizontal accelerometer to find the angle up to the top of the structure. Estimate L by pacing or some other method. Then use h=LtanӨ and add to your own height. Never enter an area that is closed to the public. Guess your measurements if necessary. MEASURING ACCELERATION 1. Horizontal Acceleration – The ball bearings rise up the tube as the acceleration increases. Record the angle that they reach. The acceleration is given by a=gtanӨ, where g = 10ms-2. Be careful to hold the accelerometer along the line you expect the force to act. 2. Vertical Acceleration – The tube of the vertical accelerometer is marked with red bands which indicate multiples of acceleration due to gravity. It must be held vertically. Both accelerometers must be secured to your wrist using the rubber band when in use. Useful Formulae Ep = mgh V=d/t Vr = 2 (V average) Power = work / time Ek = ½ mv2 Ep = Ek F = mg sinӨ or Work = mgh Force factor = force felt / weight FAMILY CARTS This experiment requires a driver and a navigator to observe the accelerometer. 1. While you were waiting for your turn, use the time to measure how fast the cars go along the starting straight. Length of straight (paced) Time taken Speed s = d/t 2. Use the horizontal accelerometer to measure the acceleration of the car as it accelerates away from the rest when you start. Hold the accelerometer along the line of the car. Ө = a = 3. To find the centripetal acceleration, hold the accelerometer across the car as you go around one of the corners. Ө = a = 4. Write down your mass 5. Calculate the straight line force as you accelerate away from the rest. 6. Calculate the centripetal force acting on you as you go around the corner. (use f = ma) 7. Assume that your speed around the corner is roughly the same as your speed along the straight. Use a=v2/r to find the radius of the corner. ROLLER COASTER A B THE FIRST DROP Measurements/Estimations Note that A is the point just before you start descending. Quantity Your mass Time from A to B Height A from Ground Height B from Ground Length AB Measurement Unit Method Used Calculations Quantity Potential Energy at A Average Speed over AB Speed at B Kinetic Energy at B Potential Energy at B Formula Value How does the loss in potential energy from A to B compare with the gain in kinetic energy? Give reasons for any differences. Note these calculations assume your velocity at A is zero. The effect this has compared to the measurement error in your results is fairly small but you could estimate velocity at A if you wished and factor it into your calculations. SENSATIONS In the spaces below describe your perceived weight at each point. e.g. heavy, normal, etc. Then measure your downwards acceleration at those points and compare to gravitational acceleration. At A Halfway down AB At B Sensation Vertical Acceleration Compare to g = 10ms-2 Explain your results THE FIRST CORNER On the first corner the track is banked at an angle of 45°. Show the forces acting on the cart in this position on the diagram below. 45° State clearly the direction of the net force acting on the cart. How does the banking help the cart go round the corner? THE LOOP Use the vertical accelerometer to measure the acceleration at the top and the bottom of the vertical loop. To measure the acceleration at the top you will need to flip the vertical accelerometer over. Repeat three times and obtain an average. Position on Loop Direction of Acceleration relative to the ground Acceleration Trial 1 ms-2 Acceleration Trial 2 ms-2 Acceleration Trial 3 ms-2 Average Acceleration ms-2 Top Bottom Now draw a force diagram showing the individual and net forces acting at the top and bottom of the loop. Use your diagrams to explain the direction of the average acceleration measurements shown in the table above. Force diagram showing individual forces acting Force diagram showing net force Top of Loop Top of Loop Bottom of Loop Bottom of Loop Explanation of acceleration direction PIRATE SHIP 1. Time Period of Pirate Ship. Measure the time period T of the Pirate Ship. Time for 5 complete swings to get 5T. Repeat this 2 more times for accuracy then average. Now calculate the measured time for one complete swing. 5T Trial 1 5T Trial 2 5T Trial 3 5T Average T Average Measured Now try obtaining the time period by a less direct method. Estimate the height of the Pirate Ship, from the centre of the ship to the top of the support structure. Use T = 2π ට ࢎ to calculate T and compare to your earlier measurement. ࢍ Working Space T = 2π ට ࢎ ࢍ Comparison To use the above formula an assumption has been made about the motion of the Pirate Ship. What is the assumption? 2. Radial Acceleration of Pirate Ship Measure the maximum angle to the vertical of the sing of the ship. Ө Calculate the Amplitude using A = Calculate maximum velocity using Calculate acceleration using a= v= ࢜ ࢘ A Ө= 2πh A= ࣊ v= ࢀ A a= Now measure maximum radial acceleration directly, using an accelerometer, by sitting in the middle of the boat. a= Compare values of a LOG FLUME Measure the length of the final slide. 1. Decide for yourselves how to estimate this. Describe your method and write down your results here. 2. Measure the average time for a log to move from the top of the slide to the bottom. Time: Readings Average time = 3. Use a vertical accelerometer to measure the acceleration down the slide. A = 4. Use d = ut + ½ at2 to calculate acceleration down the slide, using your values for average time and for the length of the slide. Assume the velocity at the top is zero. 5. Explain any differences between your answers to measured acceleration (3) and calculated acceleration (4). Remember that the log is not actually falling vertically, it is falling at an angle to the horizontal. 6. Draw a diagram identifying the forces acting on you as you go down the slide. Assume the mass of three people in the log flume is 180kg, the weight of the long alone is 60 kg and the log flume drops vertically 10m on the last drop. 1. Calculate the potential energy of the log at the top of the slide. 2. Use the potential energy value to calculate the kinetic energy and hence the velocity at the bottom of the slide. 3. Discuss the energy exchanges from the time you board the log to the time you arrive back at the start. BUILD YOUR OWN FORCE METER You will need: A Sheet of OHP transparency Clear Sellotape A paper clip A stopper (we cut a piece off an eraser, but a cork or Blue Tac will do as well – as long as it fits tight) A Vivid or marker pen A really stretchy spring (1.5gms/cm and approximately 3cm unstretched) A 10 gram fishing sinker A rubber band A drawing pin Pliers Roll up the piece of transparency into a tube approx. 15 mm in diameter. Secure the ends by folding a piece of tape over the seam at each end. Stick the seam down at the centre with a small piece of tape before running a piece right down the tube to stick down the entire edge. Straighten out your paper clip and cut off a piece approx. 25 mm long. Bend it in half and thread it through one end of your spring. Apply a small piece of tape so that it will not come off. Push the paper clip in to the bottom of your stopper. Attach the sinker to the bottom of the spring & fix with tape. Insert the stopper in to the tube so that when held vertically the sinker and spring hang freely in the centre of the tube. Make sure the stopper is secure and wont shift from its position. Apply a piece of tape over the top of the tube. Hold your force meter horizontally, around the clear tube, take your vivid and make a mark where the bottom of the spring is sitting – Mark this with a ‘0’. Now hold the force meter vertically and do the same – mark this point with ‘1’. Measure the distance between 0 and 1. Put a mark the same distance away from the last one you made. e.g. if 0 and 1 are 2 cm apart, make the next mark around the tube 2 cm down from ‘1’. Repeat this process until you have 5 marks around your force meter. Using a drawing pin, poke a hole about 5mm up from the bottom of your force meter. Poke another hole opposite the one you have just made. Thread the rest of your paper clip through one side. Thread your rubber band on to the paper clip before you poke it through the other side. Use some pliers to bend the ends of the paper clip around into the tube so they won’t get caught on anything. Put a piece of tape over right over the end of the force meter. Now you have a nifty tether to put around your wrist, so you can’t lose your force meter on the rides! NOW THAT YOU’VE MADE IT ... Here’s how to use it! Your force meter will measure the amount of g-force you are experiencing on a ride. The numbers you marked on your force meter represent ‘G’s. This is the unit used to measure that force. Ever tried to lift your feet up while going around the Coca-Cola Corkscrew loop? Try it! – You will experience the effects of G force holding them down! Hold the force meter upright to measure the amount of Gs pulling you down, or during the loop, holding you in your seat. Pointing the top of the force meter in the direction that you are travelling and holding the other end to your body, will measure how much force is pushing on you as you move forward – you could try this on the Pirate Ship. Hold your force meter upside down to measure the negative G’s as you plummet towards the ground on FearFall. Who would’ve thought physics could be this fun?!