ENERGY and the ROLLER COASTER

Key Questions What happens to the motion of a marble on a hilly track? How is energy conserved on a roller coaster? These are the key questions we will be investigating in this workshop. The investigations we will perform in this workshop are actually excerpts from investigation number 5.2 (Energy Conservation) Key topics already investigated: Basic mechanics Simple machines, work and energy Weight, gravity, and friction

Roller Coasters Millennium Force at Cedar Point: 300 ft drop 80 degree angle of descent 93 mph $25 million to build Fastest coaster: Japan, 106.9 mph Biggest wooden coaster drop: Paramount’s King Island, 214 ft drop How many people have ever been on a roller coaster? Spend a few moments bantering about this; perhaps ask about the nearest amusement park; people will usually comment on how amazingly scary the new coasters are. Rollercoaster facts: Millennium Force Roller coaster at Cedar Point: 300 ft drop Angle of descent 80 degrees Top speed 93 mph 4th fastest coaster in world Cost $25 million Fastest coaster in world: Dodonpa in Japan: 106.9 mph; 4.3 g-force Biggest wooden coaster drop: Son of Beast; Paramount’s King Island 214 ft drop www.rcdb.com give lots of statistics (roller coaster database)

Where does the marble move the fastest? Show the overhead or slide that has the diagram of the Rollercoaster with 7 numbered positions. Where do you think the marble is moving the fastest? They should pick one of 7 positions, and remember their prediction. Where do people usually scream the loudest on a roller coaster? Someone will come up with a witty remark like – “when I’m being dragged into the 2 hour line”, but most will say when the cars just go over the first hill. Ask them: Is this where the marble is moving the fastest? (open-ended question, no definitive answer necessary) Place the photogate at position #1. Make sure the back of the photogate fits snugly against the bottom of the track. One person in the group should roll the marble 3 times, and see if they get the same time each time they roll it. This is to check the consistency of the release technique. Times can be different in the 4th decimal place, but it is quite easy to get three times in a row that are exactly the same. This emphasizes the repeatability of the equipment.

At what two positions is the marble moving the fastest? What is unique about these two positions? The highest speed measured should be at position 7 or 3, the lowest points on the track. In some cases, however, position 3 is the fastest because friction (the rubbing of the ball against the track) slows the ball down by the time it gets to the end of the track. The highest speeds occur at lowest points on the rollercoaster. Why? Gravity has been acting on the marble, causing it to accelerate all the way down the hill. At the very bottom of the hill, the marble moves horizontally and is therefore no longer accelerating. The marble may ACCELERATE most at positions 2 and 6, but it will have greatest speeds at 3 and 7 since any acceleration at all, even while tiny, still increases the speed. You may stop here if you need to. It should take no more than 30 min. to reach this point.

How does the speed of marble 1 compare to the speed of marble 2? How does the time it takes each marble to reach this point compare? OPTIONAL SLIDE Some participants will still believe that the speed of the marble is determined by the steepness of the downward slope rather than the height of the marble. This is a common misconception, because it turns out they are thinking of something entirely different. Marble 1 and marble 2 are at the same speed on the diagram. However, it takes less time for marble 1 to reach this speed than it takes marble 2, because the slope is steeper and the acceleration is greater. This is where the steepness comes in! It affects the time it takes the marble to reach a certain speed, but the speed is directly dependent on height. This can be shown on the CPO coaster, because you can find that the marble is going the same speed in 3 different places on the coaster, and these places are all the same height above the table. One of these positions will even be during an uphill trip! This really blows students away! They enjoy learning that something going uphill can be traveling at the same speed as something going downhill. We are getting at the fact that the coaster is all about tradeoff between potential (height) energy and kinetic (speed) energy.

ENERGY WORK Is the ability to do work. Is stored work Unit - joules Force x Distance Unit – joules Any object that has energy has the ability to create a force

Energy of height – relative to Earth's surface. Potential Energy that is stored Energy of height – relative to Earth's surface. Ep = mgh m = mass (kg) g = gravity (m/sec2) h = ht (meters) TOP OF THE HILL Potential Energy comes from the position of an object relative to Earth. Lift an object off a table – it took work to lift it – going against gravity. The energy is now stored in the object. How much energy - ? It took work to lift the marble – energy is stored work – so the energy is = to the work it took to lift the object. E p = mgh

A moving mass exerts forces KINETIC Energy of Motion A moving mass exerts forces Ek = ½ mv2 M = mass (kg) V = speed (m/sec) Ek increase as the square of the speed. This means if you go twice as fast, your energy increases by four times (2 squared) More energy more force to stop – which is why driving fast is dangerous. Why drive so slow in a school zone?

Investigate the relationship between speed and height more closely Find the speed of the marble for each of 12 different positions on the coaster Whn finished, please complete the speed vs. position graph You may not have time to continue the investigation here. If you do not, simply refer participants to the graph in the investigation 5.2 handout, and have them predict what the speed vs. position graph will look like. Show the graph on the next slide to see how their prediction compares to the shape of an actual graph.

Input vs. Output Efficiency (%) Work Output is always less than Work Input Where does it go? Friction – thermal energy Efficiency (%) A machine is 100% efficient when input = output work. Wo / Wi x 100 As the Inv. progresses, it becomes obvious that the amount of string needed to continue to lift the block the same height mounts up quickly. The Force required decreases by half with the first arrangement, so that too becomes clear. After the calculation of the Work IN and Work Out, it makes sense that these should have close to the same value. (Any discrepancies you may have seen were probably due to limitations in the force scale used in the Inv.) Why would the Output less than Input? Our old nemesis Friction. Friction “ takes “ some of the Input Force, which reduces the total Output Force, and consequently the Work Output. The better a simple machine reduces friction, the closer the Work Input and the Work Output will match.

The Work – Energy Theorem The total amount of Work that can be done is equal to the total amount of Energy available. Objects cannot do Work without Energy Energy can be stored for later use The work-energy theorem defines energy as the ability to do work. We can store energy in objects in many different ways. Batteries are an example of stored energy, as is a tightly coiled spring or a boulder high on a mountain. Each have the ability to do work.

The Work – Energy Theorem Energy can be converted or transformed (from one form to another) Anything with energy can produce a force capable of action over a distance This is where the concept of energy enters the vocabulary, and since we have just learned about work, the transition makes a lot of sense when we think of energy as stored work and/or the ability to do work. RADIANT CHEMICAL ELECTRICAL NUCLEAR

COOL GRAPH! Height and speed are inversely related! When the marble is high (has lots of potential energy), the speed is low (not much kinetic energy) When the marble is low (little potential energy) the speed is high (lots of kinetic energy) How is energy conserved on a rollercoaster? Total energy is constant because of constant trade-offs between potential and kinetic – some energy is “lost” from our system due to what? Friction. What does this mean about the first hill of a rollercoaster? IT BETTER BE THE HIGHEST! Special challenge: See if you can find the exact release point that will allow the marble to come to a screeching halt at the top of the hill. Good luck!

THROWING A BALL INTO THE AIR