Antonia C. Physics HL Aspects of Physics Case Study: Amusement Parks On the 26th of February, 2011 our class went on a field trip in order to analyse the aspects of physics present in amusement parks. I chose two aspects based on my favourite rides: ‘Kaboom’ (which works based on free-fall) and the roller coaster. ? The Physics of Roller Coasters How does a Roller Coaster work? Roller coasters have no engines (although many still tend to think they do) and are thus not propelled around the track by a motor.
The transfer of potential energy to kinetic energy is what steers the roller coaster, and all of the kinetic energy required for the ride is present once the coaster goes down the first ‘hill’. Laws of Gravitation Gravitational energy takes place due to the gravitational force by which matter attracts other matter. As the coaster is pulled up the first ‘peak’ of the coaster, the gravitational energy increases. When the coaster Montezum Roller Coaster reaches the backside of the hill, the gravitational force is what causes it to accelerate.
A great part of the roller coaster’s gravitational energy is converted to kinetic energy on the backside of the first ‘peak’. As the coaster goes up the second ‘peak’, its kinetic energy is converted back into gravitational energy. Since the roller coaster’s kinetic energy at the end of its first ‘peak’ is less than its gravitational energy at the beginning of this same ‘peak’, the second ‘crest’ is shorter than the first.
If the second ‘hill’ were as tall as the first one, the coaster would stop before getting to the top of the second ‘peak’ and would thus start moving in reverse. Every hill in the track must be smaller than the previous one, except if the coaster is pulled once again (as it was when going up the first ‘peak’). Centripetal Forces On a looping coaster, the general rules of centripetal force are applicable since the ‘train’ is turning at every point during the loop. The force that makes it possible for the train to turn through the loop is called the centripetal force.
As the train starts going up the loop, gravity and momentum are pulling the train ‘out’ of the loop, so the structure of the track provides the “seat force” that Antonia C. Physics HL moves the train through the loop–the centripetal force. On its upward climb, the train gets to a point where gravity is no longer pulling it towards the outer direction of the loop and subsequently it is acting as part of the centripetal force pulling the ‘train’ towards the centre of the loop; ‘circle’.
It is from this point to the peak of the loop that it is crucial that the train has sufficient momentum to work against the forces pulling it toward the centre of the loop. That is a distinctive aspect of centripetal force on a vertical axis there must be a sufficient amount of outward momentum to counteract the increase in the centripetal force that takes place in the higher part of the loop. Centripetal force is what keeps people from falling from their seats!
Thus, considering the results/data collected during the field trip, we may estimate (not calculate, since we must bear in mind that the methods of data collection were not accurate) the centripetal force present in the roller coaster with the loop (Katapul) and the one without the loop (the Montezum roller coaster): Katapul Roller Coaster Fcentripetal = m Fcentripetal = 6000 x Fcentripetal = 354133. 8 N Montezum Roller Coaster Fcentripetal =m Fcentripetal = 7500 x = Fcentripetal = N (since we do not know the value of r) Antonia C. Physics HL The Physics of Free-fall rides Free Fall A free falling body is an object that moves under the effect of gravity only. Such objects have a downward acceleration toward the centre of the earth. Free-fall rides consist of three distinctive parts: the ride to the top, the brief suspension when reaching the top, and the downward thrust. In the first part (the ride to the top), force is applied to the ‘car’ to lift it to the apex of the free-fall ride. The amount of force Brief suspension before the ‘car’ suddenly required depends on the mass of the car and those riding it.
Following a short period in which the ‘passengers’ are ‘hanging’ in the air, the car drops suddenly and begins accelerating towards the ground under the effect of Earth’s gravity. The plunge is usually very thrilling to those on the ride (giving the common feeling known as ‘butterflies in the stomach’). As one is dropped down in the free-fall ride all the potential energy stored whilst the ‘car’ ascended up the tracks is converted into kinetic energy – this is an example of the law of conservation of energy.
Nevertheless, considering this is a “real life” example, all the potential energy is not changed into kinetic energy as some of the energy is lost to friction. While falling, one will be in freefall – which generates a feeling of weightlessness. This feeling is due to the fact that the only force acting on you is gravity. Theoretically, free fall, explains any motion that is affected solely by gravitational forces. In a vacuum all objects will have the same acceleration when dropped. This acceleration is known as the acceleration due to gravity, represented by g, which is equivalent to 9. 8 m/s -2.
Therefore, taking into account that: g = 9. 8 ms -2 (acceleration due to gravity) ? t = the time travelled Let us consider the results/data collected during the field trip to calculate both speed & distance, as well as the kinetic energy. drops and accelerates towards the ground. ‘Car’ dropping down I. Velocity The speed at which an object is falling during free fall can be determined, when started at rest, by: v = g x ? t g = 9. 8 ms ? t=3s v = 9. 8 x 3 = 29. 4 ms -1 -2 Antonia C. Physics HL II. Distance The distance an object travels during free fall can be determined (when started at rest) by ?s = = 9. 8 ms -2 ? t=3s ? s = 0. 5 x 9. 8 x (3)? = 44. 1m g (? t)? III. Kinetic Energy At the top of the free-fall ride, the kinetic energy is represented by: K. E. = PE K. E. = P. E. (‘car’ at rest) K. E. = mg? h K. E. = 1000 x 9. 8 x 69 (not taking the mass of the ‘passengers’ into account) K. E. = 690000 J Actual values: v = 94 kmh-1 ? 26. 1 ms -1 ? s = 69. 5 m Bibliography: http://www. hopihari. com. br/kamindamundi/conheca_kamindamundi_latoureiffel. aspx [Accessed 12, March 2011] http://ffden-2. phys. uaf. edu/211_fall2002. web. dir/shawna_sastamoinen/Gravity. htm [Accessed 12, March 2011]