Marie Ronda Gab Freedman Chapter 4 Challenge: Paper Roller Coaster The Grand Slam Gravitational potential energy is the energy an object has as a result of its position in a gravitational field. Based on the mass of the marble, the height of the position, and the gravity (9.8m/s^2), the GPE differs throughout the roller coaster ride. When the marble is going down the incline, the GPE decreases because the height is decreasing, but the speed and kinetic energy will increase. The kinetic energy is the energy an object possesses because of its motion due to its speed. The higher the starting point when going down the incline (going from A to B), the marble has a larger change in GPE and at the bottom of the incline, the KE is larger. The kinetic energy is based on the mass and the velocity of the marble. The sum of the GPE and the KE are only going to remain the same if there are no losses of energy throughout the ride. Losses of energy may be due to friction or other sources. Newton’s first law states that an object at rest stays at rest and an object in motion stays in motion unless a force acts upon the object. When the roller coaster cart is going up the hill, the object is in motion at a constant speed without a force acting on it. Newton’s second law states that the acceleration of an object equals the force divided by the mass. The object is moving at a constant speed up the incline and therefore, has zero acceleration and no net force acting upon it either. Hooke’s law states that the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring. The ending of The Grand Slam roller coaster serves as a spring because it hits the backstop and bounces back as a spring would. The harder the marble hits the backstop, the further it bounces back. The more force it exerts on the backstop, the more force it pushes back. The acceleration of the roller coaster determines the apparent weight of the people riding it or in this case, the marble. The marble used in The Grand Slam coaster weighs 1.27 grams (equals 0.0125 N), if the force of the roller coaster is smaller than 0.0125 N, this means it is accelerating downwards. If the force is larger than 0.0125 Newtons, then the acceleration would be upwards. As the roller coaster moves upwards, (before point A), it is accelerating upwards, and would therefore show a larger apparent weight. The power of the coaster is the speed at which work is done and energy is transferred. The roller coaster cart can be pulled up the hill at a variety of speeds and the power describes the speed at which the work is being done. Scale Drawings Mass of marble = 1.27 g Et = GPE (point A) Et = 4.73 J Position A: Dimensions Height: 0.38 meters Width: .03 meters GPE = mgh GPE = (1.27) x (9.8) x (.38) GPE = 4.73 J KE = 1/2mv^2 KE = (1/2) x (1.27) x (.84)^2 KE = 0.45 J Et = 4.73 J Position B: Dimensions Height: 0.14 meters Width: 0.03 meters Distance Traveled: 0.19 meters GPE = mgh GPE = (1.27) x (9.8) x (.14) GPE = 1.74 J KE = ½ mv^2 KE = (1/2) x (1.27) x (0.76)^2 KE = 0.37 J Et = 4.73 J Position C Dimensions Height: 0.25 meters Width: 0.03 meters Distance Traveled: 0.2 meters GPE = mgh GPE = (1.27) x (9.8) x (.25) GPE = 3.11 J KE = 1/2 mv^2 KE = (1/2) x (1.27) x (.83)^2 KE = 0.44 J Et = 4.73 J Position D Dimensions Height: .06 meters Width: 0.03 meters Distance Traveled: 0.29 meters GPE = mgh GPE = (1.27) x (9.8) x (.06) GPE = 0.75 J KE = 1/2mv^2 KE = (1/2) x (1.27) x (.69)^2 KE = 0.30 J Et = 4.73 J Position E Dimensions Height: 0 meters Width: 0.03 meters Distance Traveled: 0.28 meters GPE = mgh GPE = (1.27) x (9.8) x (0) GPE = 0 J KE = 1/2mv^2 KE = (1/2) x (1.27) x (.54)^2 KE = 0.19 J Et = 4.73 J Length of Whole Roller Coaster: 0.57 meters Height of Whole Coaster: 0.38 meters Free Body Diagrams Roller Coaster Safety Roller coasters have wheels on the top of the rails, wheels on the side of the rails, and wheels on the bottom of the rails to prevent the coaster from flying off of the track in any direction. The brakes of the roller coaster divides the trains into blocks, which prevents the trains from ever crashing into each other and the brakes are powered by air pressure. Roller coasters also have over the shoulder restraints to keep passengers safe. On The Grand Slam coaster, there are barriers on either side of the track to prevent the marble from falling off or going off the sides. Also, there is a backstop at the end of the ride that serves as a spring and safely brings the marble to a stop. Works Cited “All About Roller Coasters.” Library Think Quest. Oracle Think Quest, n.d. Web. 12 June 2011. <http://library.thinkquest.org/5384/Safety_Features.html>.