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Transcript
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>.