1) A Top Thrill Dragster is a popular rollercoaster at Cedar Point Amusement Par
ID: 1777687 • Letter: 1
Question
1) A Top Thrill Dragster is a popular rollercoaster at Cedar Point Amusement Park. Fully loaded cars have a mass of 7,000kg and are accelerated horizontally to 120 miles per hour over a distance of 110m. They then follow the track vertically to a height of 420 feet. The cars then roll down a vertical track to the horizontal breaking section where the cars slow to 5 miles per hour over a distance of 85 meters. Find the following... a) How much work is done to accelerate the cars? b) How much Kinetic Energy do the cars have after launch? c) How fast do the cars go when they crest over the top? d) What is the slowing force on the cars at the end of the ride? a) b)Explanation / Answer
given,
mass = 7000 kg
final velocity = 120 miles/hour or 53.6448 m/s
distance = 110 m
by third equation of motion
v^2 = u^2 + 2as
53.6448^2 = 0 + 2 * a * 110
a = 13.080748032 m/s^2
work done = force * displacement
work done = mass * a * distance
work done = 7000 * 13.080748032 * 110
a) work done = 10072175.9846 J
kinetic energy = 0.5 m * v^2
kinetic energy = 0.5 * 7000 * 53.6448^2
b) kinetic energy = 10072175.9846 J
by conservation of energy
initial energy = final energy
10072175.9846 = mgh + 0.5 * mv^2
h = 420 ft or 128.016 m
10072175.9846 = 7000 * 9.8 * 128.016 + 0.5 * 7000 * v^2
v = 19.2 m/s
c) speed of car = 19.2 m/s
final velocity = 5 miles/h or 2.2352 m/s
v^2 = u^2 + 2as
2.2352^2 = 53.6448^2 + 2 * a * 85
a = -16.8986 m/s^2
slowing force = mass * a
slowing force = 7000 * -16.8986
d) slowing force = -118290.2 N
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