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Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a spee
Question
Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 100km/h when it comes to the bottom B. Also, what should be the minimum radius of curvature p for the track at B so that the passengers do not experience a normal force greater than 4mg
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Physics
4 years
2021-07-28T06:44:48+00:00
2021-07-28T06:44:48+00:00 1 Answers
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Answers ( )
Answer:
a) 39.37 m
b) 26.25 m
Explanation:
Given
speed of the roller coaster, v = 100 km/h = 100 * (1000/3600) m/s = 27.78 m/s
Using the law of conservation of energy.
Potential Energy = Kinetic Energy
mgh = 1/2mv²
gh = 1/2v²
h = v²/2g
h = 27.78² / 2 * 9.8
h = 771.7284 / 19.6
h = 39.37 m
Also,
kmg – mg = mv²/p
kg – g = v²/p
p = v²/g(k – 1)
p = 27.78² / 9.8(4 – 1)
p = 771.7284 / 29.4
p = 26.25 m
Therefore, the height of the roller coaster is 39.37 m and the radius of curvature required is 26.25 m