z12=0.5x,? Z2 Y. X, 1 A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above. Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion in terms of the distance from the lowest point, g1 = 2. a. What is the kinetic energy of the cart? b. What is the potential energy of the cart? c. What is the equation of motion for the cart?

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Solving for the kinetic energy requires the use of Lagrangian and variational calculus. Thank you in advance!

z12=0.5x,?
Z2
Y.
X,
1
A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure
above. Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of
motion in terms of the distance from the lowest point, g1 = 2.
a. What is the kinetic energy of the cart?
b. What is the potential energy of the cart?
c. What is the equation of motion for the cart?
Transcribed Image Text:z12=0.5x,? Z2 Y. X, 1 A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above. Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion in terms of the distance from the lowest point, g1 = 2. a. What is the kinetic energy of the cart? b. What is the potential energy of the cart? c. What is the equation of motion for the cart?
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