A roller-coaster car has a mass of 491 kg when fully loaded with passengers. The

Question

A roller-coaster car has a mass of 491 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r_2 = 10.0 m and - 15.0 m, respectively. If the vehicle has a speed of 19.7 m/s at point what is the force exerted by the track on the car at this point? N What is the maximum speed the vehicle can have at ® and still remain on the track? m/s

Explanation / Answer

a)
Normal force acts upward
m*g acts downward
use:
net force = centrepetal force
N-m*g = m*v^2/r1
N - 491*9.8 = 491*(19.7)^2 / 10
N - 491*9.8 = 19055.22
N - 4811.8 = 19055.22
N = 23867.35 N
Answer: 23867.35 N

b)
for maximum speed, Normal force at B should be 0
m*g must provides centrepetal force
m*g = m*v^2/r
g = v^2/r
9.8 = v^2/15
v = 12.12 m/s
Answer: 12.12 m/s

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