A roller-coaster car has a mass of 508 kg when fully loaded with passengers. The

Question

A roller-coaster car has a mass of 508 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 [circled A] and [circled B] are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.
(a) If the vehicle has a speed of 19.1 m/s at point [circled A] , what is the force exerted by the track on the car at this point?
N

(b) What is the maximum speed the vehicle can have at [circled B] and still remain on the track?
m/s

Explanation / Answer

a) at A,

if at that point , car is at bottom point,

N - mg = mv^2 /r

N = 508 ( 9.81 + 19.1^2/10 ) = 18532.35 N

b) at point B,

mg - N = mv^2 /r

mg - mv^2/r = N

maximum speed will be when N = 0

so mg - mv^2 /r = 0

v = sqrt(rg) = 12.13 m/s

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