A roller-coaster car has a mass of 499 kg when fully loaded with passengers. The

Question

A roller-coaster car has a mass of 499 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_1 = 10. 0 m and r_2 = 15. 0 m, respectively. If the vehicle has a speed of 19. 2 m/s at point what is the force exerted by the track on the car at this point? Draw a free-body diagram of the cart at the point Include only 'real' forces (i. e. do not include anything labeled centripetal or centrifugal). In what direction should the net force point? N What is the maximum speed the vehicle can have at and still remain on the track?

Explanation / Answer

a)
At point A, normal force must exert force equal to m*g and centrepetal force
N = m*g +m*v^2/r1
= 499*9.8 + 499*(19.2)^2/ 10
= 4890.2 + 18395.136
= 23285 N
Answer: 23285 N
b)
N force should be minimum = 0
mg must provide centrepetal force
m*g = m*v^2/r2
g = v^2/r2
9.8 = v^2/15
v=12.12 m/s
Answer: 12.12 m/s

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