A roller-coaster car has a mass of 512 kg when fully loaded with passengers. The

Question

A roller-coaster car has a mass of 512 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 20.5 m/s at point circled A, what is the force exerted by the track on the car at this point?

b) What is the maximum speed the vehicle can have at circled B and still remain on the track?

Explanation / Answer

a] At point circled A,

N - mg = mv^2/r

N = mg + mv^2/r

= 512*9.8 + 512*20.5^2/10

= 26534 N

b] At point circled B,

mg - N = mv^2/r

mg = mv^2/r [ N = 0, as roller coaster leaves the track]

v = sqrt[gr]

= sqrt[9.81*15]

= 12.13 m/s answer

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