Consider a roller coaster as it travels near the bottom of its track as sketched

Question

Consider a roller coaster as it travels near the bottom of its track as sketched in the figure below.  At this point, the normal force on the roller coaster is four times its weight .  If the speed of the roller coaster is 16 m/s, what is the radius of curvature of the track?

         ? m

Consider a roller coaster as it travels near the bottom of its track as sketched in the figure below. At this point, the normal force on the roller coaster is four times its weight . If the speed of the roller coaster is 16 m/s, what is the radius of curvature of the track?

Explanation / Answer

N = mg + mv^2/r = 4mg

v^2/r = 3g

r = 8.70 m

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