The roller coaster in the figure below starts with a velocity of 17 m/s. One of

Question

The roller coaster in the figure below starts with a velocity of 17 m/s. One of the riders is a small girl of mass 31 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is circular, with the radii of curvature given in the figure. The heights at points A, B, and C are hA = 10 m, hB = 20 m,and hC = 0.

Assume friction is negligible and ignore the kinetic energy of the wheels. (The figure is not necessarily drawn to scale.)

Find weight at B and weight at C in Newtons

Explanation / Answer

At B: mg(hB - hA) = 0.5mv'^2 - 0.5mvo^2

-2*9.8*(20 - 10) = v'^2 - 17^2

v' = 9.64 m/s

Hence apparent weight = mg - mv'^2/r = 31*(9.8 - 9.64^2/(10))

W' = 15.71 N

At C: mg(hB) = 0.5mvf^2 - 0.5mv'^2

2*9.8*20 = vf^2 - 9.64^2

vf =17.29m/s

Hence apparent weight at C

mg - mvf^2/r = 31*(9.8 - 17.29^2/20) =-159.56 (negative means opposite to the direction of weight due to gravity)

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