The roller coaster in Figure P6.36 starts with a velocity of 16.4 m/s. One of th

Question

The roller coaster in Figure P6.36 starts with a velocity of 16.4 m/s. One of the riders is a small girl of mass 25 kg. At points B and C, the track is circular with the radii of curvature given in the figure. The heights at points A, B, and C are hA= 24.95 m, hB = 34.7 m, and hC=0 m. You may assume the track is frictionless.

Find the velocity of the roller coaster at point B.

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Find the velocity of the roller coaster at point C.

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Find her apparent weight at B

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Find her apparent weight at C

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Explanation / Answer

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

-2*9.8*(34.7 - 24.95) = v'^2 - 16.4^2

v = 8.82383 m/s ==============a)

mg - mv'^2/r = 25*(9.8 - 8.82383^2/(9.75))

W' = 45.3590 N ===============b)

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

2*9.8*25 = vf^2 - 8.82383^2

vf = 23.8298 m/s ================c)

mg - mvf^2/r = 25*(9.8 - 23.8298^2/20) = -464.8242N ==============d)

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