The roller coaster in Figure P6.36 starts with a velocity of 15.9 m/s. One of th

Question

The roller coaster in Figure P6.36 starts with a velocity of 15.9 m/s. One of the riders is a small girl of mass 39 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= 24.5 m, hB = 34.85 m, and hC=0 m. You may assume the track is frictionless.

Find the velocity of the roller coaster at point B. = 7.07 m/s

Find the velocity of the roller coaster at point C. = 27.07 m/s

Find her apparent weight at B

Find her apparent weight at C

Explanation / Answer

Her apparent weight will be
F = m(g ± v²/r)
where we use "-" on the crest of the hill
and "+" at the bottom of the "valley".

a) First find the velocity:
v² = u² + 2gh
(15.9 m/s)² = u² + 2 * 9.8m/s² * (34.85 - 24.5)m = u² + 202.86m²/s²
u² =49.95 m²/s²

F = 39kg * (9.8m/s² - 49.95m²/s² / 10m) = 156.56 N

(b) (15.9 m/s)² = u² + 2 * 9.8m/s² * (0 - 24.5)m = u² - 480m²/s²
u² = 732m²/s²

F = 39kg * (9.8 + 732m²/s²/20m) = 1446.51 N

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