Energy, Circular Motion, & Apparent The roller coaster in Figure P6.36 starts wi

Question

Energy, Circular Motion, & Apparent

The roller coaster in Figure P6.36 starts with a velocity of 15.1 m/s. One of the riders is a small girl of mass 35 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 h_A = 24.6 m, h_B = 34.65 m, and h_C = 0 m. You may assume the track is frictionless. Find the velocity of the roller coaster at point B. Find the velocity of the roller coaster at point C. Find her apparent weight at B Find her apparent weight at C

Explanation / Answer

Here ,

m = 35 Kg

hA = 24.6 m

hB = 34.65 m

hC = 0 m

vA = 15.1 m/s

Using conservation of energy at A and B

0.5 * m * vA^2 + m * g * hA = 0.5 * m * vB^2 + m * g * hB

0.5 * 15.1^2 + 9.8 * 24.6 = 0.5 * vB^2 + 9.8 * 34.65

solving for vB

vB = 5.57 m/s

the speed of car at point B is 5.57 m/s

at the point C

Using conservation of energy at A and C

0.5 * m * vA^2 + m * g * hA = 0.5 * m * vC^2 + m * g * hC

0.5 * 15.1^2 + 9.8 * 24.6 = 0.5 * vC^2

vC = 26.6 m/s

the speed of car at 26.6 m/s

at the point B

apparent weight at B = m * (g - vB^2/r)

apparent weight at B = 35 * (9.8 - 5.57^2/10 )

apparent weight at B = 234.4 N

at the point C

apparent weight at C = m * (g + vBC^2/r)

apparent weight at C = 35 * (9.8 -+ 26.6^2/20 )

apparent weight at C = 1581.2 N

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