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 26 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= 24.35 m, h_B = 35 m, and h_c = 0 m. You may assume the track is frictionless. Find the velocity of the roller coaster at point B. 7.76 m/s Find the velocity of the roller coaster at point C. 27.32 m/s Find her apparent weight at B 98.23 N Find her apparent weight at C

Explanation / Answer

here,

initial velocity , vA = 16.4 m/s

ha = 24.35 m

hb = 35 m

hc = 0 m

a)

let the velocity at be vB

using conservation of energy

0.5 * m * vA^2 + m * g * ha = 0.5 * m * vB^2 + m * g * hb

0.5 * 16.4^2 + 9.8 * 24.35 = 0.5 * vB^2 + 9.8 * 35

vB = 7.76 m/s

the speed at B is 7.76 m/s

b)

let the velocity at be vC

using conservation of energy

0.5 * m * vA^2 + m * g * ha = 0.5 * m * vC^2 + m * g * hc

0.5 * 16.4^2 + 9.8 * 24.35 = 0.5 * vC^2

vC = 27.32 m/s

the speed at C is 27.32 m/s

c)

apparent weight at B , W' = - m*vB^2 /rB + m * g

W' = 26 * ( - 7.76^2 /10 + 9.8)

W' = 98.23 N

d)

apparent weight at C , W' = m*vC^2 /rC + m * g

W' = 26 * ( 27.32^2 /20 + 9.8)

W' = 1225.1 N

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