Question

The roller coaster in Figure P6.36 starts with a velocity of 15.8 m/s. One of the riders is a small girl of mass 40 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 m, hB = 34.15 m, and hC=0 m. You may assume the track is frictionless. At point B r = 10m, at point C r = 20m.

Find her apparent weight at B.

Find her apparent weight at C.

Answer 1

mass, m=40 kg

initial velocity, VA=15.8 m/sec

height, hA=24m , hB=34.15 m, hC=0

at point B, radius, r=10m

at point C, radius, r=20m

a)

at point B,

1/2*m*vA^2+m*g*hA=1/2*m*VB^2+m*g*hB

vA^2+g*hA=VB^2+g*hB

VB^2=vA^2+2g*(hA-hB)

vB^2=15.8^2+2*9.8*(24-34.15)

===> VB=7.12 m/sec

apparent weight at B, F=m*g-m*VB^2/r

=40*9.8-40*7.12^2/10

=189.22 N

b)

at point C,

1/2*m*vA^2+m*g*hA=1/2*m*VC^2+m*g*hC

vA^2+g*hA=VC^2+g*hC

VC^2=vA^2+2g*(hA-hC)

vC^2=15.8^2+2*9.8*(24-0)

===> VC=26.833 m/sec

apparent weight at C, F=m*g+m*VC^2/r

=40*9.8+40*26.833^2/20

=1832.02 N