12. Question Detalls SerCP8 7 P.031 A 44.0 kg child takes a ride on a Ferris whe
ID: 2032540 • Letter: 1
Question
12. Question Detalls SerCP8 7 P.031 A 44.0 kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 23.0 m (a) What is the centripetal acceleration of the child? (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude direction o (from upward) (c) What force does the seat exert on the child at the highest point of the ride? magnitude direction o (from upward) (d) What force does the seat exert on the child when the child is halfway between the top and bottom? magnitude direction o (from upward) Need Help? Read it Talk to a Tutor Show My Work (Optional)Explanation / Answer
given data
m = 44 kg
d = 23 m
Time period, T = 60/4 = 15 s
a) angular speed of the wheel, w = 2*pi/T
= 2*pi/15
= 0.4189 rad/s
centripetal acceleration, a = r*w^2
= (d/2)*w^2
= (23/2)*0.4189^2
= 2.02 m/s^2
b) F = m*g + m*r*w^2
= 44*9.8 + 44*2.02
= 520 N
direction : 0 degrees from upward
c)
F = m*g - m*a
= 44*9.8 - 44*2.02
= 342 N
direction : 180 degrees from upward
d) F = sqrt( (m*g)^2 + (m*a)^2)
= sqrt( (44*9.8)^2 + (44*2.02)^2)
= 440 N
direction : theta = 90 + tan^-1(m*g/(m*a))
= 90 + tan^-1(g/a)
= 90 + tan^-1(9.8/2.02)
= 90 + 78.3
= 168.3 degrees
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