A 53.0 kg child takes a ride on a Ferris wheel that rotates four times each minute & has a diameter of 24.0m?

Question

a) What is the centripetal acceleration of the child?_____m/s

(b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? _____N

c)What force does the seat exert on the child at the highest point of the ride? magnitude ______N
direction_______

d) What force does the seat exert on the child when the child is halfway between the top and bottom?magnitude______N
direction_______

only need help on this on guys. keep getting the wrong answers, Thanks!

Answer 1

Given: w (angular rate in rad/sec) = 2*pi*1/15; R=12; M=53
a. CA (centripetal acceleration) = w^2*R
b. CA & g act in the same direction. F(low) = M*(g + CA), directed upward.
c. CA & g act in opposite directions. F(high) = M*(g - CA); since CA < g, F(high) is also directed upward.
d. CA & g act at right angles to each other. If there is no friction or other restraint between child and seat, F(middle) = M*g directed upward, and the horizontally-acting CA causes the child to slide sideways off the seat. F(middle) then becomes 0 and the kid plunges at least 12m to a horrible death. If friction or other restraint prevents sliding, F(middle) = M*sqrt(g^2 + CA^2) and is directed upward and inward at an angle of arctan(CA/g) from the vertical, and there is no drama.