3. 1.5 points My Notes Ask Your Teacher A 30.0 kg child takes a ride on a Ferris

Question

3. 1.5 points My Notes Ask Your Teacher A 30.0 kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 21.0 m (a) What is the centripetal acceleration of the child? m/S -Direction- (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude direction (from upward) (c) What force does the seat exert on the child at the highest point of the ride? magnitude direction (from upward) (d) What force does the seat exert on the child when the child is halfway between the top and bottom? magnitude direction(from upward) 4.-11 points SerPSE9 6.P.063.MI My Notes Ask Your Teacher

Explanation / Answer

(a) T = 60 / 4 = 15 sec

w = 2 pi /T = 0.419 rad/s

r = D/2 = 21/ 2 = 10.5 m

a = w^2 r = 1.84 m/s^2 toward the center

(b) N - m g = m a

N = 30 (9.81 + 1.84) = 349.6 N 0 deg

(c) m g - N = m a

N = 30 (9.81 - 1.84) = 239.1 N 0 deg

(d) Nx = m a = 55.2 N

Ny = m g = 294.3 N

N = sqrt(Nx^2 + Ny^2) = 299.4 N

direction = tan^-1(Nx / Ny) = 10.6 deg

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