A 36.0-kg child takes a ride on a Ferris wheel that rotates four times each minu
ID: 1497984 • Letter: A
Question
A 36.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 20.0 m. (a) What is the centripetal acceleration of the child? (a) magnitude: (b) direction (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? (a) magnitude: (b) direction (c) What force does the seat exert on the child at the highest point of the ride?. (a) magnitude: (b) direction (d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.) (a) magnitude: (b) direction
Explanation / Answer
(a) What is the centripetal acceleration of the child?
centripetal acceleration is omega^2 *R = (4*2pi/60)^2*(20/2) = 1.75 m/s^2
Magnitude= 1.75 m/s^2 direction is towards the center of the wheel.
b) What force does the seat exert on the child at the lowest point of the ride?
At lowest point writing the force equation, there are two force, force due to gravity and the normal force of seat.
Hence N - mg = ma
the magnitude of acceleration is constant because this is uniform circular motion.
N = m(g+a) = 36*(9.81+1.75) = 416.16 N
The magnitude is 416.16 N and the direction is vertically upward.
(c) What force does the seat exert on the child at the highest point of the ride?
At highest point writing the force equation for the motion,
mg-N = ma
N = m(g-a) = 36*(9.81-1.75) = 290.16 N
The magnitude = 290.16 N and the direction is vertically downward.
(d) What force does the seat exert on the child when the child is halfway between the top and bottom?
The seat will exert two forces one to balance the gravity force and another to provide centripetal acceleration.
Hence Force = mg upward + m*a to the right
F = 36*9.81 = 353.16 N upward and 36*1.75 = 63 N to the right
Hence magnitude = 358.73 N and the direction = 79.885 degree above horizontal