Question

QUESTION:

Part A: A Ferris wheel has diameter of 5.1 m and makes one revolution in 5.9 seconds. A person weighing 696 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (that is, the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

Part B: Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 264.1 m diameter rotating about its central axis. Astronauts walk on the inside surface of the space station. What rotation period will provide "normal" gravity?

Answer 1

here,

A)

diameter of wheel ,d = 5.1 m

radius of wheel , r = d/2 = 2.55 m

the time period , T = 5.9 s

weight of person , W = 696 N

the mass of person , m = W/g

m = 696 /9.81 kg = 70.95 kg

the normal force exerted on her by the beach , N = m * ( g - w^2 * r)

N = 70.95 * ( 9.81 - (2*pi/T)^2 * r )

N = 70.95 * ( 9.81 - (2*pi/5.9)^2 * 2.55 ) N

N = 491 N

B)

diameter , d = 264.1 m

radius , r = d/2 = 182.05 m

let the time period be T

the normal gravity , g = w^2 * r

g = (2*pi /T)^2 * r

9.81 = ( 2 *pi /T)^2 * 182.05

solving for T

T = 27.1 s

the rotation period is 27.1 s