Question

In an amusement park ride called The Roundup, passengers stand inside a 18.0 m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into avertical plane, as shown in the figure .
A)Suppose the ring rotates once every 4.40 s. If a rider's mass is 59.0 kg, with how much force does the ring push on her at the top of the ride?
B)Suppose the ring rotates once every 4.40 s. If a rider's mass is 59.0 kg, with how much force does the ring push on her at the bottom of the ride?
C)What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?

Answer 1

ω = 2*pi/T = 2*pi/4.4 =1.428

at top Fpush = mrω^2 - mg = 59 *(9*1.428^2 - 9.8) =504.61N

at bottom Fpush =mrω^2 + mg =59 *(9*1.428^2 + 9.8) =1661.0 N

mrω^2 = mg ==> ω = sqrt(g/r);ω =1.09 rad/sec

T = 2*pi/1.088 =5.774 seconds