Part A In an amusement park ride called The Roundup, passengers stand inside a 1
ID: 1773096 • Letter: P
Question
Part A In an amusement park ride called The Roundup, passengers stand inside a 19.0 m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure (Figure 1) Suppose the ring rotates once every 4.00 s. If a riders mass is 55.0 kg, with how much force does the ring push on her at the top of the ride? Submit My Answers Give Up Part B Suppose the ring rotates once every 4.00 s. If a rider's mass is 55.0 kg, with how much force does the ring push on her at the bottom of the ride? Figure 1 of 1 Rotation axis Submit My Answers Give Up 0 Part C What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?Explanation / Answer
formula for period is
v = 2pi r/ T= 2pi ( 9.5 m)/4.0 s = 14.915 m/s
Apply Newton second law of motion along y direction
Fy = N+mg = ma
N+ mg = m v^2/r
N = m v^2/r - mg
= 55 (( 14.915)^2 /(9.5 m) - 9.8)
=748.91 N
(b)
at bottom
Fy = N - mg= m v^2 /r
N = mv^2/ r + mg
N=55 (( 14.915)^2 /(9.5 m) +9.8)
=1826.91 N
(c)
N = 0 at the top
-mg = -mv^2/r
v= sqrt rg = sqrt 9.5 (9.8) = 9.64 m/s
T = 2pi r/ v = 2pi (9.5)/9.64 m/s = 6.18 s
(c)
N= 0 at top
Fy =