Question

In a "Rotor-ride" at a carnival, people rotate in a vertical cylindrically walled "room." If the room radius is 5.5 m, and the rotation frequency 0.5 revolutions per second (rps) when the floor drops out, what minimum coefficient of friction keeps the people from slipping down? What type of friction is this? People on this ride said they were "pressed against the wall," however what is really happening? 0.18

Answer 1

Answer:

0.181

Explanation:

We can convert the 0.5 rps into standard angular velocity unit rad/s knowing that each revolution is 2π:

ω = 0.5 rps = 0.5*2π = 3.14 rad/s

From here we can calculate the centripetal acceleration

$a_c = \omega^2r = 3.14^2*5.5 = 54.3 m/s^2$

Using Newton 2nd law we can calculate the centripetal force that pressing on the rider, as well as the reactive normal force:

$F = N = a_cm = 54.3 m$

Also the friction force and friction acceleration

$F_f = N\mu = 54.3 m \mu N$

$a_f = F_f / m = 54.3 \mu$

For the rider to not slide down, friction acceleration must win over gravitational acceleration g = 9.81 m/s2:

$g = a_f = 54.3 \mu$

$9.81 = 54.3 \mu$

$\mu = 9.81 / 54.3 = 0.181$