Question

On an amusement park ride, riders stand inside a cylinder of radius 8.0 m. At first the cylinder rotates horizontally. Then after the cylinder has acquired sufficient speed, it tilts into a vertical plane, as shown in the diagram. At top speed, the cylinder rotates once every 4.5 s.

The mass of one rider is 71 kg. When the rider is at the highest point and traveling at the top speed, with how much force is the rider pushed against the wall of the cylinder?

700 N

1800 N

410 N

1100 N

Answer 1

410 N

Step-by-step explanation:

At the highest point, there are two forces pushing the man towards the centre of the cylinder: the normal reaction (N) and his weight (W=mg). The sum of these two forces must be equal to the centripetal force. So we have

`N+mg=m\omega^2 r` (1)

where

m = 71 kg is the mass of the rider

g = 9.8 m/s^2

r = 8.0 m is the radius of the cylinder

`\omega` is the angular frequency

The cylinder rotates once every 4.5 s (period), so its angular frequency is

`\omega=(2\pi)/(T)=(2\pi)/(4.5 s)=1.40 rad/s`

So by solving eq.(1) for N, we find the force with which the wall pushes the rider:

`N=m\omega^2 r-mg=(71 kg)(1.40 rad/s)^2(8.0m)-(71.0kg)(9.8 m/s^2)=417.5 N \sim 410 N`