One of the most popular rides at carnivals is the one that resembles a large circular drum that rotates on its axis. Once the ride is spinning fast enough, the floor drops down and the riders are left pinned to the inside wall of the drum (I believe they are describing a ride called the gravitron but im not sure).
If the ride has a diameter of 5.2m and makes four complete rotations in 9.2s, determine:
a) the speed of the rider.
b) the centripetal acceleration of the rider.
c) the coefficient of friction required to keep the rider from slipping downwards along the drum wall when the floor drops down.
For part a) I used the following equations:
Δt=T time interval for one cycle is equal to a period.
For part b) I used the following equations:
For part c) I used the following equation:
The Attempt at a Solution
a) From the diameter given d=5.2m, so from this we can divide by 2 to give R=2.6m
With this value we can plug it into the Δd=2∏R equation to give 16.34m.
We go on to find the time interval for one cycle by doing Δt=9.2s/4 rotations= 2.3s
Then to find the speed of the rider we use v=Δd/Δt=16.34m/2.3s=7.10m/s and this is our final answer.
b)For this part of the question I used v=7.10m/s which was found in the previous part a) and r=2.6m, and plugged these values into ac=v2/r= 19.4 m/s2 as our final answer.
c) For the last part I simply plugged more values into v2=μgR and solved for μ. Which turned out to be μ=1.98
I would like to just ask if anyone would be able to verify that I did this problem correctly and that all the significant figures are being respected! Thank you so much for your time :)