Question

The Round Up carnival ride below has a radius of 3.90 meters and rotates 0.527 times per second. As shown, riders can be held up by only friction. What coefficient of friction is needed to keep the riders from sliding down? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

Given data:

* The radius of the carnival ride is r = 3.9 m.

* The linear frequency of oscillation is f = 0.527 Hz.

Solution:

The angular frequency (angular speed) of the oscillation is,

`\begin{gathered} \omega=2\pi f \\ \omega=2\pi*0.527 \\ \omega=3.31\text{ rad/s} \end{gathered}`

The frictional force acting on the ride is,

`F=\mu mg`

The force acting on the ride in terms of the angular speed is,

`F=m\omega^2r`

The frictional force acting on the ride is equal to the force acting on the ride for circular motion,

`\begin{gathered} \mu mg=m\omega^2r \\ \mu g=\omega^2r \\ \mu=(\omega^2r)/(g) \end{gathered}`

where g is the acceleration due to gravity,

Substituting the known values,

`\begin{gathered} \mu=((3.31)^2*3.9)/(9.81) \\ \mu=4.36 \end{gathered}`

Thus, the coefficient of friction is 4.36.