Question

To be safe, the engineers making the ride want to be sure the normal force does not exceed 1.5 times each persons weight - and therefore adjust the frequency of revolution accordingly. What is the minimum coefficient of friction now needed?

Answer 1

Answer:

The minimum coefficient of friction is 0.666

Explanation:

Suppose, In a classic carnival ride, patrons stand against the wall in a cylindrical shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the “stick” to the wall so they do not slide down. In one ride, the radius of the cylindrical room is R = 7.6 m and the room spins with a frequency of 20.9 revolutions per minute.

Given that,

The normal force does not exceed 1.5 times each persons weight

$N=1.5 mg$

We need to calculate the minimum coefficient of friction

Using balance equation

$\mu N=mg$

$\mu=\dfrac{mg}{N}$

Where, N = normal force

Put the value into the formula

$\mu=\dfrac{mg}{1.5 mg}$

$\mu=\dfrac{1}{1.5}$

$\mu=0.666$

Hence, The minimum coefficient of friction is 0.666