Question

With their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kgallowed."

What is the minimum angular speed, in rpm, for which the ride is safe?

Answer 1

w1 = 4.04 / √r

Step-by-step explanation:

This exercise should be done using Newton's second law, where the centripetal month acceleration, write the equation for the vertical axis and the radius of rotation

Y Axis

fr - W = 0

fr = W

X axis (radial)

N = m
`a_(c)`

The equation for the force of friction is

fr = μ N

Let's replace

μ (m
`a_(c)` ) = mg

Centripetal acceleration is

`a_(c)` = v² / r

v = wr

`a_(c)` = w² r

μ w² r = g

w = √(g/μ r)

In order for the trip to be safe, people must not move, so the friction must be static, let's calculate the angular velocity for the extreme values ​​of the friction increase

μ = 0.60

w1 = √ (9.8 / 0.6 r)

w1 = 4.04 / √r

μ = 1.0

w2 = √ (9.8 / 1 r)

w2 = 3.13 / √r

To finish the calculation you need the radius of the cylinder, but for the same radius the safe speed is w1