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

Answer:

w1 = 4.04 / √r

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