PLEASE SHOW ALL WORK AND STEPS!! In an old-fashioned amusement park ride, passen

Question

PLEASE SHOW ALL WORK AND STEPS!!

In an old-fashioned amusement park ride, passengers stand inside a 5.5-m-diameter hollow steel cylinder 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 0.61 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 kg allowed." What is the minimum angular speed, in rpm, for which the ride is safe? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Normal reaction = m*r*w^2

static friction must balane weight
To get minimum w, we need to have maximum coeefiecient

statis friction = m*g
miu*N = m*g
miu*m*r*w^2 = m*g
miu*r*w^2 = g
0.70*(5.5/2)*w^2 = 9.8
w^2 = 9.8*2/(5.5*0.70)
w = 2.23 rad/s

Answer: 2.3 rad/s

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