in an old-fashioned amusement park ride, passengers and inside a 5 m diameter hollow steel cylinder with their backs against the wall. the cylinder beings to ro

Question

in an old-fashioned amusement park ride, passengers and inside a 5 m diameter hollow steel cylinder with their backs against the wall. the cylinder beings to rotate about a vertical axis, then the floor on which th passengers are standing drops away. if all goes well, the passengers will stick to the wall and not slide down. if clothing has a coefficient of static friction of 0.6 - 1and kinetic coefficient pf 0.4-0.7. what is the min rotational velocity in revolutions per second for which the ride is safe?

Answer 1

The force of static friction f must be no lower than the weight mg of the person.  

 

N = normal force that cylinder wall applies to person = centripetal force

 

N = mv²/r

 

f = μ_sN  [This is the force that keeps the person from sliding down.]

 

f = mg

 

μ_sN = mg

 

μ_s(mv²/r) = mg

 

v = √(rg/μ_s)

 

Use the lowest coefficient of static friction. 

 

v_min = √(rg/μ_smin) = √[dg/(2μ_smin)] = √{5(9.8)/[2(0.6)]} m/s = 6.39 m/s