Problem 10 (25 pts) A new attraction at Six Flags has riders get into a large cy
ID: 1448953 • Letter: P
Question
Problem 10 (25 pts) A new attraction at Six Flags has riders get into a large cylinder of radius 2.1 meters which rotates with a speed of 6.5 m/s before the floor drops out. It is your job to design the attraction such that riders will stick to the wall when the floor drops. (A) Calculate the necessary coefficient of static friction that the walls must have (10 pts) (B) If the walls of the cylinder can only stand a force of 2000 Newtons, what is the maximum mass a rider can have and still go on the ride (10 pts) (C ) What is the centripetal acceleration experienced by the riders during the ride (5 pts)
Explanation / Answer
Given that
radius R=2.1 m
speed V=6.5 m/s
this problem belong to newtons laws of motion with friction
according to vechicle taking a turn on a horizontal road
so speed V^2 =(co -efficient of static friction )*g*r
(A) ans
the co.efficient of static friction = V^2 /gr
=(6.5)^2 /9.8*2.1
=42.25 /20.58
=2.053
(B) ans
the force F=2000 N
this basing on vechicle taking a turn on horizantal road
force F= (co.efficient of static friction) Mg
2000 = 2.053 M *9.8
2000 =20.1194 M
Mass =2000/20.1194 =99.41 Kg
(C) ans
the centripetal acceleration a = V^2 /r
=(6.5)^2 /2.1
=20.119 m/s^2
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