Please show work, Thank you! The figure below shows a Ferris wheel that rotates
ID: 1344504 • Letter: P
Question
Please show work, Thank you!
The figure below shows a Ferris wheel that rotates four times each minute. It carries each car around a circle of diameter 18.0 m.
(a) What is the centripetal acceleration of a rider?
(b) What force does the seat exert on a 42.0 kg rider at the lowest point of the ride?
.
(c) What force does the seat exert on the rider at the highest point of the ride?
(d) What force (magnitude and direction) does the seat exert on a rider when the rider is halfway between top and bottom, going up?
° (measured inward from the vertical)
Explanation / Answer
The wheel rotates four times around the circle in a minute
a)
Then the speed of the wheel is
v = 4(2r/T)
=4(2*3.14*9/60)
=3.768m/s
centripetal acceleration is
ac =v2/r
=(3.768m/s)2/9m
=1.577m/s2
b)
The force acting at the lowest point is
Fbot =mg(1+v2/rg)
=(42 kg)(9.8 m/s2)(1+(3.768)2/(9)(9.8))
=477.86 N
c)
The force exerted by the seat at the highest pointis
Fhigh=m(g-ac)
= (42kg)(9.8-1.577)
= 345.366 N
d)
Force exerted by seat on a rider when the rider is half between toand bottom is
Fmid =mg2+ac2)
= (42) (9.8)2+(1.577)2
=416.89 N
The direction is
=Tan-1(ac/g)
=Tan-1(1.577/9.8)
=9.14o