Question

The figure below shows a Ferris wheel that rotates five times each minute. It carries each car around a circle of diameter 20.0 m.What force (magnitude and direction) does the seat exert on a 53.0-kg child when the rider is halfway between top and bottom? (direction is measured inward from the vertical)

I got 588.7365. It is telling me i am within 10% of the correct value but i cant seem to get the right answer. i tried again and got 538 which obviously isnt right because the correct answer is within 10% of 588

Answer 1

Important point to remember in this case is that at this point acceleration due to gravity will be downward, while centripetal acceleration will be inward, So there will be 90 deg angle between both acceleration,

So Now

g = 9.81 m/sec^2

ac = centripetal acceleration = V^2/R

V = 2*pi*R/T

R = radius of circle = 20/2 = 10.0 m

T = time period of one complete rotation = 5 times each minute = 60/5 = 12 sec

V = 2*pi*10/12 = 5.23 m/sec

Now

ac = 5.23^2/10 = 2.73 m/sec^2

Net acceleration will be

a = ac i - g j

a = 2.73 i - 9.81 j

|a| = sqrt (2.73^2 + (-9.81)^2)

|a| = 10.18 m/sec

Now net force at the mid point will be

Fnet = m*|a|

Fnet = 53*10.18 = 539.54 N

Now about the direction

direction = arctan (ac/g)

direction = arctan (2.73/9.81) = 15.55 deg inward

See that it's within the 10% of 588, as 10% of 588 = 58.8, so answer is in between

588 - 58.8 < Ans < 588 + 58.8

529.2 < Ans < 646.8

PLEASE UPVOTE.