A 34.0-kg child takes a ride on a Ferris wheel that rotates...

A 34.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 22.0 m. (a) What is the centripetal acceleration of the child? magnitude 3.88 m/s² direction toward the center of the path (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude 464.4 N direction up toward the center (c) What force does the seat exert on the child at the highest point of the ride? magnitude 201.96 N direction down toward the center (d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.) magnitude 131.24 N direction ° counter-clockwise from the horizontal

Transcript

00:01 Hi, here in this given problem mass of the child in the ferris wheel, that is m is equal to 34 .0 kilogram.

00:17 Its rate of rotation means time period that will be 15 seconds as he makes four revolutions in one minute.

00:32 1 minute means 60 second.

00:35 So time period for 1 rotation that will be 15 second.

00:39 Its diameter diameter of ferris wheel, this is given as 22 .0 meter.

00:59 So its radius will be half of diameter means 11 .0 meter.

01:09 In the first part of the problem we have to find centipital acceleration of the child.

01:32 And that will be ac is equal to v square by r.

01:37 For v we may use, v is equal to r omega square by r means that is r into omega square and for omega 2 pi by t whole square.

01:52 So it comes out to be equal to 4 pi square into r by t square.

01:59 So plugging in the known values here, ac, that will be given by 4 pi square means 4 into 3 .14 square into radius 11 into t square means square of 15.

02:19 So it is calculated to be equal to 1 .93 meter per section.

02:25 Square one of the answer answer for the first part of the problem and its direction it is always directed towards center directed towards center always now in the second part of the problem at the lowest point of the ferris wheel if we draw the ferris wheel here at the lowest point suppose this is the chair this is the child over the chair is weight acting down centrifugal force that is also acting down and that is given as m -a -c so the reaction means force exerted by the seat over the child that will be equal to at the lowest point force exerted on the the child by the seed that will be n is equal to m g plus mac both downward.

04:01 Means this is m taken out 34 in the bracket 9 .8 plus 1 .93.

04:08 And finally it is calculated to be equal to 398 .8 newton.

04:16 Answer for the second part of this given problem and that will be directed up...

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