You are riding on a Ferris wheel that rotates at a constant speed. The chairs swivel so you are always sitting upright. Explain why you feel weightless (i.e. the normal force of contact from the chair on you is zero) when your chair is at one specific location during the ride. Identify your chair’s location at the point where you feel weightless.

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Originally Posted by magus

You are riding on a Ferris wheel that rotates at a constant speed. The chairs swivel so you are always sitting upright. Explain why you feel weightless (i.e., the normal force of contact from the chair on you is zero) when your chair is at one specific location during the ride. Identify your chair's location at the point where you feel weightless.

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You need to do your own homework.
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I am helping with this because it is a very interesting question - may be of interest to many students.

For mass m to move in verticle circle, it must have centripetal force mv^2/r directed towards the centre.

Suppose it is at point P on the circle when normal reaction is 0. Let O be the centre of the circle and suppose OP makes angle X with the horizontal line.

There being no Normal Reaction, the vertically downward component of the
centripetal force mv^2/r (acting towards the centre) must equal the weight mg.

Hence mv^2/r Sin X = mg

Solving the above will give you the value of angle X and hence the location of P.