weighless at the top of a Ferris Wheel?

Question

How many revolutions per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point of the trip?

I don't understand under what conditions a person would feel weightless.

If someone could explain it to me, I'll be able to solve it on my own.

Answer 1

You would feel weightless under two conditions, either when gravity was offset by another force like centrifugal force, or when you were falling at the same acceleration as gravity. On a ferris wheel those two would max out after you reached the top and were starting down.

My integral Calculus is not good enough to calculate that point or the speed, and I wouldn't know how to type such a formula if it was, but I'm sure that you could add the vectors to find when it reached zero. It would of course be for an instant only, as a higher speed would have two points when it was zero and a space when you would be launched out of the chair unless you were held in.

Answer 2

When you travel in circular motion, like on a Ferris wheel you feel a force pushing you away from the center of the Ferris wheel. This is the same force you feel in a string with a weight on the end when you swing it in a circle. This is known as centrifugal force. In order to feel weightless at the top of the Ferris wheel, the centrifugal force must equal the force of gravity. This happens at the top where the centrifugal force is in the opposite direction of gravity. At the bottom of the wheel, the centrifugal force is in the same direction as gravity so you would feel heavier.

What is the speed the Ferris wheel needs to travel? Well the centrifugal acceleration is given by v^2/r with v = velocity you are traveling along the circle and r is the circle radius. This must equal g, the acceleration of gravity so g = v^2/r, but note that the velocity is also given by wr (w is actually omega, the angular velocity) substituting we get g = wr. Finally note that w is 2 x pi x rev where rev is the number of revolutions per second and you get rev = g/(2 x pi x r).

Answer 3

The earth pulls all objects toward its center with a force = mg. (m: mass g: acceleration due to gravity = 9.8m/s^2).

When we stand on the floor, we press the floor with this force. The floor prevents us from going into the floor by providing an equal but opposite force.

This upward force acting on us is the normal reaction.

This normal reaction is called ‘apparent weight’

What we normally sense as weight is this apparent weight only.

When the normal reaction and the weight are equal and opposite, the net force acting on us is zero and we stand still.

The situation at the top most point of the trip in a Ferris wheel is different from this.

At that point we are not at rest; we are moving horizontally with certain velocity at that instant. Of course, the next instant the direction of motion will change.

At that point also, the earth is pulling us down ward.

Any object, moving in a particular direction, is acted on by a force perpendicular to the motion, and then the path of the object will be an arc of a circle at that instant.

The point to note is that the object is not moving in the direction of the force. If we imagine a floor beneath the object, then the object will not press the floor. That is there will not be any reaction force on the object.

Thus at the top point of Ferris wheel, even though the earth is pulling us down, there is no reaction force on us. This situation is stated as weight less ness.

However, this condition is achieved only when the speed and radius of the circle is such that v v / r = g. (v: velocity r: radius)

Or w w r = g (w: angular speed at that point)



w w r = 9.8, (Radius = 7.5 m).
w = (9.8 / 7.5) ^ (0.5) =1.14 radian/s. = 68.4 radian / minute.
‘N’ be the number of revolutions per minute.
Angular speed = 2pi N radian /minute.
2pi N = 68.4
N = 10.8 revolutions /minute


Do not confuse yourself with the centrifugal force. There is no such force acting on a body in circular motion. The centrifugal force is ,as per Newton's third law ,is acting on the object which produces the centripetal force. If these two forces were acting on one and the same object then the net force will be zero and the object will not move in a circular path.

Answer 4

You will always have a force acting on you at the top of a ferris when no matter what speed you go at. Whenever you travel in a circle, by definition, your velocity is always changing. Ergo, you have to have acceleration, which is incompatible with weightlessness.

While coming down though, if the wheel moves down faster than you would fall normally, you would experience brief moments of weightlessness, or even negative weight as the wheel pulls you down along with it.

You will feel weightess when you are in free fall. Theoretically, even in deep space, you are in free fall.

Answer 5

A person would feel wieightless with the absence of a Normal Force, or if there is another force pulling you upwards. There is a distance between the earth and the moon where you would feel weightless because of the gravity pulling equally in opposite directions.