# Circular Motion of a Ferris wheel

• 2Big2Bite
In summary, the conversation discusses finding the centripetal acceleration of a Ferris Wheel with a radius of 16m and a rotation rate of once every 20 seconds. It also explores calculating the effective weight of a 45 kg person at the highest and lowest points of the wheel. The correct equation for calculating the centripetal force is a=ω^2*r, and the net force at the top and bottom can be found by adding the force of gravity and the centripetal force. The effective weight of the person at the top is 512.91N and at the bottom is 370.89N. The conversation also mentions using free body diagrams and Newton's 2nd law to find the normal force at each

## Homework Statement

An Ferris Wheel has a radius of 16m and rotates once every 20 seconds.

a) Find Centripedal acceleration.
b) Whats the effektive wheight of a 45 kg person at highest point?
c) Lowest point?

## Homework Equations

a) I tried using the a=ω2*r in a) but not sure if its right
b)
c) We = mg - ma
Is this the correct equation for a and b?

## The Attempt at a Solution

I got out 1,578m*s-2 in a) but not sure if that's correct really.
and also strugling with b) and c)

But here's c) atleast trying using that equation:
45kg*9,82m*s-2 - 45kg*1,578m*s-2= 370,89N Is that right?

and b) do i use same equation for upward motion?

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for a you should end up with an acceleration, not a velocity

a=ω^2*r works but you need the correct value of omega, what did you use?

b and c are just adding up the forces acting at those points. Just make sure you have a good understanding of which direction the centripetal force is directed.

Oh yeah it was -2 not -1. Spelling error.

I Used for omega, ω = $\frac{(2π*3)}{60}$
The motions are up and down verticaly, but not sure if that formula is right or if i need to add other things to it

well, basically the centripetal force is always pointing towards the center of the circle, and the force due to gravity is always pointed downwards.

So at the top, they are pointed in the same direction, at the bottom they are pointed in opposite directions. So how would you find the net force acting on someone at the top and then at the bottom?

SHISHKABOB said:
well, basically the centripetal force is always pointing towards the center of the circle, and the force due to gravity is always pointed downwards.

So at the top, they are pointed in the same direction, at the bottom they are pointed in opposite directions. So how would you find the net force acting on someone at the top and then at the bottom?

Well when going upward you add weight since your pushed "into the seat", and down you take weight when the seat accelerate away from you.

So it would be F = mg+ma at the top since its "added weight"
45kg*9,82m/s^2+45*1,578m/s^2= 512,91N

And when you go down it will be the same but with (-):

45kg*9,82m/s^2-45*1,578m/s^2 = 370,89NOr is this as wrong as I can get? I'm new to this things so I might not be so good at it.

yeah that looks correct

Okey thanks for the help!

2Big2Bite said:
Well when going upward you add weight since your pushed "into the seat", and down you take weight when the seat accelerate away from you.

So it would be F = mg+ma at the top since its "added weight"
45kg*9,82m/s^2+45*1,578m/s^2= 512,91N

And when you go down it will be the same but with (-):

45kg*9,82m/s^2-45*1,578m/s^2 = 370,89N

Or is this as wrong as I can get? I'm new to this things so I might not be so good at it.
This is not correct. The person's effective or 'apparent' weight is the magnitude of the normal force of the seat that pushes up on him or her. The person feels lighter at the top than at the bottom. Use good free body diagrams and Newton's 2nd law to find the normal force at the top, and then at the bottom.

## 1. What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path. This means that the object maintains a constant distance from a fixed point, while also continuously changing direction.

## 2. How does a Ferris wheel demonstrate circular motion?

A Ferris wheel is a perfect example of circular motion because it rotates around a central axis while keeping its occupants at a constant distance from the center. The wheel's rotation causes the riders to experience both centripetal and centrifugal forces.

## 3. What is the difference between centripetal and centrifugal forces in a Ferris wheel?

Centripetal force is the force that pulls an object towards the center of a circle, while centrifugal force is the force that pushes an object away from the center. In a Ferris wheel, the centripetal force is provided by the wheel's structure, while the centrifugal force is experienced by the riders due to their inertia.

## 4. How is the speed of a Ferris wheel calculated?

The speed of a Ferris wheel can be calculated using the formula: v = 2πr/T, where v is the speed in meters per second, r is the radius of the wheel in meters, and T is the time for one complete rotation in seconds.

## 5. What factors can affect the circular motion of a Ferris wheel?

The circular motion of a Ferris wheel can be affected by several factors, such as the size and shape of the wheel, the speed of rotation, the weight and distribution of the riders, and external forces such as wind. The design and construction of the wheel also play a crucial role in ensuring smooth and safe circular motion.