What is the centripetal acceleration of the Ferris wheel?

• smashbrohamme
In summary, the 39.0 kg child takes a ride on a Ferris wheel with a diameter of 17.0 m that rotates four times per minute. To find the angular velocity, revs must be multiplied by 2π and then divided by 60 to convert minutes to seconds. The centripetal acceleration can be calculated using the formula A=v^2/r, and this will be the same at all positions on the ride. However, the force exerted by the seat on the child will vary at different points due to the changing relationship between the child's weight and the centripetal force.
smashbrohamme
A 39.0 kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 17.0 m.

(a) What is the centripetal acceleration of the child?

(b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride?

(c) What force does the seat exert on the child at the highest point of the ride?

(d) What force does the seat exert on the child when the child is halfway between the top and bottom?

Ok I need to know theory and a few questions about how to find Angular Velocity.

I understand V=RW. I also understand I can take the A=v2/r to get the centripetal acceleration.

I forgot how to take 4 revs per minute and convert it over to a angular velocity using a radius of 8.5.

but even when I finally get the angular velocity and centripetal acceleration, I am not sure how B,C, and D will be getting different answers. Since it is a radius shouldn't they all share the same distance and gravity values? Wether it is the highest point and lowest point they share the same distance and weight doesn't change??

Angular velocity...I take the distance of the circle, which would be 17*Pie=53.4.

So it revolutes 4 times per minute. This is where I am drawing a blank...this stuff use to be so easy for me 2 years ago but I am seriously drawing a blank here...ugh

Well, ω is measured in rad/s, so you need to multiply revs by 2π to get the radian representation and then divide by 60 to turn minutes into seconds.
B,C,D give different answers because the weight of the child has a different relation to the centripetal force at each position. (For example, while the weight acts down towards the centre of the wheel at the highest point, it acts away from the centre at the lowest point.)

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences when it moves in a circular path. It is always directed towards the center of the circle and its magnitude is determined by the object's speed and the radius of the circle.

2. How is centripetal acceleration related to the Ferris wheel?

The Ferris wheel is a circular ride, which means that the riders are constantly moving in a circular path. Therefore, the Ferris wheel experiences centripetal acceleration that keeps the riders moving in a circular motion and prevents them from flying off the ride.

3. What factors affect the centripetal acceleration of the Ferris wheel?

The centripetal acceleration of the Ferris wheel is affected by two main factors: the speed of the ride and the radius of the circle. The higher the speed and the smaller the radius, the greater the centripetal acceleration will be.

4. How is the centripetal acceleration of the Ferris wheel calculated?

The centripetal acceleration of the Ferris wheel can be calculated using the formula a = v^2/r, where a is the centripetal acceleration, v is the speed of the ride, and r is the radius of the circle. This formula can also be written as a = ω^2r, where ω is the angular velocity of the ride.

5. Is the centripetal acceleration of the Ferris wheel constant?

Yes, the centripetal acceleration of the Ferris wheel is constant as long as the speed and the radius of the ride remain the same. This is because the force that causes the centripetal acceleration, also known as the centripetal force, is always directed towards the center of the circle and has the same magnitude.

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