(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a Ferris wheel that rotates 5 times each minute and has a diameter of 19 m, with the acceleration of gravity as 9.8 m/s^2, what is the centripetal acceleration of a rider? Answer in units of m/s^2.

(There's a diagram that shows a ferris wheel with radius 9.5 m spinning at ω radians per second.)

2. Relevant equations

centripetal acceleration = v^{2}/ r = ω^{2}r

3. The attempt at a solution

one rotation was equal to 2pi * r, so

5 rotations = 5(2pi * r) radians in one minute

or 10pi * r / 60 radians/second = ω

I used centripetal acceleration = ω^{2}r = (10pi * r / 60)^{2}* 9.5. I got 4.97 for centripetal acceleration. But this was wrong! I don't know where I made a mistake.

Oh, also, how does the force due to gravity figure into this problem? Shouldn't it be ignored since the ferris wheel is being powered by a motor?

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While I'm at it, I might as well ask about the other three parts of the problem.

Part b

1. The problem statement, all variables and given/known data

What force does the seat exert on a 72 kg rider at the lowest point of the ride? Answer in units of N.

2. Relevant equations

F_{net}= F_{centripetal}, so since net force must be upwards to maintain a centripetal force, normal force will be stronger than net force.

So: F_{normal}- F_{g}= F_{net}= F_{c}= m * v^{2}/r

F_{normal}= F_{g}+ F_{c}= m(g + a_{c})

3. The attempt at a solution

Isn't the force exerted by the seat the normal force?

I think it would just be the mass times the sum of acceleration due to gravity and the centripetal acceleration, or m(g + a_{c}). I can't do this though as I have not found centripetal acceleration yet. That was part one.

Part c

1. The problem statement, all variables and given/known data

What force does the seat exert on a 72 kg rider at the highest point of the ride? Answer in units of N.

2. Relevant equations

At the highest point, F_{net}= F_{c}= F_{g}- F_{normal}

F_{normal}= mg - ma_{c}

3. The attempt at a solution

Operation seems wasy with the information from part a.

Part d

1. The problem statement, all variables and given/known data

What force (magnitude) does the seat exert on a rider when the rider is halfway between top and bottom? Answer in units of N.

2. Relevant equations

F_{g}= mg

3. The attempt at a solution

Wouldn't this just be the weight of the rider since there would be no centripetal force pulling him up or down? Or would it be the equilibrant to the force due to gravity nd the centripetal force?

Thanks for help in advance!

Bonus information: I have only two hours to submit the answer to this problem electronically. Because I am a procrastinator. :(

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# Ferris wheel problem - vertical circles and centripetal acceleration

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