Ferris Wheel acceleration Problem

[JoshMP]

Homework Statement

While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 15 m, and you use your watch to find that each loop around takes 25 s.

What is the magnitude of your acceleration?
What is the ratio of your weight at the top of the ride to your weight while standing on the ground?
What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground?

Homework Equations

F=ma

The Attempt at a Solution

I started by finding the angular velocity. I don't know how to find the angular acceleration or the tangential acceleration.

 

[Doc Al]

I don't know how to find the angular acceleration or the tangential acceleration.

If we presume that the wheel turns at a uniform rate, those will be zero. What other acceleration is involved?

 

[JoshMP]

If we presume that the wheel turns at a uniform rate, those will be zero. What other acceleration is involved?

Radial acceleration. Got it, thanks.

So what about the ratios of weight...would they just be 1 to 1?

 

[Doc Al]

So what about the ratios of weight...would they just be 1 to 1?

No. (That would be too easy.) When they say "weight", they really mean apparent weight, not the force of gravity. You'll need to analyze forces using Newton's 2nd law.

 

[JoshMP]

No. (That would be too easy.) When they say "weight", they really mean apparent weight, not the force of gravity. You'll need to analyze forces using Newton's 2nd law.

Ok tell me if I'm on the right track. I know that the radial acceleration is 0.95 m/s^2, which means that the net force is pointing down at the top of the wheel and up at the bottom. I use this net acceleration and solve for Fnet. Does this value of Fnet = the apparent weight?

 

[Doc Al]

Does this value of Fnet = the apparent weight?

No, but you'll use it to determine the apparent weight. The apparent weight of an object is the normal force exerted by the surface supporting it. Find that normal force.

 

[JoshMP]

Ok I got the ratio at the bottom correct. But I'm having trouble with the top. My FBD has gravity pointing down and normal pointing down (is that right? - it's a Ferris wheel...). When I solve for the normal force, I get a negative value, which is impossible!

 

[Doc Al]

My FBD has gravity pointing down and normal pointing down (is that right? - it's a Ferris wheel...).

No. Think of yourself sitting in a seat which is always upright. The normal force of the seat on you is always up.

 

[JoshMP]

No. Think of yourself sitting in a seat which is always upright. The normal force of the seat on you is always up.

Wouldn't that mean that the normal force at the top is equal to the normal force at the bottom? If the net force is the same at the top and bottom, and gravity is the same too, then the normal force must also be the same, and the ratios would be the same too.

 

[Doc Al]

Wouldn't that mean that the normal force at the top is equal to the normal force at the bottom? If the net force is the same at the top and bottom, and gravity is the same too, then the normal force must also be the same, and the ratios would be the same too.

Careful: While the net force has same magnitude at top and bottom, it does not have the same direction.