Amusement Park Centripetal Force Question.

[HangingOnByAPulley]

Homework Statement

The amusement park ride shown in Figure 10 is a
large, rapidly spinning cylindrical room with a radius
of 3.0 m. The riders stand up against the wall, and the
room starts to spin. Once the room is spinning fast
enough, the riders stick to the wall. Then the floor
slowly lowers, but the riders do not slide down the
wall. Assume the coefficient of friction between
the wall and the riders is 0.40.

(b) Calculate the minimum speed of the rider
required to keep the person stuck to the wall
when lowering the floor.

Relevant Equations

Fc = mv^2/r

Fs = μsFn

Hi, I just had a question about this homework question.

I am not given the mass at all in any portion of the question. Fs = Fc because the static friction is the thing that keeps the rider stuck to the wall

My answer came out to about 3.4 m/s for the minimum speed that keeps the rider stuck to the wall, however, the textbook answer is 8.6 m/s and I am not entirely sure why. Am I supposed to factor in the fact that the floor is being lowered? I am not given the acceleration at which the floor is being lowered.

I isolated for V by doing Fs = Fc
μsmg = mv^2/r
v= √μs(g)(r)

v came out to 3.26 m/s. Where did I go wrong?

 

[kuruman]

Where is Figure 10? You got the directions of the forces mixed up. Which force prevents the person from sliding? Which force provides the centripetal acceleration?

 

[HangingOnByAPulley]

Forgot to include it, my bad.

 

[kuruman]

View attachment 289712

Forgot to include it, my bad.

Thanks. Please see my edited reply above about the forces acting on the person.

 

[HangingOnByAPulley]

Where is Figure 10? You got the directions of the forces mixed up. Which force prevents the person from sliding? Which force provides the centripetal acceleration?

I guess the force that prevents the person from sliding would be the frictional force and the force that provides the centripetal acceleration would be the normal force of the wall pushing back on the person? Is that correct?

 

[kuruman]

Yes. Now write F = ma for the horizontal and the vertical direction (two equations).

 

[HangingOnByAPulley]

Ahh, now I see, thank you for the help, I got the correct answer now.

 

[kuruman]

Ahh, now I see, thank you for the help, I got the correct answer now.

Glad to be of assistance. I experienced this ride several decades ago and it didn't quite work as advertised in this physics problem. Yes, the wall surface was some kind of rubbery material with an expected high coefficient of static friction, however, the coefficient of static friction between my shirt and my body was lower. I started sliding down with my shirt being pulled over my head. Thankfully, I was able to stop the sliding using my hands to push against the wall until the ride was over.

 

[bob012345]

Glad to be of assistance. I experienced this ride several decades ago and it didn't quite work as advertised in this physics problem. Yes, the wall surface was some kind of rubbery material with an expected high coefficient of static friction, however, the coefficient of static friction between my shirt and my body was lower. I started sliding down with my shirt being pulled over my head. Thankfully, I was able to stop the sliding using my hands to push against the wall until the ride was over.

I was wondering if the floor went completely away or was just lowered yet still rotating?

 

[kuruman]

I was wondering if the floor went completely away or was just lowered yet still rotating?

It was lowered, about 2 meters below the feet of the riders, enough to give one the feeling of being suspended. Not going completely away is probably required by their insurance company and also makes good sense.

 

[bob012345]

It was lowered, about 2 meters below the feet of the riders, enough to give one the feeling of being suspended. Not going completely away is probably required by their insurance company and also makes good sense.

So if you slipped to the floor was it rotating with the cylinder or fixed? Seems if it was also rotating you would not have suffered much damage if you slipped down but if not it could have injured you.

 

[kuruman]

So if you slipped to the floor was it rotating with the cylinder or fixed? Seems if it was also rotating you would not have suffered much damage if you slipped down but if not it could have injured you.

I don't remember if it was rotating or not. My primary concern was my shirt rising over my face and knocking my glasses off.