What Is the Maximum Rotation Period for a Cylinder Ride to Prevent Falling?

[orb88]

Homework Statement

An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that a person inside is stuck to the wall and does not slide down when the floor drops away. The acceleration of gravity is 9.8 m/s^2. Given g=9.8 m/s^2, the coefficient mu=.447 of static friction between a person and the wall, and the radius of the cylinder R=4.8 m. For simplicity, neglect the persons depth and assume he or she is just a physical point on the wall. The persons speed is v=2(pi)r/T, where T is the rotation period of the cylinder (the time to complete a full circle) Find the maximum rotation period T of the cylinder which would prevent a 74 kg person from falling down. Answer in units of s.

Homework Equations

A=v^2/r
v=2(pi)r/T

The Attempt at a Solution

i set sum of the forces in the y direction equal to Fn=Fg, since the person is not moving in the y direction
thus able to find Fn, i plugged that into the formula Fs= (mu)s(Fn), and got 324.1644. Then i did the sum of the forces in the x directoin, which i had as Fs=mv^2/r, thus i found v^2, and plugged v into the v formula to get T. I think i am missing centripetal force in my x direction, but i don't know how to represent it, and get a number for it. Please respond with explanation, and answer will be also greatly appreciated.

 

[Kurdt]

I'm not sure what your misunderstanding is. From what you've written as your attempt it sems that you initially done the right thing. You needed to equate the weight of the person with the maximum force needed to overcome static friction. Form that you can work out what the normal force must be. This normal force can be equated to the centripetal force to find the minimum (assuming the question has a typo) T.

 

[orb88]

no actually the question says maximum, so does it change then?

 

[orb88]

so are you saying the Fc (centripetal force) is equal to 74 kg (the weight of the person)?

then this would change the whole equation i think

 

[Kurdt]

No I'm saying its equal to the normal force on the person from the wall.

P.s. yes it should be maximum I've just gone mad at the end of a long day.

 

[orb88]

yea i had that, but I am not sure...Is an answer of about 6 seconds wrong for the T, because I am thinking that it is too high

 

[Kurdt]

I get approximately half your answer.

 

[orb88]

Fs=324.1644
v= 4.585507
T=6.577089398

those are the exact answers i got

 

[Kurdt]

Your F_s is wrong. remember that the static friction has to hold the weight of the person. Therefore F_s is just their weight. You only need this to solve for the normal force. In fact if you work algebraically throughout you see that the mass is not needed at all. So to clarify:

$$F_s = \mu_s N = mg$$

You will need to solve for N and set that equal to the centripetal force.