# Uniform circular motion and coefficient of friction

1. Oct 30, 2007

### KatieLynn

1. The problem statement, all variables and given/known data
You are standing on a merry-go round spinning at 12 rpm. The radius of the merry-go round is 5 meters, and you have a mass of 57kg. What static frictional force between your shoes and the merry-go round is required to keep you from flying off?

2. Relevant equations

Vc=(2*pi*r)/T

Ac=(Vc^2)/R

Fnet=MA

3. The attempt at a solution

Alright here goes...

Vc=(2*pi*r)/T so Vc=(2*pi*5)/.2 = 157

Ac=(157^2)/5 =4934

here is where I get confused... I think I should use Fnet=ma

so it would be Fnet=(57)(4934)

I'm not sure what Fnet is composed of though...where does the coefficient of friction come in?

2. Oct 30, 2007

### pinkyjoshi65

Use the equation Fs= Ms*Fn

Fs is the static force, Fn is the normal force and Ms is the coefficient of static friction..Is is better now?

3. Oct 30, 2007

### KatieLynn

so it would be

Ms*Fn=(57)(4934)

Fn = (57)(-9.81)

Ms*(57)(-9.81)=(57)(4934)

Ms=502.96 which isnt right did I calculate the acceleration or something wrong?

4. Oct 30, 2007

### pinkyjoshi65

wait a minute, they are askig you to find the force, not Ms.

5. Oct 30, 2007

### KatieLynn

So any words of advice for finding that? I'm honestly still pretty lost.

6. Oct 30, 2007

### hage567

"Fnet" is your answer. Since that is the only force present and it what is keeping you on the merry-go-round. The problem isn't asking you to specify any further.

7. Oct 30, 2007

### KatieLynn

My teacher gave us the answer its.... Ff=450N required, Ff=45N available therefore you would slide off, how does Fnet equal that?

I'm not trying to be difficult, I just really do not understand.

8. Oct 30, 2007

### hage567

Have you posted all of the information for this problem?

Also, your calculation of linear velocity is incorrect. You've divided by the frequency, not the period. T = 1/frequency, and is expressed in seconds. Do you know how to fix that?

It would be beneficial if you carried your units through your calculations, to see that they work out properly.

9. Oct 30, 2007

### KatieLynn

!!I think I've got it this time :)

Vc=(2*pi*r)/T so Vc=(2*pi*5)/(1/.2) = 6.283

Ac=(6.283^2)/5 =7.9

so now fnet=ma

fnet is only force of friction

Ff=(57)(7.9) =450N so thats how much force is required to keep you on the merry-go round.

Actually I did leave this part out because I wanted to figure out the first part first, which I see has made it confusing. So anyway the rest of the problem reads...

If the coefficient of static friction between your shoes and merry-go round is 0.08, would you slide off the merry-go round?

so...

450N is whats needed to keep you on

Force of friction=(coefficient of friction)(force normal)

Ff=(.08)(57) = 45N

then 45.6N<450N so you slide off.

I'll try to keep track of my units better in the future.

Is all the right now?

Last edited: Oct 30, 2007
10. Oct 30, 2007

### hage567

Ah! That makes more sense.

You do have to multiply by 9.81. You starting off by saying the coefficient of friction was 0.08, but you used 0.8 in your calculation. Your answer just happened to work out because you increased it by a factor of 10, which is approximately g.

Other than that, I think everything looks OK.

11. Oct 30, 2007

### KatieLynn

Yep I figured that out shortly after I posted that, thanks for all your help :)

12. Oct 30, 2007

### hage567

You're welcome.