Find Friction Constant in Lisa's Carousel Problem

[shanie]

Hey, I'm having trouble finding the friction constant in the following question:

Lisa is sitting on a carousel 0.55m from the centre. The carousel rotates at 15laps/min and Lisa weighs 33kg.

a) what is Lisa's velocity?
b) Lisa moves away from her spot so that she is rotating 1.2m from the centre. What is the lowest friction constant that will keep her in place?

Now I calculated the velocity by setting v=s/t=2πr/T, where T = 60s/15laps=4
so v=0.864 m/s (I'd appreciate if someone could tell me if this is right..)
I'm trying to pick between 2 methods for finding the friction constant:

1) calculating the friction constant could be done by v=(μrg)^1/2
which gives μ=0.05.

2)But then F_μ=μmg, and since F_μ is also = ma, I could calculate the centripetal acceleration by having a=v<sup>2/r=0.62 m/s2
And then putting it into F=ma, giving F_μ=20.5N.
Putting the force back into F_μ=μmg, giving μ=0.063.

So which answer is right? I would really appreciate if someone could help me out!</sup>

 

[Doc Al]

Now I calculated the velocity by setting v=s/t=2πr/T, where T = 60s/15laps=4
so v=0.864 m/s (I'd appreciate if someone could tell me if this is right..)

Looks OK. (For part a, not for part b.)

I'm trying to pick between 2 methods for finding the friction constant:

Those two methods seem identical to me: They both derive from setting static friction equal to centripetal force.

But neither of your answers are correct. (How did you calculation the speed?)

 

[shanie]

Thanks for helping out!
Is the assumption wrong? So then I should calculate the normal&gravitational force and then split the centripetal force between them? How would you do that?

 

[Doc Al]

Is the assumption wrong?

What assumption? That static friction must equal the centripetal force? No, that's perfectly correct. It's just an application of Newton's 2nd law.

If you follow through on your method 2 approach symbolically (not by plugging in numbers), you'll get the same equation as in your method 1.

 

[shanie]

Oh, I used the wrong velocity! So now I did it with Lisa sitting 1.2m from the centre, v=s/t=2πr/T giving v = 1.88m/s. Plugging into v^2/rg= μ=0.3..?

 

[Doc Al]

Good!