What is the minimum frequency to keep the mass moving?

[Smartgurl]

Homework Statement

A mass of 2.0 x 10^2 g is tied to a 1.6 m long string and spun in a vertical circle. What is the minimum frequency to keep the mass moving?

Homework Equations

Fc=m4(pie)rf^2

The Attempt at a Solution

I know I have to use this equation and make it equal to another to find Fc however I don't know which other equation.

 

[BvU]

Well, perhaps this isn't done in outer space but on earth...

 

[haruspex]

Fc=m4(pie)rf^2

That equation is not quite right. (And it's spelt pi, not pie.)

 

[Smartgurl]

That equation is not quite right. (And it's spelt pi, not pie.)

Is the equation Fc = m4(pi)^2rf^2

 

[haruspex]

Is the equation Fc = m4(pi)^2rf^2

Yes.
Now what about BvU's point? You need to consider gravity.

 

[Smartgurl]

Yes.
Now what about BvU's point? You need to consider gravity.

Would Fg = Fc?
So I could get mg = m4(pi)^2rf^2. Then solve for f?

 

[haruspex]

Would Fg = Fc?
So I could get mg = m4(pi)^2rf^2. Then solve for f?

Yes, but is that just a lucky guess or can you mount an argument to say it should be that?

 

[Smartgurl]

Yes, but is that just a lucky guess or can you mount an argument to say it should be that?

I drew a diagram and I think that when the mass is at the top it will need the minimum Fc as gravity will help bring it down. Where at the bottom the Fc will have to overcome gravity to bring the mass back up. So gravity will be the only force acting on the mass and bringing it down when it is at the top.

 

[haruspex]

I drew a diagram and I think that when the mass is at the top it will need the minimum Fc as gravity will help bring it down. Where at the bottom the Fc will have to overcome gravity to bring the mass back up. So gravity will be the only force acting on the mass and bringing it down when it is at the top.

Good.

 

[Smartgurl]

Good.

Thank you so much! Now it seems simple since I understand it