What Is the Minimum Frequency for a Mass in Vertical Circular Motion?

[ninetyfour]

Homework Statement

A 0.2kg mass attached to a rope 1.6m long is being spun in a vertical plane. Find the minimum frequency.

Homework Equations

F = 4(pi^2)(r)(f^2)(m)
Ft min = Fc - mg

- minimum frequency occurs at minimum tension

The Attempt at a Solution

I had this question on a test and spend like 45 minutes on it. I have no idea what to do, and I am curious as to what I should have done. I tried inserting numbers and re arranging formulas and substituting here and there and nothing seemed to work.

HELP? D:

 

[ehild]

F = 4(pi^2)(r)(f^2)(m)
Ft min = Fc - mg

- minimum frequency occurs at minimum tension

What kind of force is F in your first equation?
How much is the minimum tension?

ehild

 

[ninetyfour]

F = 4(pi^2)(r)(f^2)(m)

That F is centripetal force. It can also be written as:

F = m(v^2) / r

 

[dulrich]

Thinking physically, if the frequency is not high enough what happens? The mass will not make it to the top of the circle, right? It will execute free-fall motion (i.e., a parabola) until the string catches it again. So the key is to consider the top of the circle.

What are the forces acting? Weight and tension. These combine together to provide the centripetal force maintaining the circular motion. The smallest the tension can be is zero. So we want to find the frequency in which the weight alone is able to provide the sufficient centripetal force.

I think you can probably take it from here...