Circular motion-mass and radius given- finding frequency and force

[sean-820]

Homework Statement

A 0.2kg mass is tied on the end of a 1.6m long string and whirled around a circle that describes a vertical plane.

a) What is the minimum frequency of rotation needed to keep the mass moving in a circle?
b) Calculate the maximum tension in the string at this frequency.

Givens=
mass=0.2kg
r=1.6m
f=frequency which is unknown

Homework Equations

f=ma
a=4(pi)^2rf^2
f=4(pi)^2rmf^2
a=v^2/r

The Attempt at a Solution

Im stuck on the fact that i only have two givens and i don't seem to be able to use two equations as it solves one variable, but introduces a new one.

FBD

(top) Fc-mg<------(0.2kg)-------> mg+Fc (bottom)


Part b) is easy to solve once a) is done as i know the highest tension on the string will be at the bottom of the loop where the tension equals mg+ the centripetal force



It would be appreciated if somebody could guide me in the right direction for part A

 

[PhanthomJay]

Homework Statement

A 0.2kg mass is tied on the end of a 1.6m long string and whirled around a circle that describes a vertical plane.

a) What is the minimum frequency of rotation needed to keep the mass moving in a circle?
b) Calculate the maximum tension in the string at this frequency.

Givens=
mass=0.2kg
r=1.6m
f=frequency which is unknown

Homework Equations

f=ma
a=4(pi)^2rf^2
f=4(pi)^2rmf^2
a=v^2/r

The Attempt at a Solution

Im stuck on the fact that i only have two givens and i don't seem to be able to use two equations as it solves one variable, but introduces a new one.

FBD

(top) Fc-mg<------(0.2kg)-------> mg+Fc (bottom)


Part b) is easy to solve once a) is done as i know the highest tension on the string will be at the bottom of the loop where the tension equals mg+ the centripetal force



It would be appreciated if somebody could guide me in the right direction for part A

The string tension can't be negative, but it can be zero, at the top, just as it was about to go slack...

 

[Filip Larsen]

It may help to draw a diagram of the forces acting on the mass at various positions in its circular motion. Then think about what angular speed has to do with the mass keeping its circular motion.

 

[sean-820]

The string tension can't be negative, but it can be zero, at the top, just as it was about to go slack...

Thanks a lot. I got the answer a)0.39Hz and b) 3.9N

I think i was over thinking it and totally forgot that if the minimum frequency would be at the top when Fc-mg=0

 

[jbjohnybaker]

The string tension can't be negative, but it can be zero, at the top, just as it was about to go slack...

why is the tension 0 if it is acting down with the gravity.. i know that the tension is suppose to be 0 but i don't understand why :S