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

AI Thread Summary
To find the minimum frequency required to keep a 0.2kg mass moving in a vertical circle with a 1.6m string, it is crucial to recognize that the minimum frequency occurs when the tension in the string is zero at the top of the motion. The centripetal force needed at this point is provided solely by gravity, leading to the equation Fc - mg = 0. The calculated minimum frequency is 0.39Hz, and the maximum tension in the string at the bottom of the loop is 3.9N, where tension equals the gravitational force plus the centripetal force. Understanding the dynamics of forces and their roles at different points in the circular motion clarifies why tension can be zero at the top.
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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
 
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sean-820 said:

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...
 
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.
 
PhanthomJay said:
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
 
PhanthomJay said:
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
 
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