Centripetal Force Homework: Effect of Increasing Mass on Revolutions

[Richer Su]

Homework Statement

Refer to this pic https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page37/page37.htmlor
I was wondering how increasing the mass at the bottom would influence the time taken for the object to complete 10 revolutions, my hypothesis was that it would decrease in an inverse ration manner of which I am still trying the find mathematically[/B]

Homework Equations

I understand that the centripetal force is F=mv^2/r
And the V=d/t = 2(pi)r/t
therefore the equation is
F=m(2(pi)r/t)^2 all divded by radius

The Attempt at a Solution

The
mass m1 will be the mass of a rubber stopper moving at a constant tangential speed of athttps://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png the end of a nylon cord of length.https://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png The centripetal force will be supplied by a mass thathttps://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png is attached to the bottom of the nylon cord. See the above figure. Mass will include both the slotted mass and a hanger. The weight of this hanging mass is determined by the equation:https://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.png The weight of the hanging mass is the centripetal force applied to the mass https://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.png, keeping it in a horizontal circular orbit.

or
https://www.physicsforums.com/file:///C:/Users/RICHER~1/AppData/Local/Temp/msohtmlclip1/01/clip_image014.png
the final result in terms of T period was
See capture10000.Png
I'm not sure if this relationship is inverse manner and whether it is mathematically correct.
Any help would be appreciated!
Thanks

 

[Richer Su]

the

 

[haruspex]

I was wondering how increasing the mass at the bottom would influence the time taken for the object to complete 10 revolutions

There is another free variable. E.g. you could specify L to remain constant as you vary M, or θ constant, or the speed. The answer to your question might depend on which you choose.

 

[haruspex]

the

There is an error in the text in capture12. It says the weight of the hanging mass equals the centripetal force. What has been overlooked?

 

[Richer Su]

Is the tension of the string that is being overlooked as that also is a contributing factor to the centripetal force?

 

[Richer Su]

My teacher gave me this hint but I'm not sure what the lowercase f stands for
See capture13 below
He said to Linearizing the equation, from this I was guessing that I would get a logarithmic function

 

[haruspex]

My teacher gave me this hint but I'm not sure what the lowercase f stands for
See capture13 below
He said to Linearizing the equation, from this I was guessing that I would get a logarithmic function

f stands for frequency here, but capture13 makes the same error as capture12, and others beside.

First, ΣF_net makes no sense. F_net is the sum of forces, so ΣF=F_net.
Secondly, F_net is not the tension; there is also gravity.
The blunder capture12 and capture13 make is that they ignore the angle.

If T is the tension, can you write the expressions for the vertical sum of forces and the horizontal sum of forces?