Circular Motion of a spinning mass

1. Oct 24, 2007

sighman

In my lab, we were spinning a mass (stopper) in a uniform circular motion attached to a string. The string went through a hollow tube and at the other of the string, a weight was hanged. We were trying to find out how frequency of the revolution were affected by mass, radius and tension force (which was also the net force in this case). Attached is a picture because it worth a thousand words. We had to time how many seconds it took to take 20 cycles, which was our frequency.

c) use graphing techniques to determine the relationship (proportionality statement) between the frequency of revolution and each of the follwing
• The magnitude of tension force
• radius of the circle
• the mass of the object in motion

This part I understood, but I just added it in because it goes with the question (d) that I am having a hard time with. I had created the proportionality statements:
tension force ∝ frequency
r ∝ (1/frequency)
m ∝ (1/frequency)

1. The problem statement, all variables and given/known data

d)Combine the three results from (c) to obtain an equation for the frequency in terms of tension, the radius and the mass. Check your equation using your data points.

Although there are variables, I have already discovered their values.

The given data is what I are the plotted points on my 3 graphs:

For graph 1: 0.98N=1.44 cyc./s 1.47N=1.77 cyc./s 1.96N=1.97 cyc./s
This is when comparing tension force to frequency. Mass and radius are constant @ .0165kg and 0.75m respectively.
For graph 2: 0.45m=1.82cyc./s 0.60m=1.6 cyc./s 0.75m=1.44 cyc./s
comparing radius to frequency. Mass and tension force are constant at .0165kg and .98N.
For graph 3: 0.0165kg=1.97cyc./s 0.033kg=1.41cyc./s 0.0495kg=1.15 cyc./s
comparing mass of the stopper to frequency. Radius and tension force are constant at 0.75m and 1.96N.
These are how I derived the proportionality statements.

Now, here is what I do not understand: how am I supposed to make an equation from frequency in terms of tension, radius or the mass from those proportionality statements and those graph points?

2. Relevant equations

Fnet(centripetal) = mv^2 / r
Fnet=4π^2 mrf^2 <--- given in the textbook but it is introduced after question d, so I'm not sure

3. The attempt at a solution

I just thought that the equation would be the first relevant equation, but how am I supposed to show how I to get to that step by combining the mass, radius, and tension force points from their points on each graph and proportionality statement.

-OR-

i use the equation Fnet(centripetal) = mv^2 / r
to get the equation
Fnet= m(d/t)^2 / r
Fnet= m(20(2πr) / t)^2 /r <--- I took out 20 /t because this was frequency
Fnet= m (f(2πr))^2 /r
Fnet= 4mf^2π^2r^2 /r
Fnet= 4π^2 mrf^2

Wierdly enough, it is the same equation in the next part (e)... I am wondering why on earth would they give me the answer in the next question if they asked me to solve it here?

And in question (e), they expect me to have discrepencies between the equation I derive and the equation they give ("Compare this result (Fnet=4π^2 mrf^2) with the equation you derived in (d). Indicate the likely causes for any discrepancies")

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Last edited: Oct 24, 2007
2. Mar 20, 2010

watermellon

hey yea i have the same exact question and i dont understand how to do it, does anyone know?

the first two parts for me are the same, as for the the attempt this s what i got..

F = frequency
T= tension
M= mass

F ∝ 1/R
F ∝ 1/M
F ∝ root(T) <<< this is also what am confused about, is it simply T or root(T)

and then u can combine those to get that

F ∝ root(T)/MR
F = Kroot(T)/MR where k is a constant, and then u use the experimental data plug it in and get the values of k...

thoguh i keep getting wrong answers and different values of k

Last edited: Mar 20, 2010