Exploring Centripetal Force: Lab Results & Proportionality Statements

[Vesper89]

We're doing a lab on centripetal force where we swing a mass on a string over our heads. The string passes through a glass sleeve and has masses suspended at the bottom of the string like this...http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Circular%20Motion/labs/cf_and_speed.htm"
Although the experiment is not the same.

We had to adjust the radius and mass and then calculate the frequency for each trial. We then had to graph the relation between Force centripetal and the mass, Fc and frequency squared and finally Fc vs Radius. We then have to come up with proportionality statements for each and then combine each statement into one proportionality statement that relates all three.

We have the first two...
1) As mass increases Fc increases
2) As frequency increases Fc increases
But we are stuck at the radius. Our data shows that at a constant frequency and mass, then as the radius increases, Fc also increases (which makes sense since a greater velocity would be required to maintain the frequency of a string with a greater radius). But various internet sources state that as the radius increases, the force decreases?? Is this just because they are not taking frequency into account? Which is it?

Finally what should the radius proportionality statement and the final proportionality statement look like? Bear in mind the equation Fc= 4pi(2)rf(2)

Thanks for any help,
Andrew

 

[Doc Al]

There are two equivalent expressions for centripetal force:
$$F_c = m v^2/r$$
or
$$F_c = m \omega^2 r$$

Since $v = \omega r$, the two expressions are equivalent. ($\omega$ is the angular speed; it equals the frequency times $2 \pi$.)

Since you are holding the frequency constant while you vary the radius, your results will follow the 2nd equation. If you held the speed constant as you varied the radius, your results would be described by the first equation.

 

[samdiah]

Really! We did this lab last week too. How cool!

Anyways what we foun was that Fc is directly proportional to Radius to the power of n if both mass and frequency are kept constant.

For the constant frequency you have to square the frequency and then plot a graphy of squared frequency and Fc. (it shouls pass throught the orgin since when frequency square is zero so is Fc). Using this graph determine 4 values of freq. sqr. for contant Fc. Then find radis required for contant frequency. Then plot a graph of Fc vs. radius and use the graph to find relationship, or use log eqn.

 

[samdiah]

For the final proportianality satement combine all the above proportianality. ours lookes a bit like this:
Fc is proportional to (m to the power of 0.816)(R to the power of 1.07)(freq. to the power of 1.31)
The above is just:
mR(f(squared))

 

[Vesper89]

I think that helped. I have the equation Fc=4п²rf² (which is the same as Fc=mw²r). I think the main reason we were having difficulty was because our data isn't very accurate. Anyway, thanks.