Finding Centripetal Force Using Lab Data

[haackeDc]

Homework Statement

So in lab, we had this setup where we had a string, two masses, and a tube. We attached one of the masses, then put the string through the tube, and attached the other mass on the other end.

Then, by holding the tube, we were to spin a mass above our heads and time how long it took to get 10 revolutions, then divide this time by 10 to get the Period (T). We then change the radius, and repeat 4 times.

So, at the end, we have results for 5 different radii and 5 different periods. We are then told to make a graph of Radius vs Period² (T²)

According to the lab, the slope of this line is supposed to give us the Centripetal Force.

However, according to the following equation:

Homework Equations

r = (F/4$\pi$²m)T²

The Attempt at a Solution

The slope of r/T² seems like it should be (F/4$\pi$²m)... not simply F.

Also... which mass am I supposed to use in this equation?

 

[LawrenceC]

A picture/sketch of what was being done would be helpful.

 

[obafgkmrns]

If I understand, there is one mass dangling out the bottom of the tube, and another attached to the string whirling around the top of the tube. The force of gravity acting on the bottom mass is balanced by the centripetal force on the top mass. That gives you

$m_1g = m_2rω^2 = m_2r(2π/T)^2$

What do you get when you solve for $r/T^2$ ?