- #1

mattpd1

- 13

- 0

## Homework Statement

Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to counter act the friction of the spool. Call this Mf. I then calculated the work done by friction to be Mf*g*r (is this correct?) We then added a set mass to the hanger, and timed how long it took to hit the ground. From this, we calculated the final velocity of the falling mass Vf. The ultimate goal is to calculate the experimental value for the I, the moment of inertia of the spool, and compare this to the theoretical values (for a disk). I don't need any help with that part, but I do need help with some questions at the end!

The question verbatim is "

**Use Work and Mechanical Energy to derive the expression for the experimentally determined moment of inertia.**"

## Homework Equations

mf=mass it took to overcome friction(this mass is always present)

m=extra mass added to hanging weight

(m+mf)=the entire falling apparatus

h=height the mass fell

r=radius of the spool

t=time it took to fall

vf=velocity of falling mass the instant it hit the ground

wf=work done by friction

I think this is all that was necessary...

## The Attempt at a Solution

The formula for I was given to us as:

[tex]I = r^2[m(\frac{gt^2}{2h}-1)-m_{f}][/tex]

So I basically need to derive that formula from the work energy:

[tex]W_{f}=\Delta E=E_{f}-E_{i}[/tex]

I know that:

[tex]E_{i}=mgh[/tex]

[tex]E_{f}=\frac{1}{2}(m+m_{f})v_{f}^{2}+\frac{1}{2}I\omega _{f}^{2}[/tex]

So how in the world do I go from work/energy -> moment of inertia?