What Should the Expected Slope of T^2 vs. L and T^2 vs. M' Graphs Be?

[brimister47]

Homework Statement

What is the expected slope of the line? What was the actual slope of the line of best fit? Calculate the gravity constant g from the slope of your graph

Homework Equations

k = (Mg) / (y_0 - y)

4pi^2/g x L = T^2

The Attempt at a Solution

I understand how to acquire gravity using the second equation for T^2 vs L. But I don't have a clue what my expected slope should be for either graph. My calculated slope for T^2 vs L is 3.223 and for T^2 vs. M' 3.616

 

[Delphi51]

If you graph y vs x and the formula is y = mx,
then the slope is expected to be m.
If you graph T² vs L and the formula is T² = (4pi²/g) x L
then the expected slope is (4pi²/g). The calc for g would then be
g = 4pi²/slope

I don't see a formula relating T² and M'. What is M'?
It looks like you might be doing a pendulum experiment?

 

[brimister47]

So that means my expected slope would be ~4? This was a pendulum experiment for T^2 vs L and and oscillating spring for T^2 vs M'. M' is the mass of our hook + spring + added weight, while M is just the mass of our weight added to the hook and spring.

Through my notes I found the equation T^2 = (4pi^2m)/k. So if I replace y=T^2 and x=m does that mean my slope is (4pi^2)/k?

 

[Delphi51]

Yes, that is the idea. Good luck.