T^2 vs. L and T^2 vs M' Graphs

[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.

 

[asteriatic]

.

As a scientist, the expected slope for both graphs should be approximately 4pi^2/g. This is because according to the equation T^2 = (4pi^2/g)L, the slope of the graph should be equal to 4pi^2/g. This is because the gravitational constant, g, is the proportionality constant between the period of oscillation (T) and the length of the pendulum (L). Therefore, the expected slope for both graphs should be close to this value.

To calculate the actual slope of the line of best fit, you can use the formula for slope: slope = (y2-y1)/(x2-x1). In this case, y represents T^2 and x represents L or M'. So the slope for T^2 vs L would be (T^2_2 - T^2_1)/(L_2 - L_1), and the slope for T^2 vs M' would be (T^2_2 - T^2_1)/(M'_2 - M'_1).

Once you have calculated the actual slope for each graph, you can use it to find the gravitational constant, g. Rearranging the equation for T^2 = (4pi^2/g)L, we get g = (4pi^2)/(slope). So for T^2 vs L, the calculated value of g would be (4pi^2)/(slope of T^2 vs L), and for T^2 vs M', it would be (4pi^2)/(slope of T^2 vs M').

Remember to use the units consistently throughout your calculations, as the units for g will depend on the units used for T^2, L, and M'. Once you have calculated the values for g, you can compare them to known values of the gravitational constant (9.8 m/s^2 or 32.2 ft/s^2) to see how close your results are. Any discrepancies could be due to experimental error or other factors that may have affected your data.