How Do You Derive the Gravitational Constant from a Rigid Pendulum Experiment?

[TOPOG]

1. Homework Statement

Determine the general equation for "g" in terms of measurable quantities(M, Mbar, h, L, b, T, To, Tbar) from the following equations: (refer below)


2. Homework Equations

(1) T = 2pi(I / Mgh)^(0.5)

(2) (Io / Ibar) = (To / Tbar)^(2)

(3) Ibar = (Mbar / 12)(L^2 + b^2)

(4) I = Io + Mh^2



3. The Attempt at a Solution

- Alright first i re - arranged eqn. (1) so that g = [ (I*4pi^2) / (T^2)] / (Mh)

- Then i re - arranged eqn. (2) so that Io = [(To / Tbar)^(2)](Ibar)

- I then used eqn (3) and subbed it into the new equation (2)

Io = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] (5)

- I then subbed in our newly formed eqn (5) into eqn (4)

I = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2 (6)

- Now i sub eqn (6) back into our re arranged equation for g

g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh)

and that's my final answer



taken from following lab

http://courseweb.edteched.uottawa.ca...2008%20pdf.pdf

 

[anathema]

Thank you for your question. I can confirm that your final equation for g is correct. However, I would like to offer some further explanation and clarification for others who may be reading this forum post.

From the given equations (1), (2), (3), and (4), we can see that there are several measurable quantities involved in determining g: mass (M and Mbar), height (h), length (L), base (b), time (T, To, and Tbar), and moments of inertia (I and Ibar). In order to find an equation for g in terms of these quantities, we need to manipulate these equations and substitute in values for the given variables.

Firstly, we can rearrange equation (1) to solve for g:

g = [ (I*4pi^2) / (T^2)] / (Mh)

Next, we can rearrange equation (2) to solve for Io:

Io = [(To / Tbar)^(2)](Ibar)

Now, we can substitute in the value for Ibar from equation (3) into the above equation:

Io = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)]

Then, we can substitute in the value for I from equation (4) into the above equation:

I = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2

Finally, we can substitute this value for I into our rearranged equation for g:

g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh)

Therefore, the general equation for g in terms of the given measurable quantities is:

g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh)

I hope this explanation helps. Keep up the good work on your lab assignments!

 

[Moetasim]

Dear student,

Your solution looks correct to me. You have correctly rearranged the equations and substituted for the variables to get a general equation for g in terms of measurable quantities. It is always important to carefully rearrange and substitute equations to ensure that you get the correct final answer. Great job!