Cavendish Balance

You can measure the value of G, the universal gravitational constant, with this device. The description of the device is worth reading, see it here:

https://www.telatomic.com/mechanics/cavendish-balance

The manual can be downloaded at the bottom of that page.

Here is the procedure

1. Prepare to measure the gravitational constant G! The following steps are based on the manual.

2. You can skip the calibration step, the machine will be calibrated at the start of the semester.

3. You must loosen the screw on the top of the balance which allows you to raise the beam holding the 2 small lead spheres. Let this beam swing midway between the capacitor plates, see Fig. 1 of the manual.

4. The beam will swing and take a while to settle. You can speed things up by inserting a pin to hold t at 0, and slowly withdraw the pin. You may need to wait a while (15 mins) to let it settle.

5. We will use the driven resonance method, starting on page 10 of the manual. Follow the steps there.

6. After driving the pendulum so that there are 11 or so turning points, let it decay uninterrupted. Take the data from the last turning point which you moved the big spheres, the system is now in free decay (no more pumping). You can now se SciDaVis to fit Eq. 1 in the manual, and extract a value for “b” and “ω1”.

7. Use the data for the driven pendulum to get ϴD, from which you can get G.

8. The torque is given by τ = K ϴD , but the big spheres exert the torque, so

We have τ = 2GMmd/R2

9. There is a SciDaVis cheat sheet on the webpage, so consult it, or use Excel if you like.

10. Report your value for G, with a reasonable error analysis.

Here is the SciDaVis cheat sheet

sciDAVis-cheat.pdf

Here is a sample data file,

Mark-Jake-Static.csv

here is the SciDaVIS script used to analyse it

Mike-Jesse-Cavendish.sciprj

Here is a spreadsheet used to get G