# [Physics] Inaccuracy at measuring gravity constant with Cavendish experiment

educationerror analysisexperimental-physicsMeasurementsnewtonian-gravity

For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment.

I set up a structure like the one suggested on this website: http://www.school-for-champions.com/science/gravitation_cavendish_experiment.htm

I actually know there will be some inaccuracy, because I did not build a case for the experiment.
It is standing in the basement of a house so vibrations have nearly no influence.
The small masses are wrapped lead sheets, that weigh each about 120 g. The bigger masses are weighing 2 kg.

Today I measured all the needed values ($L, \theta, R_e, M$, like described on the site; $T$ was only measured quite inaccurate yet[+-50 secs possible])

My values are:
$L=0.23 m, \theta = 7.44° = 0.13 rad, R_e = 0.09m, M=2kg, T=100s\pm50s$

But when inserting this into the equation I get an inaccuracy of 1000 to 10000 (depending on values for $T$):

$$G=\frac{2*\pi^2*L*\theta*R_e^2}{T^2*M}=2.4*10^{-7}$$

Where does this huge inaccuracy come from or how can I make the experiment more accurate (20% accuracy would be the best)?

I have to conclude that other factors (air currents?), not gravity, were the cause of the displacement you observed. You really need to build a box, and be much more patient in your measurement. You should observe many oscillations of the pendulum in order to determine both the very small displacement, and the period of oscillation. Since the result scales with $T^2$, a 10 % error in $T$ results in a 20% error in $G$...