Experimental set-up for the determination of the gravity constant by the help of a mathematical pendulum (error calculation included)

1. Explanation of the term: mathematical pendulum

2. Explanation of the formula of the deflection period :

3. Formulas of the mean value, standard deviation , Gaussian law of error propagation

Heavy iron pendulum, filament, stand, slide caliper, measure tape, stop-watch or digital counter

The experiment is carried out in the physics course SPP ( scientific projects and presentations).In this course there are 6 - 10 students at the age of 17.( English: intermediate to advanced.

- each student carries out his own experiment
- Individual evaluation of the experiment by writing a scientific protocol
- Presentation of the results (Informatik)

The presentation and the quality of the protocol

A mathematical pendulum is a punctiform mass m mounted on a weightless filament having the length s.
As a means to demonstrate this, we use a heavy iron sphere fixed on a stand with a file or thread of different lenghts.
For small deflections the pendulum oscillates by the exert influence of the gravity force with a deflection period of

Therefore the determination of the gravity force g is enabled :

To do so you have to deflect the mass of the pendulum at the angle of maximal 10 degrees and measure the oscillation time in a series of about ten times.And this is done for different lenghts.

The results are plotted in a tables ( protocol)

The mean value of T and g is calculated. The mean value is defined by dividing the sum of the single measurement values ( xi ) by the number ( n) of measurements.

Next step is the calculation of the standard deviation of the single measurement values

Furthermore

The error of the length could be determined but is arbitrary in this case (delta l = 0.3 mm) and applying the Gaussian law of error propagation leads to final results.

and hence