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 propagationMaterials
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.Teaching targets:
The presentation and the quality of the protocolLesson-plan:
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.