Student Freindly Kater Pendulum System

Consists of the Kater Pendulum and the TEL-ET41 timing system. Supply two lab stands and you will have everything you need to measure g.

Kater Precision Pendulum

• Measure g to a few parts per thousand in less than ten minutes.
• Measure g to a few parts in ten thousand in one lab period.
• Take data with a photogate or a stopwatch.

Finally a Kater Pendulum has been designed to allow a measurement of g to within a few parts per thousand in about 10 minutes. In addition, a very precise measurement of g (to within a few parts in ten thousand) can be performed in a single lab period.

The axes of rotation are by means of a “knife edge” which is inserted through one or the other of two holes; whose placement in the pendulum were carefully chosen. Although period measurements may be made with a stopwatch, a photogate is preferred to: (i) eliminate large reaction time errors, and (ii) insure that data is collected in an amplitude regime that is essentially isochronous.

A quick method operates with a single mass configuration of the pendulum. The period of swing about each axis is measured and g can be determined by using:

Although the errors of this “quick” method are about 5 times larger than those of the more precise method; the total time for data collection and analysis is correspondingly reduced.

The more precise method collects a different T₁ and T₂ for each of several positions of a small slider whose mass is approximately 2% of the mass of the pendulum. By performing a regression analysis on the graphs of T₁ and T₂ as a function of slider position, the position for which T₁ = T₂ = T can be determined and g calculated from:

Apparatus Includes:

• Precision cut and drilled brass rod
• clamp with knife-edge
• lab manual with all equations derived
• detailed instructions for performing the experiment

TEL-ET41 Timing System

The TEL-ET41 measures the period of the Precision Kater Pendulum with a resolution of .0001s using a 40kHz ± 0.02% quartz crystal. The TEL-ET41 is line powered, so there are no batteries to go dead or AC adapters to loose track of. The TEL-ET41 includes a photogate which can be easily mounted on a lab stand, as shown in figure 1 above. The ET-40 can also be used with our air tracks to measure the speed of a cart.