25-Aug.-2014: Deriving A Power Law For An Inertial Pendulum

PURPOSE: To find a relationship between mass and period for an inertial balance.

Mass is a quantitative measure of an object's inertia, and is not dependent upon gravity. Therefore, the mass of an object remains constant, regardless of the presence or strength of a gravitational pull.

The Inertial Balance is a device that is used to measure inertial mass by comparing objects' resistances to changes in their motion.

PROCEDURE:

We began by setting up the apparatus-

1. A C-clamp was used to secure the inertial balance to the tabletop. To aid the precision of our measurements a thin piece of masking tape was placed at the end of the inertial balance.
2. A photogate was set up so that when the balance oscillated the tape completely passed through the beam of the photogate.
3. LabPro was then set up (power adapter, USB cable and plug adapter>DIG/SONIC1 input)
4. Under the Physics Applications Folder/LoggerPro/Experiments/Probes and Sensors/Photogates Folder the "Pendulum Timer.cmbl." folder was launched.
   Choosing the "Collect" button, while simultaneously pulling and releasing the Inertial Balance, allowed the computer to began measuring a period.
5. The period of the Inertial Balance was first recorded with no mass in the tray(0g).
   After measuring the empty tray, a 100g mass was attached to the tray, using more masking tape, and the period-recording-process was repeated.
6. After, retrieving data for the 100g mass, a 200g mass was used, and the process was repeated. Six more mass were then recorded, for a total of eight periods measured, with each mass increasing by 100g after each measure.

Data Table:

Mass in Tray - Period

    0g - 0.2892sec
100g - 0.3549sec

200g - 0.4128sec

300g - 0.4652sec

400g - 0.5125sec

500g - 0.5593sec

600g - 0.5992sec

700g - 0.6557sec

800g - 0.6965sec

Graphing the data gave the desired unknown values, within the apparatus.
Analyzing the data and graph in slope-intercept form allows us to estimate the mass of the tray itself.

Starting with the general power formula and using the information extracted from the graph (above), a formula was derived to find the mass of the unknown objects after measuring their individual periods.

The first unkown mass measured was a wood block with a period of 0.3553sec.

The second mass measured was a wallet with a period of 0.3963sec.

These values were then evaluated with the derived formula to find the mass of the given objects.

The wood block's mass was calculated to be 104g,

and the wallet was calculated 175g.

After calculating the values of each unknown mass, both objects were measured on a scale to find a more accurate value for their mass to confirm the values calculated.

Scale Reading:

Wood Block - 99g

Wallet - 172g

The inaccuracy most likely occurred when the mass of the tray was estimated.