8/18/2014: Finding a relationship between mass and period for an inertial balance

In this lab we used inertial balance secured to a table with a C-clamp and a photogate to measure the period of a various quantity of masses. We logged the known mass and its period we measured by the tape attached to the inertial balance passing through the photogate.

Here is a picture of our setup as described above:

With our recorded data of objects mass and its period as seen below was entered into a computer using logger pro as raw data. With this data we we expect the period is related to mass by some power-law type of equation

T = A(m + Mtray)^n

With this formula we have two unknowns Mtray and n.

Using the natural logarithm we get the formula:

lnT = n ln(m + Mtray) + lnA

This formula is in the form of y = mx + b.

With  a plot on Logger Pro of T vs ln(m + Mtray) we get a line of slope n and y-intercept lnA.

Adjusting the the unknown Mtray we can increase and decrease the size of  correlation coefficient of the line is almost %100. Graph shown below at 0.9997 correlation.

With this we now have a close value for the constants lnA and n and a vlaue for Mtray.

We also found a high and low values of what Mtray is an acceptable range by using the adjusting the value of Mtray in the graph below.

The third graph shows our tests of Mtray and the other two unknowns. It also shows the low and high range of Mtray and its matching n and lnA.

We also measured two unknown items mass and logged the period not shown in picture above. The data for the unknown masses was as follows:

Wood: 0.401 seconds

Charger: 0.432 seconds

With the low and high range of Mtray we can now find a range of the two items unknown mass by plugging the high and low Mtray, n, and lnA back into the formula as shown below.

Here is the graph of a Power law fit using the same data. Was expecting a parabola, but was surprised to see a line. While the variable n is close as to the log graph the power graph produces a different value for A which is larger then the value found from the log graph.