Wednesday, August 27, 2014

27-Aug-2014: Finding the mass of two unknown objects

Purpose of lab: Try to find the mass of two unknown objects using their periods in the universal pendulum.



This is an universal pendulum, which we used to find the periods of our objects. We found out that the heavier the object, the longer the period.

Explanation:
We started with the equation that:  T=A(Mtray+Mobject)^n
By simplifying we get:
ln T = n*ln(Mobject+Mtray) + ln A, which looks similar to the slope equation y=mx+b
Therefore, n would be the slope of the graph lnT with ln(Mobject+Mtray)
By changing the mass of the tray, we tried to find a correlation as close as possible to 1.0, so that the mass of the tray would be accurate enough for us to plug back into the equation and find the mass of the object. Looking at the pictures below, it's possible to see that our correlation was 0.999, which is really accurate. From that, we can find the slope of the line, and the Y-intercept. By plugging those numbers into the original equation, it's possible to find a good estimate of the mass of the unknown objects.




Summary: 
We built an universal pendulum in order to calculate the period of certain masses. After a few experiments, we found out that the heavier the mass, the longer the period. Then we selected two objects with unknown mass with the objective of finding their respective masses according to their period. With the given formula:  T= A(Mobject + Mtray)^n, we applied mathematical skills and came up with lnT=nln(Mobject+Mtray) + lnA, which is similar to the slope equation y=mx+b. Utilizing this information, we used the computer and created a graph to find the possible range of weights of the tray, the value of n for that weight, and the value of lnT. With those number, it was possible to reach to a conclusion of an approximation of the two unknown masses.

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