The purpose of this lab was to find a relationship between mass and period using an inertial balance. Equations were found that were able to predict the mass of certain objects fairly accurately.
Using the inertial balance (shown below) we measured the periods of certain masses (data table).
We measured the periods by placing a mass on the end of the balance and having the balance swing back and forth as the photogate measured the oscillations. We started with a mass of zero and increased the mass by increments of a hundred until 800 grams, as shown on the table below.
Next we assume that period is related to mass by a power-law equation: T=A(m+Mtray)^n
The theory portion here is that when we take the natural log of both sides we get, lnT=n*ln(m+Mtray)+lnA which looks like y=mx+b, a line.
Using Logger Pro we plot points of lnT vs ln(m+Mtray). We do a linear fit and do a guess and check method of varying Mtray weights to find a lower and upper bound point(s) in which the points were most straight. The result were the two graphs below.
upper bound
lower bound
Using these two graphs our group uses the values given for each variable in the power-law equation T=A(m+Mtray)^n to form out own equations, where the lower bound was Mtray=295g and upper bound being Mtray=335g.
Next we use the inertial balance to find the period of 2 objects and use our formulas to predict their masses. We choose a mobile phone and a golf ball.
(calculation for mobile phone)
The actual weight of the phone was 167 grams which fell between the upper and lower bound formulas predictions
(calculation for golf ball)
In conclusion the lab was a grand success. We were able to predict the mass of an object using the formulas derived from the mass x period relationship. This also shows the the mass of an object remains constant without the influence of gravity.
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