12-Sept-2016: Determination of 'g'

Lab #2 by John Demontano, Jae Yoo & Shaun Mazzio performed on August 31 2016

Purpose: to examine the validity of the statement: In the absence of all other external forces except gravity, a free falling body will accelerate at 9.8 m/s^2.

The apparatus used is a spark generator (shown below) which will produce a spark every 1/60th of a second. A free-fall body will be dropped and create sparks on a spark sensitive tape.

(Apparatus is 1.86 m tall)

We use the apparatus and obtain the tape where sparks are marked along the tape every 1/60th of a second. We measure the distances with a meter stick and record them onto excel. The data below is obtained:

In the picture above; the graph for time/velocity as well as the graph for position/time are included.

Questions/Analysis: To obtain the acceleration from the graphs, you can take the slope of the time/velocity graph from the formula given. We got a slope of 952.89; converted to m/s^2  would give us an acceleration of roughly 9.53 m/s^2. To get the acceleration from the position/time graph you can take the derivative of the formula and use the slope from that; I got 9.58 m/s^2, a difference of 0.05. Given the slight difference the acceleration should be equal theoretically and thus in a constant acceleration, the velocity in the middle of a time interval should be the same as the average velocity for the that interval.

Conclusion: We got close to 9.8 m/s^2 but not quite. I think we did an alright job given that there were other elements which were not accounted for such as friction and air resistance. Although I cannot imagine how much such factors displace data as I have not done any experiments accounting those factors. Other reasons may include calibration of the spark generator and perhaps elevation of the location of the experiment.

Part 2: Errors and Uncertainty

Here we analyzed the class data for 'g'

In the group data it looks like all groups were below 9.8 m/s^2  except group 4. Our class average value is about 9.36 m/s^2 which is a difference of  .44 and is off by about 4.49%. For our particular group's (11) values of 'g' as well as group 10's, our tape(s) was made on the day of the lab whilst the rest of the class' tape were made on a day prior. This may or may not account for any random error in the data. As for the class generally getting a value below 9.8 m/s^2 that would be a systematic error.

The point of this part of the lab is making aware the types and the fact that errors will occur. We are given a way to measure these errors and convey our confidence in our apparatus and experiment with numerical values.

7-Sept-2016: Finding a relationship between mass and period

Lab #1 by John Demontano, Jae Yoo & Tanay Shah performed on August 29 2016.

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.