Wednesday, March 25, 2015

02-Mar-2015: Free Fall Lab - determination of g (and learning a bit about excel) and some statistics for analyzing data

Purpose: The objective of the free fall lab was to examine the validity of the statement "In the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2". We also wanted to mess with Excel in order to get more comfortable with the program.

Procedure: In order to demonstrate the motion of the falling object, determine g, and study the basic laws of motion, we used an apparatus that provided an object 1.5 meters falling distance in order to get an accurate reading. When the object is released from the electromagnet, its fall is recorded by a spark generator that puts marks on a strip of spark sensitive tape. The marks, which are made at consistent time intervals, were used by us students to record distance/time and velocity/time graphs. Once recorded, we can begin to understand the system and how gravity acts on an object.

So using a two-meter stick we measured the distance between the dots and the 0-cm mark. We then opened up Microsoft Excel and began plugging in the data starting with the time intervals which were 1/60 of a sec apart. Using the names of the cells (for example cell A1, A2, A3), we were able to short cut using the Edit/Fill/Down menu and let excel fill in the cells below. Next we inputed distance in cell B1 and the data for distance under in the B column. For cell C We entered change in x. ( getting the triangle symbol by holding option and pressing j). By putting =(B3-B2) in cell C2 and using the edit/fill/down menu you can quickly input all the data for that column. In cell D1 we entered Mid-interval time and fill downed =A2+1/120 to give the time for the middle of each 1/60th's interval). In cell E1 we input Mid-interval speed and fill down from E2 =C2/(1/60).

Our data table showing time, distance, change in distance, mid interval time, and velocity.
Next we wanted to graph our data in columns D and E. We clicked on the Chart tab and chose scatter then Marked Scatter to five an XY (scatter) graph with point not connected. Using Chart Layout tab, we can give the appropriate titles with units for the graph and graph axes. Then under Trendline we chose Trendline Options to linear fit the graph. We then took the same steps for the A and B columns except we used a polynomial fit of order 2.
Velocity and Mid-interval time graph

Distance over time graph

Results/Analysis: The experiment proved that gravity was accelerating the object at a constant 9.8 m/s^2 with pretty good accuracy and agreed with the theoretical prediction because we got 9.27 m/s^2. We can get the acceleration due to gravity from our velocity/time graph by finding derivative of the equation of the graph or using the slope of the graph at any given time. Getting acceleration from the position graph takes two steps of derivatives.

Conclusion/Uncertainty: Our values were pretty close but not exactly the numbers we suspected. this is due to the fact that there were certain assumptions we made in our lab. Things such as our measurements and ignoring factors such as air resistance and friction play a role in skewing our results. Although we assumed these things to be too minuscule to take into account, they did play a small factor in deriving our results. Our result of 9.27 m/s^2 which is our experimental value, divided by the expected value (9.8 m/s^2) multiplied by 100% give us the relative difference. There was a little uncertainty in measuring our distances because of human error and our measuring apparatus to give us measurement= best estimate + or - some uncertainty. Systematic error and random error have an effect on the experiment if you don't account for all variables in the system. This is why it is important to take note of all the uncertainties and errors because it is crucial to maintain integrity in our experiments. Without proper documentation, the experiment has no real value for the scientific community.

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