Lab 2 Acceleration of Gravity

The purpose of this lab was to determine the acceleration of graity for a freely falling object and to gain familiarity with the computer as a data collector.

The equipments needed for this lab were a Lab Pro interface, Logger Pro software, Windows computer, motion detector, rubber ball, and wire basket.

The first step was to connect the motion detector to the Lab Pro interface and load up the Logger Pro software on the computer. The computer started with a blank graph of position verse time. From that graph it could also calculate the velocity versus time at any instant.

Next we placed the motion detector on the floor facing upward and a wire basket over the motion detector for protection.

Now we're ready to collect data. Gently toss the ball straight up from a point about 1 meter above the detector and do so that the ball goes straight up and down. This will equate into a parabolic graph.

Once you get a nice parabolic graph of position vs time click on the Analyze/Curve fit and fit a quadratic line fit. For the velocity vs time graph choose a linear fit. The quadratic fit will give you three coeffecients for your graph, a*t^2+b*t+C, with doubling the first (a) and you will get acceleration of gravity. The linear fit will give you an m*x+b fit where m is the value of gravity. 

Take five good trials and record their values for (a) and (m) then calculate the % difference from the actual value of gravity 9.81 m/s^2. To find percent error you use the following calculation

                                   Percent error = (Measured - actual)/actual * 100%

Trial	G(2a) (m/s^2	% error	G(m) (m/s^2)	% error
1	9.658	1.5	9.776	0.34
2	9.228	5.9	9.145	6.8
3	9.76	0.51	9.68	1.3
4	9.686	1.3	9.57	2.3
5	9.282	5.4	9.611	2

In conclusion I was at first confused as to why we multiplied the front value of the quadratic fit by 2 in order to get the value of gravity, but then remembered that the kenimatic equation for position versus time is X=X+Vt+1/2At^2. Which means gravity is multiplied by 1/2, hence the quadratic fit was expressing 1/2 the acceleration which makes complete sence. Then the lab asks why should your graph be a nice parabolic shape. The reason is because gravity, the second derivitave of position verse time, is constant at -9.81 m/s^2 meaning that the graph is concave down and that velocity is contantly decreasing. Then the lab asks why does the curve of velocity vs time graph have a negative slope, and what does the slope of the graph represent? The negative indicated the direction in which the velocity is changing, and in this case the motion sensor chose down as a negative direction, hence the slope, also gravity, was a negative value. Going back to the second question, what does the slope represent; it is the value of gravity, because acceleration is the slope of velocity. Finally coming to errors, there seemed to be errors, mainly to how well the ball was tossed up and down and whether it was straight up and down or whether it was projected at an angle. Also particles and drag could affect the resuls, drag more so.