Graphical Analysis, by Marcus Wade

The purpose of the graphical analysis lab was to basically become familiar with the logger pro software, so that we could record and interpret data for the falling object (ball). The first part of the lab was mainly to get us used to the software. After looking through a function plot graph, we chose our own function to graph:

fig 1

x*arctan(3x2)     -Graphed in fig 1







Once we became familiar with the graphical analysis software, inputting our own functions, we set up the motion detector and got ready for a few trial drops.





The run that was kept was dropped from a height of 2 meters and took approximately 0.6 seconds to fall to the ground. The equation of the object's position graph was fitted to be the parabola -4.8x^(2)+10.01x-3.211 on the domain [1,1.6]

Once the graphs had been obtained, we verified that our data matched with the equation:

d=gt^(n)

d=distance (m)

g=gravity (m/s^2)

t=time (s)

We assume the acceleration to be 9.8 m/s^2. Since the object did not start falling until t₁=1.1 s_, we subtract t₂=1.6 s from t₁=1.1 and get t=0.5 s for our equation. Also the object appeared to have fallen 1.5 m in the course of its drop.

Using dimensional analysis, we plug our values and units into the equation as follows: 

1.5 (m)=9.8 (m/s^2)*(0.5 s)^n

Dividing by 9.6, then taking logarithms of both sides of the equation to solve for n, we obtain:

log((1.5 )/(9.8))/log(0.5)=2.7 s

In order for the equation to cancel properly, n must be equal to 2. To calculate our percentage error we plug it in as follows:

((2.7 s-2 s)/2 s)*100=35% error

The purpose of this lab was quite simple, just to learn to use the logger pro software. This was achieved through creating our own graphs as well as recording position vs. time data for the falling object. Potential sources of error in this lab included fitting our graph in a bad domain, or possibly even that our object's trajectory was not exactly perpendicular to the floor.