Lab 1：Graphical Analysis

Purpose: To gain experience in drawing graphs and in using graphing software.

Equipment Needed: Windows based computer with Graphical Analysis software, Lab Pro interface, Logger Pro software, motion detector, rubber ball, wire basket.


Part 1:

We loaded the Graphical Analysis software. We used it plotted our own mathematical function.

The function we plotted by Graphical Analysis software:
f(x)=log(x)·abs("x2")

Part 2:

Connect the lab pro and motion detector to DIG/SONIC2 port on the lab pro. Load the Logger Pro software and open the graphlab file.

Then we took the position vs. time graph for a falling ball.

Position vs. time graph for a falling ball

                     ( X-axis: Time[s]  Y-axis: Position[m] )

Then we selected an appropriate data range and tried to find a function that fit the curve. 

We chose the Quadratic, our equation is: -4.4567t^2 + 9.539t - 3.094

Question: Confirm that the distance fallen adheres to the following relationship:  d α gt^n  where g = 9.8 m/s²

^{According to our graph, we found that the distance of a falling ball adheres to the quadratic function: d=At^2+Bt+C.}                         
Comparing to the d α gt^n, n equals to 2.

d α gt^n, so d=kgt^n, ("k" is a constant). Because we found n=2, so d=kgt^2 ("k" is a constant). The formula on the book shows k=0.5, so kg=0.5*9.8m/s^2=4.9m/s^2, which is close to our result 4.4567.

The data can't be perfect, but ours are close to the correct relationship. I think the error is because that our classroom is not high enough, so our ball can only fall a short distance, which makes our process have more contingency. And the air  resistance also influences the data.

Dimensional analysis:

d α gt²

^{g=（dv）/（dt）}

v=（dx）/（dt）

mass,length,time are represented by sans-serif symbols M,L,T.

so the dimension of the speed is length/time:

so:

 [v]=M/T

 [g]=M/(T^2)

 [d]=[g][t^2]=[M/(T^2)] x(T^2)=M

compare to the units:

(m,s represent meters and seconds)

v=m/s

g=m/s^2

d=(m/s^2)x(s^2)=m---- correspond to the dimension of the distance (length).


Conclusion:

      This experiment proved that the distance fallen adheres to the relationship:  d α gt^2. 

      We learnt how to use Graphical Analysis software, Lab Pro interface, Logger Pro software, motion detector in this lab, and gained experience in drawing graphs and in using graphing software. All of those helped us get into the physics class and be familiar with the equipment which we may use in the following labs.