Analysis of AirTrack Momentum Data Using Spreadsheets and MATLAB
Spreadsheet:
1. Using the spreadsheet suggested by the teacher, enter your data as follows:
column A should be the mass of glider 1,
column B should be the initial velocity of glider 1,
skip a column,
column D should be the final velocity of glider 1,
skip a column,
column F should be the mass of glider 2,
column G should be the initial velocity of glider 2,
skip a column,
column I should be the final velocity of glider 2.
2. Fill numbers for each run into the appropriate columns. Remember, a glider
as rest has a velocity of 0 and velocities may be positive or negative depending
on direction of motion. When all experimental values are filled in, save the
spreadsheet first in its native format and then once again as an ASCII text file.
Be sure to name this second file something different from the first.
3. Using the first spreadsheet saved, enter formulas for the momentum (initial
and final) in each of the skipped columns. Thus cell C2 becomes A2*B2 or
A2*B2/1000 (if your mass was in g). This formula can be copied down the
column. Repeat for the other skipped columns, using the appropriate
combinations of mass and velocity: column C should be the initial
momentum of glider 1, column E should be the final momentum of glider 1,
column H should be the initial momentum of glider 2, and column J should
be the final momentum of glider 2.
4. Now determine the total initial momentum and the total final momentum.
The total initial momentum should be in column K and represents the sum of
columns C and H. The total final momentum should be in column L and represents
the sum of columns E and J. Determine the average momentum for and the
percent difference between these two columns. If there is a sign change between
the two columns, remember to take the absolute values of the numbers.
5. In two more columns, determine the momentum change for glider one and the
momentum change for glider two. Compare these two columns and determine
a percent difference.
6. Record the results of the spreadsheet and save it.
MATLAB:
1. Open MATLAB. Open the text file saved earlier and edit out all words.
You can leave spaces and even empty lines in the program, but it should
consist of nothing but numbers - columns of masses and velocities. When
the file is edited, save it as glider.dat . MATLAB will ask about a .m
extension, but click on No .
2. From the command window, type the following:
load glider.dat loads in the data file
mass1 = glider(:,1); reads the first column of the glider
file and names that column mass1
mass2 = glider(:,4);
intvel1 = glider(:,2);
finvel1 = glider(:,3);
intvel2 = glider(:,5);
finvel2 = glider(:,6);
What did these commands do?
3. Now we calculate the total initial and final momentum. All the values are
entered as long lists (1 column matrices). We need to right our commands so
that MATLAB knows we want to multiply the first number in one column by the
first number in the next, the second by the second and so forth. We do not
want to do matrix multiplication. To achieve this, multiplication signs are
followed by a space and a period. So the commands below must be typed exactly
as they appear as far as the spaces around the multiplication and
division signs are concerned. Remember you only need the 1000 at the end if
your masses are in kg.
momint = (mass1 .* intvel1 + mass2 .* intvel2)/1000
This time we leave off the semicolon so that we can see the results.
momfin = (mass1 .* finvel1 + mass2 .* finvel2)/1000
Remember that you may need to use the absolute value function in one of these
equations. Compare these values to those generated by your spreadsheet. Comment
on any significant differences.
4. Now the percent error:
error = 100 * (momfin-momint) ./(.5*(momint +momfin))
Again, compare these results to those from the spreadsheet and comment on any
significant differences.
5. Now determine the change in momentum for glider one and the change in
momentum for glider two (You write the commands!) . Also, determine a
percent difference error.
Questions
1. Does your data support or refute the conservation of momentum? Are some
cases ÒbetterÓ then others? Suggest some sources of error and explanations
for differences between cases.
2. Does your data consistantly support a residual slope to the air track or
the existence of some friction? Explain
3. Finally, which method - the spreadsheet or MATLAB seemed to be a timesaver?
Give reasons for your choice.