PHYS-1500 PHYSICAL MODELING
FALL 2006
8/29/2006, Class 1: Free Fall
NAME: ______ SOLUTIONS ______________________
Open the Excel file "freefall.xls". The file contains data that were exported from the video.
In column B, the time has been shifted so that t = 0 at the instant the weight is dropped. This was
done by entering the formula =A6-$A$6 in cell B6, and then copying it to the cells below it. Do
the same for the values of y. That is shift the y coordinate system so that y = 0 at the point where
the weight is released. Do this by entering =D6-$D$6 in cell E6, and copying it to the cells below
it.
Now, calculate vy as a function of t. Use the formula, vy = y/t to calculate the average vertical
component of velocity over short time intervals. This can be done by entering the following
formula in cell F6:
=(E7-E6)/(B7-B6).
Then, use the "Fill Down" command found under the "Edit" menu at the top of the screen to copy
the command to cells F7 through F22.
Next, calculate ay as a function of t. Use the formula, ay = v/t to calculate the average vertical
component of velocity over short time intervals. This can be done by entering the following
formula in cell G6:
=(F7-F6)/(B7-B6).
Then, use the "Fill Down" command found under the "Edit" menu at the top of the screen to copy
the command to cells G7 through G22.
1. Use Excel to make graphs of y vs. t and vy vs. t. Sketch the graphs, and be sure to indicate
which one is y and which is vy.
0
-0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.2
0.3
0.4
0.5
-2
v (m/s)
y(m)
-0.6
-0.8
-1
-3
-4
-1.2
-1.4
-1.6
0.1
-1
-0.4
y = -4.9952x 2 + 0.025x - 0.003
-5
y = -9.9285x - 0.1635
-6
-1.8
t(s)
t (s)
0.6
2. Find the slope of the graph of vy vs. t. What is the value of the slope? What is the significance
of the slope of the graph of vy vs. t?
slope = ___9.93 m/s²______
The slope is shown on the graph. The slope is the object’s acceleration. units
3. Find the average value of the acceleration that you calculated.
aav = _____9.34 m/s²____
units
4. Finally, enter a “model” formula for the position of the weight as a function of time in column
H. Plot both the measured values of y and the values calculated from the model on the same
graph to show that they agree.
The formula used is y = – ½(9.8 m/s²)t²
0
-0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
-0.4
y (m)
-0.6
-0.8
data
model
-1
-1.2
-1.4
-1.6
-1.8
t (s)