Freefall  The acceleration of gravity
Gravity is the force of nature we are most aware of.
One can argue that other forces, such as
the electromagnetic force, which holds molecules together in solid objects, or nuclear forces, which determine the structure of atoms, are more important,
but these forces are less obvious
to us. Near the surface of Earth the force of
gravity on an object of mass m equals F_{g} = mg. It is
constant and points straight down. If we can neglect other forces and the
net force is approximately equal to F_{g}, then we have motion
with constant acceleration g.
Open a Microsoft Word document to keep a log of your
experimental procedures and your results. This log will form the basis of
your lab report. Address the points highlighted in blue.
Answer all questions.
Observation
Hold a tennis ball at about your height and then let go. Observe the
motion of the ball.
Describe the motion as the ball is falling.
 Estimate how long it takes the ball to reach
the floor.
 What can you say about the speed of the ball
as a function of the distance it has already fallen?
 If you drop the ball from about half of your
height, does it take approximately half the time to reach the floor?
Experiment
It does not take the ball a long time to reach the floor.
It is hard to get detailed information about its motion without using external
measuring instruments. In this experiment the instrument is a video
camera. You will analyze a video clip. The clip shows a person
dropping a ball. You will determine the position of the freelyfalling
ball as a function of time by stepping through the video clip framebyframe and
by reading the time and the position coordinates of the ball off each frame.
You will construct a spreadsheet with columns for time and position and use this
spreadsheet to find the velocity as a function of time. The slope of a
velocity versus time graph yields the acceleration of the ball.
Procedure:
To play the video clip or to step through it framebyframe click the "Begin" button.
The "Video Analysis" web page will open. Choose one of the ball_x.mp4 video clips.
 "Play" the video clip. When finished, "Step up" to
frame 0. In some browsers you have to click "Pause" first.
 In the setup window choose to track the ycoordinate of an
object.
 Click "Calibrate". Then click "Calibrate Y".
The video clip contains calibration markers. Each black and white stripe
is 10 cm = 0.1 m wide. Position the cursor over top end of the highest
black stripe and click the left mouse button. Then position the cursor
over the top end of the lowest black stripe, 80 cm below, and click the left
mouse button again. This will record the ycoordinates of the chosen
positions. Enter the distance between those positions into the text box in
units of meter. For the example positions, you would enter 0.8 into the
text box. Click "Done".
 Click the button "Click when done calibrating". A spreadsheet
will open up. Click "Start taking data".
 Start tracking the ball. Position the cursor over the
ball. When you click the left mouse button, the time and the ycoordinate
of the ball will be entered into the spreadsheet. You will automatically
step to the next frame of the video clip.

Repeat for each frame in the video clip as long as the ball is
moving downward. Then click "Stop Taking Data".
Highlight and copy your table. Open Microsoft Excel, and paste the table
into an Excel spreadsheet. Your spreadsheet will have two columns, time (s)
and y (m). If you followed the instructions above, the the yaxis points
down.
Produce a graph of position versus time.
Label the axes.
 Describe your graph? Does it resemble a
straight line? If not, what does it look like?
 Was the ball moving with constant velocity?
How can you tell?
Let us find the velocity of the ball as a function of time. We find v_{y}
= ∆y/∆t by dividing the difference in successive position by the difference in
the times the ball was at those positions.
 In your spreadsheet type type v (m/s) into cell C1.
 Type 0 into cell C2. The ball starts from rest, its initial
velocity is zero
 Type =(B3B2)/(A3A2) into cell C3. Copy the formula into the
other cells of column C, down to the secondtolast cell.
Produce a graph of velocity versus time.
Label the axes.
 Describe your graph? Does it resemble a
straight line? If not, what does it look like?
 Rightclick your data in the velocity versus time graph and choose
"Add Trendline". Choose "Type, Linear" and "Options, Display equation on
chart". An equation y = ax + b will appear on your graph, where the number a is
the slope and the number b is the yintercept. What is
the physical meaning of the slope of the velocity versus time graph, if the
graph is a straight line?
 Paste your velocity versus time graph (with
trendline) into your log.
 What value do you obtain for the acceleration of
the ball? How does your experimental
value of the magnitude of the acceleration compare to the accepted value of
the magnitude of the acceleration of a freefalling object?
Reminder: percent difference = 100%* accepted value  experimental
value/accepted value
 What factors do you think may cause your
experimental value to be different from the accepted value? In other words,
what are some possible sources of error?
For motion
with constant acceleration we expect that y changes as a function of time as
y = x_{0} + v_{0}t + ½at^{2}, where a is the
acceleration. For an object accelerating at a constant rate g we have y = y_{0} + v_{0}t + ½gt^{2},
so y as a function of t is a polynomial of order 2 (a section of a parabola).
We can reduce numerical errors in finding the acceleration of the ball by
fitting our position versus time data directly with a polynomial of order2.
 Rightclick the data in your position versus time graph and choose "Add Trendline".
Choose Polynomial, Order 2 and under options click "Display equation on
chart". An equation of the form y = b_{1}x^{2} + b_{2}
x + b_{3} will be displayed where b_{1}, b_{2}, and
b_{3} are numbers. Since we are plotting y versus t, the number b_{1} is the best
estimate for g/2 from the fit. Therefore the value of the acceleration
determined from the fit is g = 2b_{1}. Since our yaxis points
downward, we expect a to be close to g = 9.8 m/s^{2}.
 Paste your position versus time graph (with
trendline) into your log.
 Does the polynomial of order 2 fit the data well?
What value do you obtain for the acceleration of the ball from this fit?
 We now want to find the uncertainties in the fitting
parameters. On the menu bar click click data, data analysis,
regression. For the input y range choose the data in column C. For the
input x range choose the corresponding cells of columns A and B. Under
output options check new worksheet, and under residuals line fit plots. Click OK.
 The regression function also finds the best fitting
polynomial of the form y = b_{3 }+ b_{2}x + b_{1}x^{2}
for your data. Under SUMMARY OUTPUT, Intercept, you will find the
coefficient b_{3}. Under SUMMARY OUTPUT, X Variable 1, you will
find the coefficient b_{2}, and the standard error in this
coefficient from the fit. Under SUMMARY OUTPUT, X Variable 2, you will
find the coefficient b_{1}, and the standard error in this
coefficient from the fit. The errors are due to uncertainties in the
measurements and are computed using statistical analysis.
 The uncertainty in g from statistical analysis is 2 times the
uncertainty in the coefficient b_{1}. What value did you obtain for the
uncertainty in g?
Convert your log into a lab report.
Name:
Email address:
Laboratory 2 Report
 In one or two sentences state the goal of this lab.
 Insert your log with the requested graphs and the answers to the
questions in blue font.
Save your Word document (your name_lab2.docx), go to Canvas, Assignments, Lab
2, and submit your document.