Analyzing the motion of objects in free fall with video

Grossmont College Physics
P. Blanco
Analyzing the motion of objects in free fall with video
What does the motion of an object in free fall look like? You will use the Kodak Zi8 video camera to
record the motion of a falling object at 60 frames per second (fps). This is twice the number of frames
that are taken by standard video cameras. Increasing the frame rate causes more images to be taken
each second and enables a more accurate analysis of objects whose motion is changing rapidly, i.e.
accelerating.
Before proceeding, familiarize yourself with the operation of the Kodak Zi8 video camera.
1. Use the red directional button to set the camera to 720p/60FPS mode.
2. Make a video clip of your lab partner dropping a ball from a height of about 1.0m. The camera should be
held steady and upright. The ball should fall within the plane of the meter stick – see the diagram below. Try
not to let the ball spin or roll off your hand.
Left: Plane of the camera. Right: Plane of the falling object and meter stick.
3. You can replay the clip on the camera. If you need to record the clip again, delete the first attempt to
make room in the camera’s tiny memory. Once satisfied that you recorded the motion of the ball, connect
the camera to the laptop’s USB port. The camera’s flip-out USB connector can be accessed by a slider
with the USB symbol (
) on the bottom of the camera body, as shown.
4. When plugging in the USB connector to the PC, the computer may prompt you to open an
application or view files. You can cancel and exit this window if it pops up.
5. Copy the video to your computer Desktop as follows: Go to My Computer → Removable Disk →
DCIM.There will be folders with names that start with a number. The larger the number, the more recent
the video. Go to the most recent folder and copy (drag) your video to the Desktop. The video will be a
QuickTime format file with a name ending in .MOV.
7. Open the LoggerPro program (there should be an icon on the Desktop) and go to Insert → Movie,
navigate to the Desktop where your video is located and click Open. You should now see the first frame of
your video in LoggerPro.
8. Click on the Enable/Disable Video Analysis button (
) in the bottom right corner of the video. You
may have to resize the video to see this button. Your LoggerPro screen should look something like this:
9. To define the length scale, first resize the movie (by dragging the bottom right corner) so that it takes up
more than half of the screen, then click on the Set Scale button ( ) on the right side of the window. Your
cursor will turn into a crosshair. Now Hold down the left mouse button and drag to trace a green line to
cover the length of the meter stick. Let go of the mouse button to complete the line. Make sure the line
coincides with the start and end of the meter stick. This step sets the scale for all of your data, so is
worth repeating carefully if you did not get it quite right the first time.
10. The window shown below will pop up. Since the line you drew corresponds to 1.0 meters in the video,
enter 1.0 and m in the Scale and Units boxes as shown below.
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11. You will now add a series of points that marks the position ball in your video. Advance the video
using the slider or the double arrow (
) buttons to the time just after the ball begins to drop. The slider
below the video is good for coarse adjustments, while the left and right arrow buttons are good for
fine adjustments since they advance or reverse the video one frame at a time.
12. Click on the Add Point button ( ) on the right side of the window. Your cursor will again turn into a
crosshair. Carefully click on the center of the ball to add a point (blue dot). The video will automatically
advance by a single frame. Add another point on the center of the tennis ball. Continue this process for the
duration of the object’s fall. Stop adding points when the ball moves off the screen or hits the floor.
Note: If you make an error you can either move or delete a point. Use the Select Point button
to
select a particular point. Hit the Delete key to delete the point, or move the point using the mouse to
a new location.
13. LoggerPro will automatically generate a graph for x vs t and y vs t. Provided that the camera was
level and the ball fell vertically, the first graph should be a flat line (i.e. x is constant). Display only the y vs t graph by left-clicking on the vertical label of your graph and selecting Y.
14. Fit a quadratic function on your y vs t graph.,by clicking on the function fitting icon (
)in the top
row of the Logger Pro window, and selecting Quadratic. Record the best-fit equation in your lab report.
15. Now isplay the graph of vertical velocity Vy vs t by clicking on the vertical label of your graph and
selecting Y Velocity. Click on the fit icon (
) and select Linear. Record the best-fit equation.
16. Repeat the experiment, but this time throw the ball upwards from near ground level in the vertical
direction and capture a video clip of its up-and-down path. Try to keep the motion in the vertical direction
and make sure you the ball stays in the field of view at the top of its motion. As you will learn later though, a small
horizontal displacement will not affect your results for the vertical motion.
As before, record the best-fit quadratic equation for the ball’s height y vs t, and the best fit linear equation for its
vertical velocity height y vs t,
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PART 1 QUESTIONS (to be answered in your lab report):
1. The vertical position of a dropped object in free fall is described by the equation (assuming y is “up”):
y = y 0 − 1 2 gt 2 while its vertical speed is given by: v y = −gt For an object dropped from rest from€an initial height of y0 = 2.0m:
times 0.2s, 0.4s, 0.6s?
a . What is the height y of the object at €
b. How far has the object fallen between each of these time intervals?
c. What is the velocity of the object at these times?
2. For your falling ball, describe the spacing between successive points on your video as a function of time.
Does the spacing increase, decrease or remain the same and why? How about when the ball was thrown
upwards?
3. What are possible sources of uncertainty in your measurement? How could these be reduced?
4. Can an object be not moving and yet accelerating at the same instant in time? Explain how this relates to
the motion of the ball in this experiment.
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Part 2: Air resistance, gravity, and terminal speed
Galileo’s experiments with falling objects showed that gravity causes all objects to accelerate at the same
rate as long as other forces such as air resistance can be neglected. From Newton’s 2nd law it follows that the
force of gravity Fg must be proportional to an object’s mass, i.e.
Fg = mg
(Equation 1)
In the second part of this laboratory we shall continue using video analysis but this time we shall observe the
behavior of falling object that experiences significant air drag. For most objects moving through the air, the
drag force opposing their motion is described by the relation
FD = kv2
(Equation 2)
Where v is the speed and the constant k depends on the air density and the object’s shape and size. For
instance, the same piece of paper will experience less air drag if it is crumpled into a tight ball than compared
to its motion through the air unfolded.
Since air drag increases with speed, an object falling through the air will not accelerate at a constant rate, but
will instead gradually reach a terminal speed when the force of gravity is balanced by that of air resistance
pushing against its motion. Increasing the mass of the object means that the drag force required to balance it
must get larger – therefore the object will fall faster. We shall test the relationship in Equation 2 in this lab
by measuring the terminal speed of stacked coffee filters.
Procedure
(This assumes you are now familiar with the methods used in Part 1 to analyze the motion of a falling ball).
1. Using the meter stick to provide a scale as before, drop a coffee filter and make a video clip of its vertical
descent.
2. Once the movie clip is imported into Logger Pro, look at the graph of height y vs t Sketch a copy of this
graph in your lab notebook. (Use a ruler for axes and scales but you can draw the curve free hand.
3. Select a range of time for which the slope of y vs t appears constant, i.e. for an interval when the coffee
filter is falling at its terminal speed.
4. Fit a straight line to your graph of y vs t over this time interval using the R= tool at the top of the
display. Record the fitted slope, which is the terminal speed of the filter.
5. Repeat the experiment with 2, 3, 4, and 5 coffee filters nested together, recording the terminal speed for
each case. You do not need to copy the graph for these additional trials.
Analysis
You should now have a table in your lab notebook with column headings of {# of filters dropped together}
and {terminal speed in m/s}. But the relation in Equation 2 tells us that terminal speed increases with the
square of the speed, so add another column to your table with the calculated (terminal speed)2.
To verify if equation 2 is a good description of your data, plot a graph with {number of filters nested
together} on the horizontal axis vs. {terminal speed squared} on the vertical axis. Use a ruler and include
clear axis labels. Also mark the point (0,0) at the origin.
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Now draw a straight line through (0,0) which comes closest to fitting your data. Calculate the slope of this
straight line (= “rise over run”) and record it in your lab notebook.
Before leaving…
Show your data table, graph and results to the instructor, who will sign your lab notebook pages. These will
be included on the back of the report you will write on this 2-part experiment. After putting the equipment
away, make sure you take note of the format for this report which will be posted on the whiteboard.
Part 2 QUESTIONS (to be answered in your lab report):
1. Can your plotted points be fitted adequately with a straight line on the graph of terminal speed squared
vs. number of filters, as Equations 1 and 2 would predict? What sources of uncertainty might affect your
results? Summarize your conclusions in a few sentences.
2. A student writes: “A basketball falls faster than a ping-pong ball because the basketball experiences less
air resistance”. Given that air resistance increases with an object’s size, how would you correct their
statement?
3. For what combination of an object's physical properties and speed through the air may we "neglect air
resistance", as often assumed in science textbooks, and treat the object as falling under the influence of
gravity alone?
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