Kinematic Equations and Freefall, the Movie
Objective: To see where 2 of the kinematic equations come from by analyzing
objects in free fall.
Equipment: Computer, printer cable
Log on to Logger Pro and when the default screen comes up go to the “Insert”
Menu and choose: Movie, Sample Movies folder, Ball Toss Folder, Ball Toss.
Watch the movie a time or two. The plot is fairly simple. At exactly 1.7 seconds
into the movie, the ball leaves the prof’s hands, moving at an initial velocity of just
under 3 m/s. It rises about a half a meter in the air and then starts to fall. From
the time the ball is released into the air, until it is caught, the only influence on its
motion is the force due to gravity. It is in freefall.
Part 1 - Qualitative predictions of what graphs for acceleration, velocity and
position will look like from the instant the ball leaves the professor’s hands until
the instant he catches it:
Indicate the “turnaround point” on each graph with an arrow. When your group
agrees upon a prediction, show me!
Part 2 – Analysis; Graphs and equations for position and velocity
In this experiment, you act as the motion sensor, and your “sampling rate” is
equal to the number of frames per second of the movie.
You can undo your actions by going to the Edit Menu.
Right mouse click to move movie/graph from back to front.
1. Enable video analysis by clicking the bottom rh icon (3 red dots and an
arrow). This gives you a column of icons along the rh side of the movie. ALSO,
go to the PAGE dropdown menu at the top of Logger Pro and choose “Auto
Arrange” so the movie doesn’t hide the graph.
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2. This step synchronizes the scale of the film with the scale of the graph. Set
scale by clicking the button yellow picket fence icon. Carefully “select” the meter
stick on the table. You should get a green line and a pop-up dialog box. Pick the
default value of 1 meter.
3. Use the Next Frame button (2 black arrows, lower left corner) to find the frame
where the basketball just leaves the professor’s hand. This occurs at 1.700 s
(time is displayed in upper rh corner).
4. Click the Add Point button (red dot in crosshairs). Carefully center the
crosshairs on the top of the basketball. Top is better than center as it is easier to
find. Click once to add the data point to the movie and the graph. If you goof up,
go to Undo. Note that the movie has advanced one frame.
5. Repeat adding points until you determine the place where the professor
catches the ball. It’s a pretty delicate operation up at the top of the trajectory
where the ball is moving very slowly. Try to be precise, and check the data
columns for obvious bad data points.
6. Remove the trail of blue dots on the movie by using the Toggle Trail button (3
red dot icon).
7. Choose an origin for position. Step backwards through the film until back at
your first point (1.700 s). Set the position (vertical axis) origin to your first point
by clicking the Set Origin button (third from the top) and clicking on the data point
on the movie. A yellow set of axes will appear on the movie, and the blue data
point on the graph should be at y=0 (check on the graph, as well as the film).
The 2nd button from the bottom is the “show origin” button. Use it to lose the
yellow axes, if they annoy you.
8. Hide X (red) data by clicking on the Y symbol on the vertical axis and
choosing Y from the list.
9. Force the time(horizontal axis) origin to zero. We want 1.7 seconds to
become 0 seconds. To achieve this, make a new calculated column under the
Data menu. Change the appropriate categories as follows:
Name: Tosstime, Short name: t,
Units: s
Equation: Click on Variables (Columns) and choose “Time”. Keep the quotes.
Complete the equation by subtracting 1.7 (“Time”-1.7). Note minus sign is
outside the quotes.
10. Check the column data to make sure it worked. Replace the time axis with
tosstime, by clicking on the horizontal-axis label. Now t=0 s is when the ball was
released.
Velocity vs. time graph. – Choose Y-velocity for the vertical axis to bring up a
velocity graph of the data.
A. How does it compare to your prediction?
B. Perform a linear fit (R= ) by selecting the “good” part of the data (leave out
any points at the end which are obviously not in freefall. 2. Record the equation
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of the best-fit curve and print the graph (appropriate title on top and initials in
the footer).
Your specific equation______________________
C. Explain what each term in this equation actually represents for the ball.
Don’t use terms like slope, or y-intercept. Instead, explain what they tell you
about where the ball is, or what the ball is doing.
m (slope):
b (intercept):
D. Are the values for m and b reasonable for this motion? Explain.
E. Rewrite this equation as a general one in terms of kinematic variables (i.e.
position, velocity, acceleration).
_________________________________________
Position vs. time graph (choose Y for the y axis)
A. How does it compare to your prediction?
B. Find the equation that best fits this curve. You probably realize that the linear
fit isn’t appropriate; we’ll need another equation type. Use the curve-fit icon
[f(x) =]. Print the graph:
Record your equation of the best-fit curve
________________________________
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This is one of the kinematic equations. It describes the position of an object
with constant acceleration, which is the case for an object in free fall.
C. Explain what each term in this equation actually represents for the ball.
Don’t use terms like slope, or y-intercept. Instead, explain what they tell you
about where the ball is, or what the ball is doing.
A-
B-
C-
D. Are the values for A and B reasonable for this motion? Do they agree with
the previous kinematic equation? How so?
E. Discuss the value of C obtained from the curve fit. What should the actual
value be? If your value is different, explain why.
F. Rewrite this equation as a general one in terms of kinematic variables (i.e.
position, velocity, acceleration).
_________________________________________
G. What is the derivative of the equation above with respect to time?
_________________________________________
H. How does this compare to the equation for the velocity time graph?
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Questions
1. In both equations there are terms that represent the acceleration of the object.
Record the value that you obtained for acceleration (include sign):
____________ m/s/s.
Is this value reasonable? Explain:
2. Describe what happens on the position vs time graph when the direction of
the ball changes from up to down:
3. Describe what happens on the velocity vs time graph when the direction of
the ball changes from up to down:
4. Did the sign (i.e. direction) of the acceleration change when the direction of
the ball’s motion changed? Explain how you can tell from any of your graphs
whether it did or did not.
5. Does your predicted acceleration vs. time graph
agree with your answer to #4 above? Explain, and
change your graph if necessary.
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