Experiment
Graphing Constant Acceleration (S’12)
2
The most useful examples of motion to study are examples of constant acceleration. Many
complicated motions can be studied by breaking them into separate time intervals, each having a
different constant acceleration. Many motions that derive directly or indirectly from the pull of
gravity are good examples of constant acceleration, as long as air resistance is negligible. We
will use a track that can be tilted to generate constant accelerated motion on a cart.
Make as many predictions as possible as you work through this lab. When you correct your
predictions use a different color pencil, and make sure you and your partners understand the
corrected graphs.
OBJECTIVES/PURPOSE:
For the special case of one-dimensional motion with a constant (or nearly constant)
acceleration, student will learn:
- how to relate graphs plotting position (d) , velocity (v), and acceleration (a) vs time(t).
- how to read, draw, and analyze such graphs, using slope and area concepts.
the meaning of positive and negative positions, displacements, velocities, and
accelerations.
PRE-LAB PREPARATION/PRELIMINARY QUESTIONS
1. Before starting, sketch your predictions of distance, velocity, and acceleration vs. time graphs
for all the cases you will be trying out in the lab. Use the axes provided in pages 3, 4, 6, & 8.
The cases that you will be trying out in the lab are:
-
an object at rest (v=0)
an object moving in the positive direction and slowing down (+v & -a)
an object moving in the positive direction with a constant speed (+v & a=0)
an object moving in the positive direction and speeding up (+v & +a)
an object moving in the negative direction and speeding up (-v & -a)
an object moving in the negative direction and slowing down (-v & +a)
an object moving in the negative direction, slowing down, then turning around (-v & +a)
an object moving in the positive direction, slowing down, then turning around (±v & -a)
MATERIALS
Power Macintosh or Windows PC
Universal Lab Interface
Logger Pro
Vernier Motion Detector & protective cage
dynamics cart & track
color pencil (to correct graphs)
PROCEDURE
Part l Setting up the Computer
A. Connect the Motion Detector to PORT 2 of the Universal Lab Interface (ULI) and turn on the
ULI first with the switch in the back.
1. Log on the computer using your student password. Then click on the LoggerPro logo.
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Experiment 2
2. Place the Motion Detector at one end of the track. Make sure that the motion detector is
behind the protective bar.
It is very important NOT to let the motion detector be struck by the moving cart
during the course of this experiment, as this can damage the motion detector! One
member of the team should be assigned the task of protecting the motion detector.
3. Prepare the computer for data collection by opening file Exp06 in the Computers in
Physics folder. You do this first clicking File Menu, then Open, then Computers in Physics,
and finally Exp06.
4. The screen should show three graphs: one of position, one of velocity, and one of
acceleration vs. time. It will be necessary to change the scales of these graphs. The scales can
be changed easily by clicking a number, changing its value, then pressing the “enter” key. To
start, set the maximum distance at 1.5 m, the maximum velocities at ±1 m/s, and the maximum
accelerations at ±0.5 m/s2. Finally, change the Sampling rate under the Experiment Menu to
10 per sec so your graph will be smoother.
B. The following facts will help you understand your graphs better. So keep them in mind
when doing this experiment and refer to them when necessary.
1. The detector is the origin and it is programmed to record all positions in front of it as
positive positions. Since the detector cannot detect anything behind it, it is not possible to
generate negative positions in these examples. But a change in position (called the
displacement or ∆d) will be positive when moving away from the motion detector (+∆d) or
negative when moving toward the motion detector (-∆d)
2. As a result of the way the positive direction is defined by the motion detector, moving
away from the motion detector is moving in the positive direction and represent positive
velocities (+v). Moving toward the motion detector is moving in the negative direction and
represent negative velocities (-v).
3. The motion detector does not read anything closer than 0.5 m. You should attempt to
keep the cart further than this in all cases. The motion detector also gives you a couple of
seconds of lead-time (two warning beeps) before it actually starts recording data after
clicking the Collect button.
4. In some of these experiments you will be giving the cart an initial push to get it started.
You should practice a run before collecting data to make sure that the cart will do what you
want it to do and not run off the track or get too close the motion detector. Work together
with the members of your group to figure out the best strategy for generating a good run.
5. Because we are interested in studying constant accelerations in this experiment, you
should avoid recording any motion during an initial push or a bounce of the cart at the end of
the track. Concentrate on the motion occuring when the cart is freely moving on the track. If
you have any motion that is not constant acceleration, simply ignore it or redo that graph.
6. When reading and analyzing a graph the features of interest are: the values of the graph,
the slope (or slopes) of the graph, and the area (or areas) defined by the graph and the
horizontal axis. Pay attention to these features as you study the graphs and answer the
questions.
Positive direction
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Physics with Computers
Constant Acceleration
Part Il Comparing an object at REST (A) to an object SLOWING DOWN (B).
In these two cases you need to have more friction than provided by the wheels. Use the screw on top of
the cart to push the friction bar down so it slightly touches the track. When you produce a good example,
copy the part of the graph corresponding to the freely moving cart over the predictions that you drew
beforehand
A. Place the cart somewhere in the middle
of the track. Press Collect to start the
motion detector and wait until it Stops.
B. Place the cart 0.5 m from motion
detector. Press Collect to start the motion
detector and give the cart enough of a
push so that it will coast to the end of the
track from the friction along the way.
(+)---> direction
(+) ---> direction
d
d
t
v
t
v
t
a
a
t
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t
t
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Experiment 2
Part IIl Comparing an object moving with CONSTANT VELOCITY (C) to an object SPEEDING
UP (D) , both moving away from the detector (the positive direction).
We want to minimize friction in the rest of these cases. Use the screw to retract the friction bar back into
its original place. After generating a good example of each case, copy the part of the graph
corresponding to the freely moving cart over the predictions that you drew below in the pre-lab seection.
C. Give the cart a slight push to get it
started. The cart should continue to slide
without slowing down. If the cart shows
signs of slowing, elevate the track
slightly to cancel the effect of friction in
the wheels. Press Collect to start the
motion detector and wait until it Stops.
D. Elevate the track enough to produce a
visible acceleration of the cart down the
track and away form the motion detector.
Press Collect to start the motion detector
and let the cart go. Stop the detector
before the cart bounces back
(+)
(+)---> direction
d
d
t
v
t
v
t
a
a
t
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t
t
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Constant Acceleration
Before proceeding to the next part, answer the following questions about case A, B, C & D.
Remember that “speed” means the magnitude or value of the velocity regardless of direction.
1. What feature of each graph by itself (such as shape, slope trend, + value, etc...) indicates
that the cart is moving away from the detector … [consider each graph by itself without
reference to the other graphs]
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
2. What feature (if any) of each graph by itself indicates that the speed (magnitude of
velocity regardless of direction) of the cart is changing …
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
3. What feature (if any) of each graph by itself indicates that the speed (magnitude of
velocity regardless of direction) of the cart is increasing … (as opposed to decreasing)
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
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Experiment 2
Part IV Comparing an object SLOWING DOWN as it approaches the motion detector with an
object SPEEDING UP as it approaches the motion detector (-direction)
This is a good time to recheck the predictions you made in the pre-lab before going on with the
experiment. Proceed to generate the best example of each case and copy the part of the graph
corresponding to the freely moving cart over your predictions.
E. On the tilted track, place the cart at the
bottom. Press Collect to start the motion
detector and give the cart a slight push
up toward the motion detector. Before
the cart reaches the highest point or gets
too close to the detector, Stop recording.
F. Place the motion detector at the bottom
of the track. Press Collect to start the
motion detector and release the cart from
the top so that is speeds toward the
detector. Before the cart gets to the
detector Stop recording, and stop cart!
(+)
(+)
d
d
t
t
v
v
t
t
a
a
t
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t
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Constant Acceleration
Answer the following questions about cases E &F. Make sure you understand these concepts!
4. What feature (if any) of each graph by itself indicates that the cart’s speed is increasing vs.
decreasing…
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
5. Explain why both graphs show negative velocities values even though the cart moves uphill
in one case and downhill in the other?
6. How can an object have a (+) acceleration when its speed is decreasing (car is slowing
down)? How can an object have a (-) acceleration when its speed is increasing (car is
speeding up)?
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Experiment 2
Part V Comparing objects TURNING AROUND as they move up and down the incline
G. . With the motion detector at the bottom
of the track, place the cart at the bottom
next to it. Press Collect to start the motion
detector and give the cart a slight push
up, away from the motion detector.
Allow enough time for the detector to
record the up and down motion of the
cart. Stop when the cart is near its
starting point.
H. Put the motion detector back at the top
of the tilted track and place the cart at
the bottom. Press Collect to start the
motion detector and give the cart a slight
push up, toward the motion detector.
Allow enough time for the detector to
record the up and down motion of the
cart. Stop recording when cart is near its
starting point.
(+)
(+)
d
d
t
t
v
v
t
t
a
a
t
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t
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Constant Acceleration
Answer the following questions about cases G and H. Make sure you understand these concepts!
7. What feature (if any) of each graph by itself indicates that the cart is turning around…
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
8. What feature (if any) of each graph by itself indicates that the speed of the cart is first decreasing
and then increasing…
a) in the position graphs?
b) in the velocity graphs?
c) in the acceleration graphs?
9. Explain why the sign (+ or -) of the acceleration doesn’t change when the cart turns around at
the top of the track and goes from slowing down to speeding up?
10. Why do the two graphs look different even though they represent the same motion of the cart?
(Note how the graphs are mirror images of each other).
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Experiment 2
11. When the cart turns around the velocity is instantaneously zero. Explain why the acceleration
is NOT zero.
12. We assumed that friction between track and cart was negligible. Do you see any evidence in
the graphs that friction was not negligible? Describe the evidence.
SUMMARY OF RESULTS
1. Do motion diagrams for all the cases A->H. In each case draw three arrows representing the
velocities near the start, near the middle, and near the end of the motion; and also draw
acceleration arrows representing the change in the velocities during the motion. For the last
two cases draw a set of arrows for the up motion and another set for the down motion.
No arrows here since v=0 and a=0!
A
+v
B
-a
C
D
E
F
G
H
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Constant Acceleration
EXTENSIONS
1. Sketch your best guess of the graphs that describe the following scenarios.
Scenario 1: Move steadily (with constant speed) away from the detector for about three meters,
then stop for a while, finally return to your original position at a faster, but steady pace.
d
v
a
Scenario 2: Starting about 4 m from the detector, move steadily (with constant speed) toward the
motion detector for about 2 m, then slow down steadily (with constant acceleration) until you
come to a stop before the detector.
d
v
a
Scenario 3: Starting near the detector, accelerate steadily away from the detector for about 2 m,
then hold a constant speed for 1 meter, finally slow down steadily until coming to rest at about
4 m from detector.
d
v
a
2. What would be the changes in the position, velocity, and acceleration graphs if the motion were
being measured from a different origin (0 position). For example, if the detector were moved
further up (or lower down) the ramp.
3. Explain why we never got negative positions in any of the cases (AH) in this experiment.
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Experiment 2
4. You throw a ball up in the air over a motion detector set on the floor. Sketch the motion
graphs for the ball going up and down after it leaves your hand. Check your notes and your
homework!
d
v
a
5. You fire a toy rocket vertically and record its motion with a detector on the ground. At first the
rocket accelerates upward due to its fuel, but eventually the fuel runs out and the rocket returns
to earth after reaching a peak height. Sketch graphs of the rocket motion including the fueldriven stage of the rocket motion as well as the free-falling stage afterwards. Focus on the
differences from the case above.
d
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v
a
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