Subsections
6 Collisions in One Dimension
Figure 5:
A ``bouncy'' collision in one dimension.
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Figure 5 shows a diagram of a ``bouncy''
(elastic) collision in one
dimension between two objects of masses
and
initially
moving with velocities
and
. The law of conservation
of translational momentum for this collision is expressed
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(21) |
where
and
are the velocities of the objects after
the collision.
Figure 6:
A ``sticky'' collision in one dimension.
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Figure 6 shows a ``sticky'' (perfectly
inelastic) collision in
one dimension in which two objects collide and stick together.
In this case, Eq. 21 simplifies to
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(22) |
You will study one dimensional collisions involving two carts of the
kind used in Lab 3. You will test the law of conservation of momentum
(Eq. 21) quantitatively and get a feel for the qualitative
behavior of colliding carts.
- Connect the LabPro interface to the USB port of your
laptop with the cable provided.
- Click on File -> Open, double click on the
_Physics with Computers folder and on
19 Momentum Energy Coll.
- Place the two motion detectors at opposite ends of the track,
facing inward so that each detector tracks one of the two carts.
- Place the carts in contact with each other at the center of the
track. Make sure there are no obstructions between the motion
detectors and the carts, and press the Zero
button (to the
left of the Collect button on the toolbar).
- Check the boxes next to LabPro:1 DIG1:Motion Detector
and LabPro:1 DIG2:Motion Detector, and click
OK.
- Wait a few seconds for the motion detectors to stop clicking.
- You may find that the 10 second collection time is
inconveniently long for the measurements you'll be making. If so,
click the Data Collection button
to adjust the length of the measurement.
Note : It's important to put your data into the
spreadsheet provided (described in the Analysis section below)
as you go along so that you can determine whether or not the results
make sense to you.
- Orient the two carts with their magnetic sides inward. (The
spring cart has magnets under the Velcro on the side opposite the
spring bar.)
- Measure five collisions with a stationary ``target''
- Measure two collisions between carts of equal mass and three
with different mass combinations.
- Be sure to investigate the behavior of the system with
a large mass difference.
- Try to discover if it is possible for one or both of the carts
to be stationary after this kind of collision.
Make sure you collect ``good'' measurements. That is, look
carefully at your data to make sure that you have enough velocity data
from each cart both before and after each collision. Read the Analysis
section below so that you have a sense of what ``enough data'' means.
Also avoid ``violent'' collisions. Gentle collisions transfer
less momentum to the track and therefore conform more closely to the
assumption that the two carts are an isolated system.
- Measure five collisions in which both carts are initially
moving.
- Measure two collisions between carts of equal mass and three
with different mass combinations.
- Be sure to investigate the behavior of the system with
a large mass difference.
- Try to discover if it is possible for one or both of the carts
to be stationary after this kind of collision.
- Orient the two carts with their Velcro sides inward.
- Measure five collisions with a stationary ``target.''
- Measure two collisions between carts of equal mass and three
with different mass combinations.
- Be sure to investigate the behavior of the system with
a large mass difference.
- Try to discover if it is possible for the system to be
stationary after this kind of collision.
- Measure five collisions in which both carts are
initially moving.
- Measure two collisions between carts of equal mass and three
with different mass combinations.
- Be sure to investigate the behavior of the system with
a large mass difference.
- Try to discover if it is possible for the system to be
stationary after this kind of collision.
For each collision, use the Statistics button
on the toolbar with the velocity vs. time graph to find the average
velocity of each cart before and after the impact. Be sure to select
time frames (a) as close to the collision as possible and (b) in which
the velocities are approximately constant. When recording your
results, keep in mind that the sign of each velocity carries direction
information and must be kept. Record the standard deviation reported
by the statistics function as the uncertainty.
You have been given a spreadsheet
(Collisions.xls)
programmed to calculate the total translational momentum of the system
before and after each collision. All you need to do is measure and
enter the masses and velocities of the carts. Each (horizontal) row
corresponds to one collision. Your mass and velocity measurements and
their uncertainties go into columns B-M. Column A
(``Label'') is included so that you can identify the type of collision
considered.
Show your spreadsheet to your instructor and discuss preliminary
answers to the questions below.
Hand in your spreadsheet and answers to the following questions.
- For what percentage of the 20 collisions you studied are your
observations consistent with the law of conservation of translational
momentum? Mark each of these collisions with an asterisk (*) in your
spreadsheet before you print it out or by hand on the printout.
- (a) Under what circumstances in one dimensional
collisions between two objects is one of the objects stationary after
the collision? (b) How about both objects?
- Sketch qualitatively correct position vs. time graphs
corresponding to the following collisions.
- A ``bouncy'' collision between two objects with equal masses
initially moving toward each other with equal speeds.
- A ``bouncy'' collision between two objects with a large mass
difference initially moving toward each other with equal
speeds. (Label the trajectory of the larger mass.)
- A ``sticky'' collision between two objects with a large mass
difference initially moving toward each other with equal speeds.
(Label the trajectory of the larger mass.)
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Copyright © 2003-2010, Lewis A. Riley
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Updated Fri Aug 27 11:05:11 2010
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This work is licensed under a Creative Commons License.