Subsections
6 Collisions in One Dimension
Figure 4:
A ``bouncy'' collision in one dimension.
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Figure 4 shows a diagram of a ``bouncy'' 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 5:
A ``sticky'' collision in one dimension.
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Figure 5 shows a ``sticky'' 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 Labs 3. You will test the law of
conservation of momentum (Eq. 21) quantitatively and get a
feel for the qualitative behavior of colliding carts.
This week, you will use the white Universal Lab Interface (ULI)
instead of the blue LabPro interface.
- Plug the serial cable from the ULI into the serial port (the
9-pin port on the back labeled ``10101'') of your laptop, and run
Logger Pro.
- A Setup Interface window should appear. Make sure the
Port box is set to COM1, and click the
Scan button. An icon that looks roughly like the front panel
of the ULI should appear in the Logger Pro menu bar. If it
doesn't, ask for help.
- Click on File -> Open, double click on the
_Physics with Computers folder and on the Exp 19
Momentum Energy Coll subfolder. Open the file called Exp 19
Motion Detector.mbl.
- Place the two motion detectors at opposite ends of the track,
facing inward so that each detector tracks one of the two carts.
- Note : It's a good idea to put your data into the
spreadsheet provided (described in the Analysis section below), and
determine whether or not the results make sense to you as you go
along.
- 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 Analyze -> Statistics on the velocity
vs. time graph to find the average velocity of each cart before and
after the collision. 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 a hardcopy of 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 distance 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.
- A ``sticky'' collision between two objects with a large mass
difference initially moving toward each other with equal speeds.
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Copyright © 2003-2007, Lewis A. Riley
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Updated Tue Nov 30 13:48:34 2004
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This work is licensed under a Creative Commons License.