Conservation of Momentum
First-hand Investigation
Is your linear air track gathering dust on a shelf somewhere? Have you lost the accessories box?
Studying momentum in physics? If the answer the last question is ‘yes’, then it may be time to dust
off the linear air track. Despite the advent of air hockey games, students still have a fascination with
watching the gliders move smoothly along the track. There is an intrinsic student motivation in this.
Momentum conservation in collisions between gliders can be investigated, providing the velocity of
the gliders can be conveniently determined before and after a collision. In our investigation, we
used two gliders with the glider magnets
inserted with opposite poles facing each other so
that the gliders stuck together when they
collided.
Two light probes connected to our Texas
Instruments data logger provided a simple
method of gathering data that enabled the
velocity of two gliders before and after a
collision to be calculated. The TI calculator-based data logger is conveniently portable and at the
conclusion of the experiment, it was easy to put transfer the data to the school’s computer network
so that students could use the data to write up a formal report. The data was projected ‘live’ onto an
overhead screen in the laboratory for immediate feedback and analysis in the classroom.
Experimental Arrangement
A light source, such as a 36 W globe, is placed about 30 cm on one side of the track with the
filament about 2 cm above the level of the track. Two light probes are placed about 30 cm apart on
the other side of the track to the globe, facing the globe and vertically aligned with it. The light
probes should be placed close to the
track so that the passage of the glider
past the probe significantly reduces
the intensity of the light reaching the
probe from the globe.
When a glider passes along the track,
it blocks the light reaching the
sensor.
We set up the experiment with glider
B stationary between the light
probes. Glider A was then pushed
along the track towards B, passing
by the first light probe completely
just before colliding with and
sticking magnetically to glider B. The two gliders then continued past the second light probe. The
data logger was set up to record the light intensity from both probes for about two seconds, thus
recording data that would allow the speed of the gliders before and after the collision to be
calculated. A few trial runs were required to optimise the duration of the data collection, the timing
of the pushing of the glider and the commencement of the data collection.
In hindsight, it would have been much simpler to set up the data logger on “Trigger” mode so that
the data collection began automatically when the light intensity change was detected – we’ll do that
next year!
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Conservation of Momentum
Before carrying out this experiment, the students were asked to make a prediction of what the light
intensity curves would look like, as a function of time. They were also asked to explain how the
light curve could be used to determine the speed of the glider.
Students were also asked to consider what other data would need to be measured and recorded so
that the law of conservation of momentum could be investigated. Clearly the masses and the lengths
of the gliders must be known.
With both of these questions resolved, the experiment continued.
The Results
The following snapshots show the experiment in progress, with the data projected onto the screen
and a detail of the data from the first sensor. A TI ViewScreen connected to the calculator was
used to project the results onto the screen for classroom analysis.
One of the benefits of electronic data logging is that the progress of the experiment can be easily
monitored as it progresses. It is simple to store or record the results and to repeat the experiment a
number of times to ensure that the results are consistent and reproducible. The images below show
typical screen snapshots from the calculator during the course of the experiment. The ‘Y-value’ on
the graphs is the light intensity, and the ‘X-value’ the time. (My students were justifiably pleased
when the graphs took on the shape they had predicted!)
Light data –glider A passing first sensor
Light data – both gliders passing second sensor
Time interval = (0.48 – 0.105) s
Time interval = (1.695 – 0.615) s
The immediacy of feedback from results during the experiment is a key part of the learning
experience. It facilitates meaningful discussion of the results, focussing on their physical
interpretation rather than dealing with the mechanics of recording and graphing data.
I usually have a laptop computer in the lab, and it is a very simple process to connect the TI
calculator to the USB input of the computer and transfer the data using software such as TI
Connect or the Vernier (company) software, Graphical Analysis 3. The latter is a favourite of
mine. It makes graphing and analysing any data a breeze. It can be used to import data from the
calculators, from Vernier’s LabPro data logger, or to simply type data into a spreadsheet-type
table and have the graph appear simultaneously in another window. It also offers a raft of
sophisticated analysis tools – but that should be the subject of another story!
In this experiment, a long glider collided with a stationary short glider and the two coalesced and
moved as a single object at a slower speed than that of the long glider before the collision.
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Conservation of Momentum
The following graphs show typical data from this experiment graphed using the Graphical Analysis
3 software. Data from both light sensors are shown on the same axes. The light intensity incident
on the second probe (graph 2) is a little greater than that on the first probe (graph 1). This is not a
significant factor in the analysis of results.
Results and Analysis
In this run, a long glider (20 cm) of mass (m) 287 g collided with the stationary short glider (10 cm)
of mass 186 g and the magnets caused them to coalesce.
Combined glider mass after collision (M)
= 473 g
Time interval (t1) from graph 1
= 0.385 s
Speed of glider before collision (u)
= glider length/time interval (t1) = 20/0.385 = 52 cm/s
Time interval (t2) from graph 2
= 1.08 s
Speed of coalesced gliders after collision (v) = combined glider length/time interval (t2)
= 30/1.08 = 28 cm/s
Hence
initial momentum of long glider p = mu = 287 x 52 = 15000 g cm/s
final momentum of both gliders p = Mv = 473 x 28 = 13000 g cm/s
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Conservation of Momentum
Discussion
The final momentum (13000 g cm/s) is about 13% less than the initial momentum (15000 g cm/s).
This is not consistent with the law of conservation of momentum. The difference however is
reasonably small and the question should be asked as to whether it is possible to account for the
difference.
Since we know that momentum must be conserved in any interaction, we needed to look for a
mechanism and object/s to which the “missing” momentum could be transferred.
We deduced that the friction between the gliders and the track was not zero. Turbulence occurs in
the air under the glider, which produces drag, slowing the glider down. If when the gliders collide,
the collision results in increased turbulent drag (a reasonable hypothesis because there is observable
instability when the gliders collide) then there is an increased (frictional) force opposing the motion
of the gliders. As stated by Newton’s third law, there must be an equal and opposite force acting on
another object — the linear air track. Hence momentum would be transferred to the linear air track,
accounting for the observed reduction in the momentum of the gliders.
Since the mass of the track is very much greater than that of the gliders, and the fact that the amount
of momentum that needs to be accounted for is small, no significant movement of the track would
be observable.
Thus, the experiment produces results that are consistent with the law of conservation of
momentum, given a likely mechanism, which can justifiably account for the difference in the initial
and final momentum of the gliders.
And did the students think this experiment was cool?
You be the judge!

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Conservation of Momentum
Meeting Syllabus Requirements
Reflecting on the new NSW Physics syllabus and this experiment, many of the requirements were
met in a stimulating and fun manner for the students. Consider the following list from the syllabus
table 8.1
Students:
Y
Comments
 
11.1 identify data sources to:
(a)
analyse complex problems to determine appropriate
ways in which each aspect may be researched

Analysing different sets of data and applying the results to
the law of conservation of momentum requires the linking
of many concepts, including speed, momentum,
interpretation of a light curve.
(b)
determine the type of data that needs to be collected
and explain the qualitative or quantitative analysis that
will be required for this data to be useful

Measurement of masses and lengths of gliders
(c)
identify the orders of magnitude that will be appropriate
and the uncertainty that may be present in the
measurement of data

Students often assume electronic data logging is accurate
because it is electronic. Estimates of the glider speeds can
be made without using data logging against which
calculated results can be compared.
(d)
identify and use correct units for data that will be
collected

Quantities encountered distance (m), mass (kg), time (s),
velocity (ms–1) and momentum (kg ms–1)
(e)
recommend the use of an appropriate technology or
strategy for data collection or information gathering
that will assist efficient future analysis

Discussion in the planning stages of how to measure the
speed of the gliders over short time intervals leads to the
data logging solution. The type of sensor and how best to
use it is explored.
Application of vav = r/t
Use the “Trigger” feature of the data logger (auto start
when a variable changes by a user selected amount) so
that no judgement is required in timing the commencement
of data collection.
11.2 plan first-hand investigations to:
(a)
demonstrate the use of the terms ‘dependent’ and
‘independent’ to describe variables involved in the
investigation

Time is the independent variable, and light intensity is the
dependent variable in the data collection process.
(b)
identify variables that need to be kept constant,
develop strategies to ensure that these variables are
kept constant, and demonstrate the use of a control

If the experiment is to be repeated using the same initial
velocity, a mechanism must be developed to propel the
glider at the same initial velocity. This is not essential.
Repetition can take place at different speeds – probably
even more appropriate.
(c)
design investigations that allow valid and reliable data
and information to be collected

Possible sources of error were identified in both the
planning and analysis stages. A key problem in this
experiment is friction, which although low, means that
momentum transfers to the track, and this cannot be
directly measured.
(d)
describe and trial procedures to undertake
investigations and explain why a procedure, a
sequence of procedures or the repetition of procedures
is appropriate

A strategy must be developed to ensure that the data
logger records data for an appropriate time interval (to
enable the velocities before and after to be calculated and
that the time interval between data points is small enough
to produce a meaningful light curve. Practice is required to
coordinate the data collection and the manual pushing of
the first glider.
(e)
predict possible issues that may arise during the
course of an investigation and identify strategies to
address these issues if necessary

Issues include the duration of data collection, giving the
glider an appropriate initial velocity.
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Conservation of Momentum
11.3 choose equipment or resources by:
(a)
identifying and/or setting up the most appropriate
equipment or combination of equipment needed to
undertake the investigation

Initial discussion of how to measure the glider speed
involves discussion of the choice of an appropriate sensor
– discuss why a light probe is better than a motion sensor.
(b)
carrying out a risk assessment of intended
experimental procedures and identifying and
addressing potential hazards

Check electrical safety (vacuum cleaner used with linear
air track)
(c)
identifying technology that could be used during
investigations and determining its suitability and
effectiveness for its potential role in the procedure or
investigation

The role of data logging technology in permitting the
collection of data over short time intervals was a significant
aspect of the investigation.
(d)
recognising the difference between destructive and
non-destructive testing of material and analysing
potentially different results from these two procedures

This is a non-destructive test – one hopes!

Adjusting the time interval over which the data was
collected was an important factor in gathering appropriate
data.

Checking of 240 V equipment used – vacuum cleaner,
specifically the power lead – should be tagged with safety
check tag by a licensed person.
Appropriate use of LAT to avoid damage – don’t use high
speeds and avoid moving the gliders on the track with the
air switched off.
12.1 perform first-hand investigations by:
(a)
carrying out the planned procedure, recognising where
and when modifications are needed and analysing the
effect of these adjustments
(b)
efficiently undertaking the planned procedure to
minimise hazards and wastage of resources
(c)
disposing carefully and safely of any waste materials
produced during the investigation
(d)
identifying and using safe work practices during
investigations
12.2 gather first-hand information by:
(a)
using appropriate data collection techniques,
employing appropriate technologies, including data
loggers and sensors

The use of data logging technology directly met this
requirement.
(b)
measuring, observing and recording results in
accessible and recognisable forms, carrying out repeat
trials as appropriate

Repetition of the experiment using different glider speeds
was a part of the investigation.

Relating the experiment to the law of conservation of
momentum could involve research using traditional physics
texts and the Internet.

Collected data was graphed as a light curve and
information had to be deduced from the graph to calculate
the speed of the gliders.

There is a misconception that because the data logger is
electronic, that it is error-free. Reliability of both equipment
and experimental procedure should be discussed as a part
of this experiment.
12.3 gather information from secondary sources by:
(a)
accessing information from a range of resources,
including popular scientific journals, digital
technologies and the Internet
(b)
practising efficient data collection techniques to identify
useful information in secondary sources
(c)
extracting information from numerical data in graphs
and tables as well as from written and spoken material
in all its forms
(d)
summarising and collating information from a range of
resources
(e)
identifying practising male and female Australian
scientists, the areas in which they are currently
working and information about their research
12.4 process information to:
(a)
assess the accuracy of any measurements and
calculations and the relative importance of the data
and information gathered
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Conservation of Momentum
(b)
identify and apply appropriate mathematical formulae
and concepts

Application of vav = r/t, p = mv
(c)
best illustrate trends and patterns by selecting and
using appropriate methods, including computer
assisted analysis

The use of the Vernier computer software Graphical
Analysis was a useful adjunct in this experiment.
(d)
evaluate the validity of first-hand and secondary
information and data in relation to the area of
investigation
(e)
assess the reliability of first-hand and secondary
information and data by considering information from
various sources
(f)
assess the accuracy of scientific information presented
in mass media by comparison with similar information
presented in scientific journals
13.1 present information by:
(a)
selecting and using appropriate text types or
combinations thereof, for oral and written presentations

Formal reporting of the investigation was required.
(b)
selecting and using appropriate media to present data
and information

Pencil and paper, as well as electronic and calculator and
computer based presentation of data.
(c)
selecting and using appropriate
acknowledge sources of information
(d)
using symbols and formulae to express relationships
and using appropriate units for physical quantities

Application of vav = r/t, p = mv
methods
to
(e)
using a variety of pictorial representations to show
relationships and present information clearly and
succinctly
(f)
selecting and drawing appropriate graphs to convey
information and relationships clearly and accurately
(g)
identifying situations where use of a curve of best fit is
appropriate to present graphical information
Mass (kg or g), distance (m or cm), time (s), speed (ms–1
or cms–1) and momentum (kg ms–1 or g cms–1)
Digital photographs as well as diagrams used in report.
Digital photographs taken during the experiment can be
uploaded to the school intranet for student access, as can
the data.

Prediction and interpretation of light intensity vs time graph
in relation to the glider motion is a key component of the
experiment.
14.1 analyse information to:
(a)
identify trends, patterns and relationships as well as
contradictions in data and information

The calculated momenta are unlikely to show total
agreement with the law of conservation of momentum – it
is important to determine whether results contradicting the
law can be satisfactorily resolved.
(b)
justify inferences and conclusions

The resolution of any discrepancy between the calculated
momenta and the law of conservation of momentum is an
important part of the discussion of the results and their
analysis.
(c)
identify and explain how data supports or refutes an
hypothesis, a prediction or a proposed solution to a
problem

The discussion of whether the calculated results are
consistent with the law of conservation of momentum,
given the number of trials carried out is an important part
of this experiment
(d)
predict outcomes and generate plausible explanations
related to the observations

See 14.1 (a)
(e)
make and justify generalisations

Discussion of whether and how the results of this
investigation relate to collisions involving motor vehicles is
instructive. Identifying similarities and differences is an
important extension of this experiment.
(f)
use models, including mathematical ones, to explain

Application of vav = r/t, p = mv
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Conservation of Momentum
phenomena and/or make predictions
Comparison of initial and final momenta
(g)
use cause and effect relationships to explain
phenomena

Apply Newton’s third law to this experiment. A mutual force
is exerted in opposite directions on the gliders during the
collision, slowing one down and speeding the other up.
Unless momentum is transferred outside the glider system
(it is), the momentum remains unchanged as the
momentum gained by one equals the momentum lost by
the other. Discuss impulse in the context of this
experiment.
(h)
identify examples of the interconnectedness of ideas or
scientific principles

The general principle embodied in the law of conservation
of momentum is applied specifically to this situation. The
results are generalised in the class discussion to other
types of interactions.
14.2 solve problems by:
(a)
identifying and explaining the nature of a problem

Problem solving and experimental design are significant
parts of this process
(b)
describing and selecting from different strategies,
those which could be used to solve a problem

How to collect the appropriate data, including the choice of
sensor / probe.
(c)
using identified strategies to develop a range of
possible solutions to a particular problem

The use of data logging technology to eliminate human
reaction time as a variable was a significant part of this
investigation. How to measure the glider speed over short
time intervals and distances had to be solved.
(d)
evaluating the appropriateness of different strategies
for solving an identified problem

Relate to 14.2 (c) above.

Resolution of differences between predicted and actual
results was an important part of this experiment.
14.3 use available evidence to:
(a)
design and produce creative solutions to problems
(b)
propose ideas that demonstrate coherence and logical
progression and include correct use of scientific
principles and ideas
(c)
apply critical thinking in the consideration of
predictions, hypotheses and the results of
investigations
(d)
formulate cause and effect relationships
Relate momentum conservation to Newton’s third law and
the concept of impulse.

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