Conservation of Momentum Investigation

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!

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.

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

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!        

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  Analysing different sets of data and applying appropriate ways in which each aspect may the results to the law of conservation of be researched 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  Measurement of masses and lengths of gliders collected and explain the qualitative or Application of v = r/t quantitative analysis that will be required av for this data to be useful (c) identify the orders of magnitude that will be  Students often assume electronic data logging appropriate and the uncertainty that may be is accurate because it is electronic. Estimates present in the measurement of data 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  Quantities encountered distance (m), mass will be collected (kg), time (s), velocity (ms–1) and momentum (kg ms–1) (e) recommend the use of an appropriate  Discussion in the planning stages of how to technology or strategy for data collection or measure the speed of the gliders over short information gathering that will assist time intervals leads to the data logging efficient future analysis solution. The type of sensor and how best to use it is explored. 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  Time is the independent variable, and light ‘dependent’ and ‘independent’ to describe intensity is the dependent variable in the data variables involved in the investigation collection process. (b) identify variables that need to be kept  If the experiment is to be repeated using the constant, develop strategies to ensure that same initial velocity, a mechanism must be these variables are kept constant, and developed to propel the glider at the same demonstrate the use of a control initial velocity. This is not essential. Repetition can take place at different speeds – probably even more appropriate. (c) design investigations that allow valid and  Possible sources of error were identified in reliable data and information to be both the planning and analysis stages. A key collected 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  A strategy must be developed to ensure that investigations and explain why a procedure, the data logger records data for an appropriate a sequence of procedures or the repetition time interval (to enable the velocities before

of procedures is appropriate 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  Issues include the duration of data collection, during the course of an investigation and giving the glider an appropriate initial velocity. identify strategies to address these issues if necessary 11.3 choose equipment or resources by: (a) identifying and/or setting up the most  Initial discussion of how to measure the glider appropriate equipment or combination of speed involves discussion of the choice of an equipment needed to undertake the appropriate sensor – discuss why a light probe investigation is better than a motion sensor. (b) carrying out a risk assessment of intended  Check electrical safety (vacuum cleaner used experimental procedures and identifying with linear air track) and addressing potential hazards 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. (c) identifying technology that could be used  The role of data logging technology in during investigations and determining its permitting the collection of data over short suitability and effectiveness for its potential time intervals was a significant aspect of the role in the procedure or investigation investigation. (d) recognising the difference between  This is a non-destructive test – one hopes! destructive and non-destructive testing of material and analysing potentially different results from these two procedures 12.1 perform first-hand investigations by: (a) carrying out the planned procedure,  Adjusting the time interval over which the data recognising where and when modifications was collected was an important factor in are needed and analysing the effect of gathering appropriate data. 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  Checking of 240 V equipment used – vacuum during investigations cleaner, specifically the power lead – should be tagged with safety check tag by a licensed person. 12.2 gather first-hand information by: (a) using appropriate data collection  The use of data logging technology directly techniques, employing appropriate met this requirement. technologies, including data loggers and sensors (b) measuring, observing and recording results  Repetition of the experiment using different in accessible and recognisable forms, glider speeds was a part of the investigation. carrying out repeat trials as appropriate 12.3 gather information from secondary sources by: (a) accessing information from a range of  Relating the experiment to the law of

resources, including popular scientific conservation of momentum could involve journals, digital technologies and the research using traditional physics texts and Internet the Internet. (b) practising efficient data collection techniques to identify useful information in secondary sources (c) extracting information from numerical data  Collected data was graphed as a light curve in graphs and tables as well as from written and information had to be deduced from the and spoken material in all its forms graph to calculate the speed of the gliders. (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  There is a misconception that because the and calculations and the relative data logger is electronic, that it is error-free. importance of the data and information Reliability of both equipment and experimental gathered procedure should be discussed as a part of this experiment.

(b) identify and apply appropriate  Application of vav = r/t, p = mv mathematical formulae and concepts (c) best illustrate trends and patterns by  The use of the Vernier computer software selecting and using appropriate methods, Graphical Analysis was a useful adjunct in including computer assisted analysis 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  Formal reporting of the investigation was or combinations thereof, for oral and required. written presentations (b) selecting and using appropriate media to  Pencil and paper, as well as electronic and present data and information calculator and computer based presentation of data. (c) selecting and using appropriate methods to acknowledge sources of information

(d) using symbols and formulae to express  Application of vav = r/t, p = mv relationships and using appropriate units Mass (kg or g), distance (m or cm), time (s), for physical quantities speed (ms–1 or cms–1) and momentum (kg ms–1 or g cms–1) (e) using a variety of pictorial representations Digital photographs as well as diagrams used to show relationships and present in report. Digital photographs taken during the information clearly and succinctly experiment can be uploaded to the school

intranet for student access, as can the data. (f) selecting and drawing appropriate graphs  Prediction and interpretation of light intensity to convey information and relationships vs time graph in relation to the glider motion is clearly and accurately a key component of the experiment. (g) identifying situations where use of a curve of best fit is appropriate to present graphical information 14.1 analyse information to: (a) identify trends, patterns and relationships  The calculated momenta are unlikely to show as well as contradictions in data and total agreement with the law of conservation information 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  The discussion of whether the calculated refutes an hypothesis, a prediction or a results are consistent with the law of proposed solution to a problem conservation of momentum, given the number of trials carried out is an important part of this experiment (d) predict outcomes and generate plausible  See 14.1 (a) explanations related to the observations (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,  Application of vav = r/t, p = mv to explain phenomena and/or make Comparison of initial and final momenta predictions (g) use cause and effect relationships to  Apply Newton’s third law to this experiment. A explain phenomena 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  The general principle embodied in the law of interconnectedness of ideas or scientific conservation of momentum is applied principles 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 solving and experimental design are problem significant parts of this process (b) describing and selecting from different  How to collect the appropriate data, including strategies, those which could be used to the choice of sensor / probe. solve a problem

(c) using identified strategies to develop a  The use of data logging technology to range of possible solutions to a particular eliminate human reaction time as a variable problem 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  Relate to 14.2 (c) above. strategies for solving an identified problem 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  Resolution of differences between predicted of predictions, hypotheses and the results and actual results was an important part of this of investigations experiment. (d) formulate cause and effect relationships Relate momentum conservation to Newton’s third law and the concept of impulse.

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