In this paper we describe a classical experiment with an air track in which smartphones
are used as experimental devices to obtain physical data. The proposed experiment allows
users to easily observe and measure relationships between physical magnitudes, conservation of momentum in collisions and friction effects on movement by utilizing the users’
own mobile devices

González Delgado, Manuel Ángel

González Rebollo, Miguel Ángel

Gómez Bravo, Alfonso

English

Repositorio Documental de la Universidad de Valladolid

Papers in Physics, vol. 10, art. 100005 (2018)Received: 20 September 2017, Accepted: 4 May 2018Edited by: A. Mart́ı, M. MonteiroReviewed by: J-L Richter, Lycée Polyvalent J-B Schwilgué, FranceLicence: Creative Commons Attribution 4.0DOI: http://dx.doi.org/10.4279/PIP.100005www.papersinphysics.orgISSN 1852-4249Smartphones on the air track. Examples and difficultiesManuel Á. González,1∗ Alfonso Gómez,1 Miguel Á. González1In this paper we describe a classical experiment with an air track in which smartphonesare used as experimental devices to obtain physical data. The proposed experiment allowsusers to easily observe and measure relationships between physical magnitudes, conserva-tion of momentum in collisions and friction effects on movement by utilizing the users’own mobile devices.I. IntroductionSmartphones and tablets have sensors that can beused to redesign physics experiments by substitut-ing laboratory equipment with those devices [1].This technique can enrich data availability in anexperiment and also reduces its costs. The work inthe laboratory under controlled conditions can alsohelp experimenters to learn the use and limitationsof smartphones and to apply them in experimentsoutside the laboratory. In this paper, we show someresults obtained in a classical experiment, pointingout basic concepts that can be explored and ana-lyzed by using smartphones, as well as some diffi-culties of the work.II. Using the smartphone in an air-track experimentA simple and usual mechanics experiment consistsin studying linear movement on an air track with-out friction. On it, positions, speeds and acceler-ations can be measured by using measuring tapes,chronometers or more sophisticated photoelectric∗E-mail: manuelgd@termo.uva.es1 Universidad de Valladolid, 47011 Valladolid, Spain.cells. Here, we discuss how smartphones can beused to analyze the movement of a body in threedifferent configurations of the experiment: elasticcollisions between two carts, accelerated movementof a cart pulled by a falling body via pulley, andmovement of a cart when the air pump is switchedoff and it is stopped by friction.As experimental devices in our work we usedtwo smartphones, a Samsung Galaxy S3 mini anda Samsung Galaxy S4. These smartphones wereplaced horizontally on the moving carts with theirY-axis pointed along the direction of the movementand their Z-axis vertically. The carts can hold ad-ditional weights so that we could study interactionsbetween bodies with same or different masses. Toaccess the data recorded using the sensors of thesmartphones, we used two Android apps: Sensor-Mobile [2] and Physics Toolbox [3], so that the ad-vantages or disadvantages, accuracy and numericalnoise, of different apps can also be analyzed.i. Elastic collisions between carts in a hor-izontal air trackThis is a simple experiment that is done by usingtwo carts, each with a smartphone measuring itsacceleration, allowing us to check the momentumconservation in a collision between two bodies. Inour experiments, we used different configurations100005-1Papers in Physics, vol. 10, art. 100005 (2018) / M. Á. González et al.-5-4-3-2-1 0 1 2 3 4 5 100  200  300  400  500  600  700  800  900Area #2 = +282.54 10-3 m/sm2*area2 = +89.87 10-3 kg m/sArea #1 = -276.44 10-3 m/sm1*area1 = -88.07 10-3 kg m/saccel. (m/s2)t (ms)Mobile #1, m1 = 318.60 gMobile #2, m2 = 318.76 gFigure 1: Accelerations of two bodies of equal massduring a collision. A spreadsheet can be useful to cal-culate the area under the acceleration curves and checkmomentum conservation readily.that can be explored: both carts moving on theair track in the same or in opposite directions, orone cart at rest while the other moves towards it.Moreover, by adding different masses to the cartswe have analyzed collisions between bodies with thesame or with different masses.Figure 1 shows the results of one of such ex-periments corresponding to an elastic collision be-tween two bodies (cart plus smartphone) of similarmasses. In this case only one of the bodies wasmoving before the impact. Once the accelerationof each body is measured by the smartphones, theCSV files generated by the apps can be transferredto a computer and analyzed easily using a spread-sheet program. Here the spreadsheet was used toobtain the area under the curve of each accelerationusing a simple numerical method like the trape-zoidal rule. As can be seen in Fig. 1, when themasses are nearly equal the areas calculated fromthe smartphone data are also similar (the differenceis a little larger than the 2%) considering the ex-perimental noise. And multiplying those areas bythe masses of the bodies the conservation of linearmomentum is checked, as shown in Fig. 1.ii. Frictionless movement of a cart pulledby a falling body through pulleyAnother dynamics problem studied in the firstcourses of physics is the movement of a body, on africtionless horizontal or inclined plane, connectedto a cable that passes over a pulley and then isfastened to a falling object. Here, we study suchmovement by placing a smartphone on the movingcart and measuring its acceleration.Figure 2 shows some results of two measurementsof this type. They correspond to the accelerationsuffered by a body (cart plus smartphone) of massmc = 318.76 g on a horizontal plane when thefalling body has different masses in two differentexperiments, mb = 20.02 g and 29.99 g. Accord-ing to the theory studied in the classroom, assum-ing that there is no friction, the acceleration ofthe cart is a = mbmc+mb g that for our conditionsgives accelerations a(mb=20.02) = 0.579 m/s2 anda(mb=29.99) = 0.843 m/s2. As can be seen theseresults agree well with the average acceleration ofthe cart as measured by the smartphone on it.The users could also add a second smartphone onthe falling body and check that the accelerationof the cart and that of the falling body are thesame within the experimental accuracy, accordingto this simple model. From the accelerometer mea-surements, the dependence of the travelled spacewith acceleration and time in the uniformly accel-erated movement can be checked. If the length ofthe cable is the same in two measurements withdifferent falling masses, then the ratio of travellingtimes ∆t2/∆t1 must be equal to the square rootof the ratio of the average accelerations measuredby the smartphones√a2/a1. As can be seen fromthe measurements in the figure, ∆t2/∆t1 ≈ 1.199,while for the accelerations√a2/a1 ≈ 1.207, so thatthe the theoretical dependence s = 12at2 is easilyproved.iii. Movement with friction of a cart pulledby a falling body through pulleyIn this section, we show some results that can beobtained if the air pump of the track is set off andthe cart moves with friction. For this experimentthe lower part of the cart should be protected, forexample with duct tape, to avoid damaging the airtrack with scratches, which will also vary the fric-tion coefficient as the experiment is performed. Theexperiment is the same as in the section ii., exceptfor the existence of friction. The acceleration ofthe cart is lower than the one without friction, thecart decelerates, and finally stops if the cable islong enough for the falling object to reach the floor100005-2Papers in Physics, vol. 10, art. 100005 (2018) / M. Á. González et al. 0 0.2 0.4 0.6 0.8 1 1.2 500  1000  1500  2000∆t2 = 1659 ms∆t1 = 1402 msaccel. (m/s2)t (ms)m1 = 29.99 gm2 = 20.02 gFigure 2: Measurements of the acceleration of a carton an air track when pulled by different masses in twoexperiments. The average values of acceleration, in thetwo experiments, marked with lines in the figure, werea1 ≈ 0.84 m/s2 and a2 ≈ 0.58 m/s2before the cart gets to the track end.Figure 3 shows an example of the results withthe smartphone accelerometer in such experiment.That figure shows acceleration data of three inde-pendent measurements under the same conditionsto illustrate the repeatability of the results. Somecomments are necessary about the results shown inthe figure. As can be seen there, the accelerationis positive when the movement is accelerated, andchanges its sign when the falling body reaches thefloor and the friction decelerates the movement ofthe cart. A very remarkable result that immedi-ately calls our attention is the oscillations in theaccelerated part of the movement. As can be seenin Fig. 3 (and in Fig. 4), these oscillations appearconsistently in all the experiments and then, can-not be considered an experimental artifact. In ouropinion, these oscillations appear due to the com-bined effect of the push on the string of the fallingbody and the pull due to the friction on the cartattached to the end of the string. These oscillationsdo not appear when the air pump is working andthere is no friction. From our point of view, theseoscillations reflect variations in the acceleration ofthe cart due to changes in the string tension. Thisis a problem that we consider very interesting tosee. When this experiment is done using classicalmeasurement devices the usual approximation thatconsiders inextensible strings and constant tensionseems to hold true, but smartphone sensors are sen-sible to small variations in them, as can be seenhere. This observation can help the experimentersto consider the limitations of the physical modeland the influence of the string characteristics. Fig-ure 3 shows in an inset the experimental points ofthe three measurements together with a dampedoscillation with period T ≈ 0.105 s. For the the-oretical behaviour we have tested accelerations forpure Coulomb and pure viscous damping but theexperimental results seems to be a mixing of bothbehaviours, what makes more difficult its analysis.The inset in Fig. 3 shows a comparison of the ex-perimental points with a theoretical curve for theacceleration. From this comparison, we have an es-timation of the initial elongation of the string to bearound 1.2 ·10−3 m (the length of the string used inthis experiment was approximately 1.75 m). In ad-dition, a qualitative analysis of the oscillations wasacomplished by using strings with different elastic-ity. We observed that these oscillations were lessnoticeable for strings with lower elasticities, andthat even for low elastic strings these oscillationswere masked by the experimental noise. On theother hand, for more rigid strings, such as metal-lic strings, the amplitude of the oscillations wassmaller due to their lower deformation. Anyway,both the mixing of effects in this result and its ex-perimental difficulties could make an exact analysisharder than in the classical version of the experi-ment.Other results can be obtained easily by the users.From the masses of the cart (mc = 318.8 g) and ofthe falling body (mb = 358.05 g) they can calculatethe theoretical acceleration without friction, result-ing ateo = 5.18 m/s2, that is clearly higher thanthe experimental value in the accelerated part ofthe movement, whose average value is aexp = 2.386m/s2 (see Fig. 3). Using this experimental value,the students can obtain the friction coefficient be-tween the duct tape protecting the cart and thetrack with µ = (mbg − (mc +mb)aexp)/(mcg), re-sulting µ = 0.61. Once µ is known the frictiondeceleration afriction = µg = 5.94 m/s2 can be cal-culated, that, as shown in Fig. 3, agrees well withthe experimental results within the experimentalnoise. From the experimental data the impulse-momentum relationship can also be observed. Asthe cart started and ended its movement with nullspeed, the areas under the acceleration and decel-eration curves in Fig. 4 must have the same value100005-3Papers in Physics, vol. 10, art. 100005 (2018) / M. Á. González et al.-8-6-4-2 0 2 4 6 1  1.5  2  2.5  3anf = 5.184 m/s2<aexp> = 2.386 m/s2Experimental µ = 0.61Calculated -µg = -5.94 m/s2accel. (m/s2)t (s)Experiment #1#2#3T ≈ 0.105 sFigure 3: Results of four independent measurements ofthe acceleration of a cart pulled by a falling body viaa pulley when there is friction between the cart andthe air track. The values of the theoretical accelerationwithout friction, at, and of the experimental averageacceleration, ae, are marked with straight lines. One ofthe measurements has been represented with lines andpoints to show the position of the experimental points.but opposite signs. By using a spreadsheet programand the numerical trapezoidal rule, those areas canbe easily obtained.Finally, Fig. 4 shows another result that can bediscussed. Results for two different conditions offriction are shown in it: an aluminium cart on analuminium track and a duct tape covered cart onan aluminium track. Due to different friction co-efficients, the cart accelerations are different and,consequently, their travelled times. As for Fig. 3,the users can calculate the dynamic friction coef-ficients and the corresponding decelerations, andcompare them with the experimental results. A fi-nal result that can be discussed is the influence ofdifferent friction coefficients on the stopping times.III. ConclusionsSmartphone sensors are very useful tools that per-mit to do measurements in the laboratory andoutside it. The use of these devices can also in-crease the interest in physics and facilitate the un-derstanding of the physical phenomena. We haveshown some results of an air track experiment us-ing a smartphone. Some of the concepts reinforcedwith this experiment are acceleration, collisions,momentum, friction, friction coefficient, impulse--6-4-2 0 2 4 6 200  400  600  800  1000  1200  1400  1600  1800Calculated deceleration -µg= -4.31 m/s2accel. (m/s2)t (ms)-8-6-4-2 0 2 4 6Calculated deceleration -µg= -6.64 m/s2accel. (m/s2)Figure 4: Accelerations recorded by the smartphone inan experiment like that in Fig. 3 but two different fric-tion coefficients: painted Al cart on Al track (above)and duct tape covered cart on Al track (below). Thecart and the falling body masses were mc = 317.3 gand mb = 359.1 g, respectively. The experimental av-erage accelerations of each case have been marked withhorizontal lines, as well as the deccelerations once thefalling body reaches the floor.momentum theorem and even elasticity. These ex-periments can also be useful to learn the impor-tance of sensors accuracy and measuring frequency,as well as the reliability of the used applications.Acknowledgements - This work has been sup-ported by the University of Valladolid withinits Teaching Innovation Program under grantsPID2016 64 and PID2016 67.[1] R Vieyra, C Vieyra, P Jeanjacquot, A Mart́ı,M Monteiro, Turn your smartphone into a sci-ence laboratory, The Science Teacher 82, 32(2015).[2] SensorMobile https://play.google.com/store/apps/details?id=com.sensor.mobile, last accessed September 13, 2017.[3] PhysicsToolbox https://play.google.com/store/apps/details?id=com.chrystianvieyra.physicstoolboxsuite,last accessed September 13, 2017.100005-4

Smartphones on the air track. Examples and difficulties

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