Papers in Physics, vol. 10, art. 100005 (2018)

Received: 20 September 2017, Accepted: 4 May 2018
Edited by: A. Mart́ı, M. Monteiro
Reviewed by: J-L Richter, Lycée Polyvalent J-B Schwilgué, France
Licence: Creative Commons Attribution 4.0
DOI: http://dx.doi.org/10.4279/PIP.100005

www.papersinphysics.org

ISSN 1852-4249

Smartphones on the air track. Examples and difficulties

Manuel Á. González,1∗ Alfonso Gómez,1 Miguel Á. González1

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, conserva-
tion of momentum in collisions and friction effects on movement by utilizing the users’
own mobile devices.

I. Introduction

Smartphones and tablets have sensors that can be
used to redesign physics experiments by substitut-
ing laboratory equipment with those devices [1].
This technique can enrich data availability in an
experiment and also reduces its costs. The work in
the laboratory under controlled conditions can also
help experimenters to learn the use and limitations
of smartphones and to apply them in experiments
outside the laboratory. In this paper, we show some
results obtained in a classical experiment, pointing
out 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 experiment

A simple and usual mechanics experiment consists
in 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.es

1 Universidad de Valladolid, 47011 Valladolid, Spain.

cells. Here, we discuss how smartphones can be
used to analyze the movement of a body in three
different configurations of the experiment: elastic
collisions between two carts, accelerated movement
of a cart pulled by a falling body via pulley, and
movement of a cart when the air pump is switched
off and it is stopped by friction.

As experimental devices in our work we used
two smartphones, a Samsung Galaxy S3 mini and
a Samsung Galaxy S4. These smartphones were
placed horizontally on the moving carts with their
Y-axis pointed along the direction of the movement
and their Z-axis vertically. The carts can hold ad-
ditional weights so that we could study interactions
between bodies with same or different masses. To
access the data recorded using the sensors of the
smartphones, we used two Android apps: Sensor-
Mobile [2] and Physics Toolbox [3], so that the ad-
vantages or disadvantages, accuracy and numerical
noise, of different apps can also be analyzed.

i. Elastic collisions between carts in a hor-
izontal air track

This is a simple experiment that is done by using
two carts, each with a smartphone measuring its
acceleration, allowing us to check the momentum
conservation in a collision between two bodies. In
our experiments, we used different configurations

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Papers 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  900

Area #2 = +282.54 10
-3

 m/s

m2*area2 = +89.87 10
-3

 kg m/s

Area #1 = -276.44 10
-3

 m/s

m1*area1 = -88.07 10
-3

 kg m/s

a
c
c
e

l.
 (

m
/s

2
)

t (ms)

Mobile #1, m1 = 318.60 g
Mobile #2, m2 = 318.76 g

Figure 1: Accelerations of two bodies of equal mass
during a collision. A spreadsheet can be useful to cal-
culate the area under the acceleration curves and check
momentum conservation readily.

that can be explored: both carts moving on the
air track in the same or in opposite directions, or
one cart at rest while the other moves towards it.
Moreover, by adding different masses to the carts
we have analyzed collisions between bodies with the
same 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 similar
masses. In this case only one of the bodies was
moving before the impact. Once the acceleration
of each body is measured by the smartphones, the
CSV files generated by the apps can be transferred
to a computer and analyzed easily using a spread-
sheet program. Here the spreadsheet was used to
obtain the area under the curve of each acceleration
using a simple numerical method like the trape-
zoidal rule. As can be seen in Fig. 1, when the
masses are nearly equal the areas calculated from
the smartphone data are also similar (the difference
is a little larger than the 2%) considering the ex-
perimental noise. And multiplying those areas by
the masses of the bodies the conservation of linear
momentum is checked, as shown in Fig. 1.

ii. Frictionless movement of a cart pulled
by a falling body through pulley

Another dynamics problem studied in the first
courses of physics is the movement of a body, on a
frictionless horizontal or inclined plane, connected

to a cable that passes over a pulley and then is
fastened to a falling object. Here, we study such
movement by placing a smartphone on the moving
cart and measuring its acceleration.

Figure 2 shows some results of two measurements
of this type. They correspond to the acceleration
suffered by a body (cart plus smartphone) of mass
mc = 318.76 g on a horizontal plane when the
falling body has different masses in two different
experiments, 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 of
the cart is a = mb

mc+mb
g that for our conditions

gives accelerations a(mb=20.02) = 0.579 m/s
2 and

a(mb=29.99) = 0.843 m/s
2. As can be seen these

results agree well with the average acceleration of
the cart as measured by the smartphone on it.
The users could also add a second smartphone on
the falling body and check that the acceleration
of the cart and that of the falling body are the
same within the experimental accuracy, according
to this simple model. From the accelerometer mea-
surements, the dependence of the travelled space
with acceleration and time in the uniformly accel-
erated movement can be checked. If the length of
the cable is the same in two measurements with
different falling masses, then the ratio of travelling
times ∆t2/∆t1 must be equal to the square root
of the ratio of the average accelerations measured
by the smartphones

√
a2/a1. As can be seen from

the measurements in the figure, ∆t2/∆t1 ≈ 1.199,
while for the accelerations

√
a2/a1 ≈ 1.207, so that

the the theoretical dependence s = 1
2
at2 is easily

proved.

iii. Movement with friction of a cart pulled
by a falling body through pulley

In this section, we show some results that can be
obtained if the air pump of the track is set off and
the cart moves with friction. For this experiment
the lower part of the cart should be protected, for
example with duct tape, to avoid damaging the air
track with scratches, which will also vary the fric-
tion coefficient as the experiment is performed. The
experiment is the same as in the section ii., except
for the existence of friction. The acceleration of
the cart is lower than the one without friction, the
cart decelerates, and finally stops if the cable is
long enough for the falling object to reach the floor

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Papers 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 ms

a
c
c
e

l.
 (

m
/s

2
)

t (ms)

m1 = 29.99 g
m2 = 20.02 g

Figure 2: Measurements of the acceleration of a cart
on an air track when pulled by different masses in two
experiments. The average values of acceleration, in the
two experiments, marked with lines in the figure, were
a1 ≈ 0.84 m/s2 and a2 ≈ 0.58 m/s2

before the cart gets to the track end.
Figure 3 shows an example of the results with

the smartphone accelerometer in such experiment.
That figure shows acceleration data of three inde-
pendent measurements under the same conditions
to illustrate the repeatability of the results. Some
comments are necessary about the results shown in
the figure. As can be seen there, the acceleration
is positive when the movement is accelerated, and
changes its sign when the falling body reaches the
floor and the friction decelerates the movement of
the cart. A very remarkable result that immedi-
ately calls our attention is the oscillations in the
accelerated part of the movement. As can be seen
in Fig. 3 (and in Fig. 4), these oscillations appear
consistently in all the experiments and then, can-
not be considered an experimental artifact. In our
opinion, these oscillations appear due to the com-
bined effect of the push on the string of the falling
body and the pull due to the friction on the cart
attached to the end of the string. These oscillations
do not appear when the air pump is working and
there is no friction. From our point of view, these
oscillations reflect variations in the acceleration of
the cart due to changes in the string tension. This
is a problem that we consider very interesting to
see. When this experiment is done using classical
measurement devices the usual approximation that
considers inextensible strings and constant tension
seems to hold true, but smartphone sensors are sen-

sible to small variations in them, as can be seen
here. This observation can help the experimenters
to consider the limitations of the physical model
and the influence of the string characteristics. Fig-
ure 3 shows in an inset the experimental points of
the three measurements together with a damped
oscillation with period T ≈ 0.105 s. For the the-
oretical behaviour we have tested accelerations for
pure Coulomb and pure viscous damping but the
experimental results seems to be a mixing of both
behaviours, what makes more difficult its analysis.
The inset in Fig. 3 shows a comparison of the ex-
perimental points with a theoretical curve for the
acceleration. From this comparison, we have an es-
timation of the initial elongation of the string to be
around 1.2·10−3 m (the length of the string used in
this experiment was approximately 1.75 m). In ad-
dition, a qualitative analysis of the oscillations was
acomplished by using strings with different elastic-
ity. We observed that these oscillations were less
noticeable for strings with lower elasticities, and
that even for low elastic strings these oscillations
were masked by the experimental noise. On the
other hand, for more rigid strings, such as metal-
lic strings, the amplitude of the oscillations was
smaller due to their lower deformation. Anyway,
both the mixing of effects in this result and its ex-
perimental difficulties could make an exact analysis
harder 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 of
the falling body (mb = 358.05 g) they can calculate
the theoretical acceleration without friction, result-
ing ateo = 5.18 m/s

2, that is clearly higher than
the experimental value in the accelerated part of
the movement, whose average value is aexp = 2.386
m/s2 (see Fig. 3). Using this experimental value,
the students can obtain the friction coefficient be-
tween the duct tape protecting the cart and the
track with µ = (mbg − (mc + mb)aexp)/(mcg), re-
sulting µ = 0.61. Once µ is known the friction
deceleration afriction = µg = 5.94 m/s

2 can be cal-
culated, that, as shown in Fig. 3, agrees well with
the experimental results within the experimental
noise. From the experimental data the impulse-
momentum relationship can also be observed. As
the cart started and ended its movement with null
speed, the areas under the acceleration and decel-
eration curves in Fig. 4 must have the same value

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Papers 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  3

anf = 5.184 m/s
2

<aexp> = 2.386 m/s
2

Experimental µ = 0.61

Calculated -µg = -5.94 m/s
2

a
c
c
e
l.
 (

m
/s

2
)

t (s)

Experiment #1
#2
#3

T ≈ 0.105 s

Figure 3: Results of four independent measurements of
the acceleration of a cart pulled by a falling body via
a pulley when there is friction between the cart and
the air track. The values of the theoretical acceleration
without friction, at, and of the experimental average
acceleration, ae, are marked with straight lines. One of
the measurements has been represented with lines and
points to show the position of the experimental points.

but opposite signs. By using a spreadsheet program
and the numerical trapezoidal rule, those areas can
be easily obtained.

Finally, Fig. 4 shows another result that can be
discussed. Results for two different conditions of
friction are shown in it: an aluminium cart on an
aluminium track and a duct tape covered cart on
an 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, and
compare them with the experimental results. A fi-
nal result that can be discussed is the influence of
different friction coefficients on the stopping times.

III. Conclusions

Smartphone sensors are very useful tools that per-
mit to do measurements in the laboratory and
outside it. The use of these devices can also in-
crease the interest in physics and facilitate the un-
derstanding of the physical phenomena. We have
shown some results of an air track experiment us-
ing a smartphone. Some of the concepts reinforced
with 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  1800

Calculated deceleration -µg= -4.31 m/s
2a

c
c
e

l.
 (

m
/s

2
)

t (ms)

-8

-6

-4

-2

 0

 2

 4

 6

Calculated deceleration -µg= -6.64 m/s
2

a
c
c
e

l.
 (

m
/s

2
)

Figure 4: Accelerations recorded by the smartphone in
an 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). The
cart and the falling body masses were mc = 317.3 g
and mb = 359.1 g, respectively. The experimental av-
erage accelerations of each case have been marked with
horizontal lines, as well as the deccelerations once the
falling 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 within
its Teaching Innovation Program under grants
PID2016 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

https://play.google.com/store/apps/details?id=com.sensor.mobile
https://play.google.com/store/apps/details?id=com.sensor.mobile
https://play.google.com/store/apps/details?id=com.sensor.mobile
https://play.google.com/store/apps/details?id=com.chrystianvieyra.physicstoolboxsuite
https://play.google.com/store/apps/details?id=com.chrystianvieyra.physicstoolboxsuite
https://play.google.com/store/apps/details?id=com.chrystianvieyra.physicstoolboxsuite

	Introduction
	Using the smartphone in an air-track experiment
	Elastic collisions between carts in a horizontal air track
	Frictionless movement of a cart pulled by a falling body through pulley
	Movement with friction of a cart pulled by a falling body through pulley

	Conclusions