A simple experiment in relating a time-dependent linear acceleration function to height is explored through the use of a smartphone and an elevator. Given acceleration as a function of time1, a(t), the velocity function and position functions are determined through integration as in
v(t)= a(t) dt
(1)
and
x(t)= v(t) dt.
Mobile devices such as smartphones or tablets have accelerometers that capture slowly evolving acceleration with respect to time and can deliver those measurements as a CSV file. A recent example measured the oscillations of the elevator as it starts its motion.2 In the application presented here the mobile device is used to estimate the height of the elevator ride. By estimating the functional form of the acceleration of an elevator ride, it is possible to estimate the height of the ride through Eqs. (1) and (2).
1.
H. D.
Young
,
R. A.
Freedman
, and
A. L.
Ford
,
University Physics
, 13th ed. (
Addison-Wesley
,
2012
).
2.
J.
Kuhn
,
P.
Vogt
, and
A.
Müller
, “
Analyzing elevator oscillation with the smartphone sensors
,”
Phys. Teach.
52
,
55
56
(Jan.
2014
).
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