Determination of Young's modulus of a cylindrical bar

Authorship SCIMAGO INSTITUTIONS RANKINGS

The following work makes use of smartphones in order to determine the elasticity modulus or Young's modulus of a cylindrical brass bar (copper-zinc alloy), employing two different devices: A microphone, to determine the components frequencies of the bar's oscillation, which is compressed at one end and free at the other, and an accelerometer to calculate oscillation frequency of a body attached to the end of the bar (using the phone as an inertial mass). Both methods are compared to each other, and with the reference value for the Young's modulus belonging to the material.

Keywords: Vibrations; normal modes for continuos systems; Young's modulus; physics with smartphones

$(L \pm 0, 5 \times 1 0^{- 3}) m$	$(f_{1} \pm 0, 3) (H z)$	$f_{1} L^{2} (H z m^{2})$
0,1100	158,0	1,912
0,1400	98,5	1,931
0,1600	75,4	1,929
0,1900	53,4	1,927
0,2500	31,0	1,938

$\begin{matrix} (L \pm 0, 001) (m) \end{matrix}$	$(f \pm 0, 001) (H z)$	fL $^{3 ∕ 2}$ (Hzm $^{3 ∕ 2})$
0,250	5,506	0,688
0,300	4,143	0,681
0,400	2,722	0,689
0,460	2,202	0,687
0,600	1,493	0,694

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Sociedade Brasileira de Física Caixa Postal 66328, 05389-970 São Paulo SP - Brazil - São Paulo - SP - Brazil
E-mail: marcio@sbfisica.org.br

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Módulo de Young.	Oscilación de la barra prensadalibre.	Oscilación de la masa.	Valor de referencia.[¹]
$E (\times 1 0^{10} N ∕ m^{2})$	$10,0 \pm 0,2$	$9,9 \pm 0,2$	10,0