Drag coefficient of vertically moving popcorns

To take the students attention in physics lectures is always a challenge. The projectile motion is not an exception. Then, study of popcorn motion can be a way to introduce and motivate the students in this subject. In this work, the popcorn flight, caused by the popping process was recorded by a cellular phone and analyzed frame by frame. Then, the drag coefficient (C_D) of vertically moving popcorns is determined and its dependency with the vertical velocity (v_y) and with the Reynolds number (Re) is explored. Our results show that C_D increases exponentially when v_y decreases. Also, C_D shows higher uncertainties when the popcorn is close to its maximum vertical trajectory. The dependency of C_D with Re shows that the popcorn flights are governed, mainly, by a laminar flow motion (Re ＜ 2000).

Keywords
Drag coefficient; popcorn; tracker

Authorship

Eduardo do Carmo ^** Correspondence email address: eduardo.carmo@unila.edu.breduardo.carmo@unila.edu.br

Universidade Federal da Integração Latino-Americana, Instituto de Ciências da Vida e da Natureza, Foz do Iguaçu, PR, Brasil.Universidade Federal da Integração Latino-AmericanaBrasilFoz do Iguaçu, PR, BrasilUniversidade Federal da Integração Latino-Americana, Instituto de Ciências da Vida e da Natureza, Foz do Iguaçu, PR, Brasil.

https://orcid.org/0000-0001-8796-1856

Marcelo Goncalves Hönnicke

https://orcid.org/0000-0003-3276-4323

* Correspondence email address: eduardo.carmo@unila.edu.breduardo.carmo@unila.edu.br

SCIMAGO INSTITUTIONS RANKINGS

Figures | Formulas

Figures (4)
Formulas (9)

Thumbnail

Figura 1
(a) General view of the experiment, showing where the cellular phone was set in order to record the popping process. (b) Details on the experiment for determining the drag coefficient (C_D) of vertically moving popcorns. (c) Multiframe image, mounted with the software Tracker from one of the multi-frame popcorn motion movie segmentations (popcorn flights), over a time interval of 0.56 s, i.e., 67 frames. However, only 15 frames, sort overall the full time interval, are shown.

Thumbnail

Figura 2
(a) Position (y) versus time (t) data, acquired with software Tracker, for the popcorn flight shown in Figure 1(b). The data follow a 3^rd order polynomial function, as specified. For all the 17 analyzed flights, the data, even being different, show the same behavior. The error bars in y and t are also indicated (appears as crosses in the figure).

Thumbnail

Figura 3
Drag coefficient (C_D) versus vertical popcorn velocity (v_y) for 10 different flights. C_D increases exponentially when v_y decreases, has lower uncertainties for higher v_ys (percent error ∼10%) and higher uncertainties for lower v_ys (in general, percent error ∼60%, diverging when v_y → 0). The result for the popcorn flight shown in Figure 1(b) is shown in dark purple and emphasized in the inset with the error bars indicated by the dashed lines.

Thumbnail

Figura 4
Drag coefficient (C_D) versus Reynolds number (Re) for 10 different flights. Again, the result for the popcorn flight shown in Figure 1(b) is shown in dark purple. C_D increases exponentially when Re decreases. The result for the popcorn flight shown in Figure 1(b) is shown in dark purple and emphasized in the inset with the error bars indicated by the dashed lines. The error increases when Re decreases showing a divergence when Re → 0.. The popcorn flights are governed, mainly, by a laminar flow motion (Re ＜ 2000).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Figura 1 (a) General view of the experiment, showing where the cellular phone was set in order to record the popping process. (b) Details on the experiment for determining the drag coefficient (C_D) of vertically moving popcorns. (c) Multiframe image, mounted with the software Tracker from one of the multi-frame popcorn motion movie segmentations (popcorn flights), over a time interval of 0.56 s, i.e., 67 frames. However, only 15 frames, sort overall the full time interval, are shown.

Figura 2 (a) Position (y) versus time (t) data, acquired with software Tracker, for the popcorn flight shown in Figure 1(b). The data follow a 3^rd order polynomial function, as specified. For all the 17 analyzed flights, the data, even being different, show the same behavior. The error bars in y and t are also indicated (appears as crosses in the figure).

Figura 3 Drag coefficient (C_D) versus vertical popcorn velocity (v_y) for 10 different flights. C_D increases exponentially when v_y decreases, has lower uncertainties for higher v_ys (percent error ∼10%) and higher uncertainties for lower v_ys (in general, percent error ∼60%, diverging when v_y → 0). The result for the popcorn flight shown in Figure 1(b) is shown in dark purple and emphasized in the inset with the error bars indicated by the dashed lines.

Figura 4 Drag coefficient (C_D) versus Reynolds number (Re) for 10 different flights. Again, the result for the popcorn flight shown in Figure 1(b) is shown in dark purple. C_D increases exponentially when Re decreases. The result for the popcorn flight shown in Figure 1(b) is shown in dark purple and emphasized in the inset with the error bars indicated by the dashed lines. The error increases when Re decreases showing a divergence when Re → 0.. The popcorn flights are governed, mainly, by a laminar flow motion (Re ＜ 2000).

(1)

F_{D} = \frac{1}{2} ρ A C_{D} v^{2},

(2)

P + F_{D} = m a_{y},

(3)

- m g - \frac{1}{2} ρ A C_{D} v_{y}^{2} = m a_{y} .

(4)

a_{y} = - g - \frac{1}{2 m} ρ A C_{D} v_{y}^{2} .

(5)

γ = \frac{ρ A C_{D}}{2 m g},

(6)

a_{y} = - g (1 + γ v_{y}^{2}) .

(7)

C_{D} = - \frac{2 m (a_{y} + g)}{ρ A v_{y}^{2}} .

(8)

R e = \frac{ρ v_{y} L}{η},

(9)

L = 2 \sqrt{\frac{A}{π}} .

How to cite

copy

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

Acompanhe os números deste periódico no seu leitor de RSS

Versão para download de PDF

PDF

Inglês

Versões e tradução automática

Versão original do texto

English

Tradução automática

Google Translator
Microsoft Translator

Como citar

RIS

BIBTEX

Outros formatos de citação e exportação:

SciELO - Scientific Electronic Library Online
Rua Dr. Diogo de Faria, 1087 – 9º andar – Vila Clementino 04037-003 São Paulo/SP - Brasil
E-mail: scielo@scielo.org

Leia a Declaração de Acesso Aberto

Métricas

Drag coefficient of vertically moving popcorns

PlumX

Mensagem

[1] * Correspondence email address: eduardo.carmo@unila.edu.breduardo.carmo@unila.edu.br