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Equation

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Para cosechar fruta existe la posibilidad de liberarla y capturarla en pleno vuelo. Para ello se dispone del tiempo que se puede calcular de

$S = \displaystyle\frac{v_t^2}{g}\ln(\cosh\displaystyle\frac{gt}{v_t})$

Conditions

Variables

Relation

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Equation

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The resistance force ($F_W$) kann mit the density ($\rho$), the coefficient of resistance ($C_W$), the total object profile ($S_p$) und the speed with respect to the medium ($v$) entsprechend berechnet werden folgende Formel:

$F_W =\displaystyle\frac{1}{2} \rho S_p C_W v ^2$

Conditions

Variables

$C_W$

Coefficient of resistance

$-$

6122

$\rho$

Density

$kg/m^3$

5342

$F_W$

Resistance force

$N$

6124

$v$

Speed with respect to the medium

$m/s$

6110

$S_p$

Total object profile

$m^2$

6123

Relation

Development

Similarly to how the equation for the lift force ($F_L$) was derived using the density ($\rho$), the coefficient of lift ($C_L$), the surface that generates lift ($S_w$), and the speed with respect to the medium ($v$)

$F_L =\displaystyle\frac{1}{2} \rho S_w C_L v ^2$

in this analogy, what corresponds to the surface that generates lift ($S_w$) will be equivalent to the total object profile ($S_p$) and the coefficient of lift ($C_L$) to the coefficient of resistance ($C_W$), thus the resistance force ($F_W$) is calculated:

$F_W =\displaystyle\frac{1}{2} \rho S_p C_W v ^2$

The drag coefficient is measured and, in turbulent flows over aerodynamic bodies, values are generally found around 0.4.

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Si se resta la fuerza de flotación de la fruta en el aire la fuerza gravitacional será

$F_g = m_b g \displaystyle\frac{ \rho_b - \rho }{ \rho_b }$

Conditions

Variables

Relation

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Equation

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Si se iguala la fuerza de resistencia aerodinámica con la de gravedad menos la de flotación se obtiene la velocidad de caída relativa como

$ v_r ^2 = 2 g m_b \displaystyle\frac{ \rho_b -

Conditions

Variables

Relation

O sea que una fruta en una corriente de esta misma velocidad flotara y impurezas serán arrastradas con la corriente. El sistema también se puede usar para separar calibres.

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Regarding the physical pendulum:

The energy is given by:

$E=\displaystyle\frac{1}{2}I\omega^2+\displaystyle\frac{1}{2}mgl\theta^2$

As a result, the angular frequency is:

$\omega_0 ^2=\displaystyle\frac{ m g L }{ I }$

Conditions

Variables

$\omega_0$

Angular Frequency of Physical Pendulum

$rad/s$

6288

$g$

Gravitational Acceleration

9.8

$m/s^2$

5310

$m_g$

Gravitational mass

$kg$

8762

$I$

Moment of inertia for axis that does not pass through the CM

$kg m^2$

5315

$L$

Pendulum Length

$m$

6282

Relation

Development

Given that the kinetic energy of the physical pendulum with moment of inertia $I$ and angular velocity $\omega$ is represented by

$K_r =\displaystyle\frac{1}{2} I \omega ^2$

and the gravitational potential energy is given by

$V =\displaystyle\frac{1}{2} m_g g L \theta ^2$

where $m$ is mass, $l$ is string length, $\theta$ is the angle, and $g$ is angular acceleration, the energy equation can be expressed as

$E=\displaystyle\frac{1}{2}I\omega^2+\displaystyle\frac{1}{2}mgl\theta^2$

As the period is defined as

$T=2\pi\sqrt{\displaystyle\frac{I}{mgl}}$

we can determine the angular frequency as

$\omega_0 ^2=\displaystyle\frac{ m g L }{ I }$

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