Free Fall Equation (Air Drag) (Q3836): Difference between revisions

Revision as of 11:11, 10 October 2024

Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

Language	Label	Description	Also known as
English	Free Fall Equation (Air Drag)	Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

Statements

instance of

Q3832 (Deleted Item)

0 references

defining formula

{\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\\v(t)&=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}

has characteristic

nonlinearity

1 reference

described at URL

https://en.wikipedia.org/wiki/Free_fall

in defining formula

v

symbol represents

Free Fall Velocity

0 references

m

symbol represents

Free Fall Mass

0 references

g

symbol represents

Gravitational Acceleration

0 references

\rho

symbol represents

Q3851 (Deleted Item)

0 references

C_{D}

symbol represents

Drag Coefficient

0 references

A

symbol represents

Cross Section

0 references

v_{0}

symbol represents

Free Fall Initial Velocity

0 references

v_{\infty }

symbol represents

Free Fall Terminal Velocity

0 references

t

symbol represents

Q3846 (Deleted Item)

0 references

y

symbol represents

Free Fall Height

0 references

y_{0}

symbol represents

Free Fall Initial Height

0 references

community

MathModDB

0 references

P853 (Deleted Property)

The value is invalid and cannot be displayed. Property P853 not found, cannot determine the data type to use.

P891 (Deleted Property)

The value is invalid and cannot be displayed. Property P891 not found, cannot determine the data type to use.

0 references

Identifiers

Wikidata QID

Q38083707

0 references

@@ Property / defining formula / Property / defining formula @@
- $m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}$ 
m\dot{v}=mg-\frac{1}{2}\rho C_DAv^2
+ ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\\v(t)&=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ v(t) &= v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \end{align}
+has characteristic: nonlinearity
+described at URL: https://en.wikipedia.org/wiki/Free_fall
@@ Property / defining formula @@
- $y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$ 
y(t)=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)
-Normal rank
@@ Property / P853 (Deleted Property) @@
-The value is invalid and cannot be displayed. Property P853 not found, cannot determine the data type to use.
-Normal rank
-Vanishing Air Density:  $\rho \rightarrow 0$ 
\rho \rightarrow 0
-Vanishing Drag Coefficient:  $C_{D}\rightarrow 0$ 
C_D \rightarrow 0
@@ Property / P853 (Deleted Property) @@
+The value is invalid and cannot be displayed. Property P853 not found, cannot determine the data type to use.
+Normal rank
+P891 (Deleted Property): The value is invalid and cannot be displayed. Property P891 not found, cannot determine the data type to use.
+P891 (Deleted Property): The value is invalid and cannot be displayed. Property P891 not found, cannot determine the data type to use.

Free Fall Equation (Air Drag) (Q3836): Difference between revisions

$m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}$

${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\\v(t)&=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$

$y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

Revision as of 11:11, 10 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

Free Fall Equation (Air Drag) (Q3836): Difference between revisions

m v ˙ = m g − 1 2 ρ C D A v 2 {\displaystyle m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}}

y ( t ) = y 0 + v 0 t − v ∞ 2 g ln ⁡ cosh ⁡ ( g t v ∞ ) {\displaystyle y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)}

ρ → 0 {\displaystyle \rho \rightarrow 0}

C D → 0 {\displaystyle C_{D}\rightarrow 0}

Revision as of 11:11, 10 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$m{\dot {v}}=mg-{\frac {1}{2}}\rho C_{D}Av^{2}$

$y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)$

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$