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

Latest revision as of 11:41, 2 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

Mathematical Formulation

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)\end{aligned}}

has characteristic

nonlinearity

0 references

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

Density of Air

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

Time

0 references

y

symbol represents

Free Fall Height

0 references

y_{0}

symbol represents

Free Fall Initial Height

0 references

community

MathModDB

0 references

Is Linear

0

0 references

Generalizes Formulation

Free Fall Equation (Vacuum)

subject has role

Mathematical Formulation

object has role

Mathematical Formulation

Vanishing Air Density

\rho \rightarrow 0

Vanishing Drag Coefficient

C_{D}\rightarrow 0

0 references

Identifiers

Wikidata QID

Q38083707

0 references

@@ Property / Generalizes Formulation @@
-Free Fall Equation (Vacuum)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / rank @@
-Normal rank
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Air Density:  $\rho \rightarrow 0$ 
\rho \rightarrow 0
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
-Vanishing Drag Coefficient:  $C_{D}\rightarrow 0$ 
C_D \rightarrow 0
@@ Property / defining formula @@
+ ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\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) \end{align}
+Normal rank
+has characteristic: nonlinearity
@@ Property / in defining formula @@
+ $t$ 
t
@@ Property / in defining formula: $t$ / rank @@
+Normal rank
@@ Property / in defining formula: $t$ / qualifier @@
+symbol represents: Time
@@ Property / in defining formula @@
+ $y_{0}$ 
y_0
@@ Property / in defining formula: $y_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: $y_{0}$ / qualifier @@
+symbol represents: Free Fall Initial Height
@@ Property / Generalizes Formulation @@
+Free Fall Equation (Vacuum)
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / rank @@
+Normal rank
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+subject has role: Mathematical Formulation
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+object has role: Mathematical Formulation
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+Vanishing Air Density:  $\rho \rightarrow 0$ 
\rho \rightarrow 0
@@ Property / Generalizes Formulation: Free Fall Equation (Vacuum) / qualifier @@
+Vanishing Drag Coefficient:  $C_{D}\rightarrow 0$ 
C_D \rightarrow 0

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

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

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

$t$

$y_{0}$

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

Latest revision as of 11:41, 2 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

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

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

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

m v ˙ = m g − 1 2 ρ C D A v 2 y ( t ) = y 0 + v 0 t − v ∞ 2 g ln ⁡ cosh ⁡ ( g t v ∞ ) {\displaystyle {\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)\end{aligned}}}

t {\displaystyle t}

y 0 {\displaystyle y_{0}}

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

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

Latest revision as of 11:41, 2 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$

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

$t$

$y_{0}$

$\rho \rightarrow 0$

$C_{D}\rightarrow 0$