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

← Older edit

@@ description / en / description / en @@
+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.
@@ 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
+ ${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ 
\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}
+has characteristic: nonlinearity
@@ Property / Generalizes @@
-Free Fall Equation (Vacuum)
@@ Property / Generalizes: Free Fall Equation (Vacuum) / rank @@
-Normal rank
@@ Property / in defining formula @@
+ $m$ 
m
@@ Property / in defining formula: $m$ / rank @@
+Normal rank
@@ Property / in defining formula: $m$ / qualifier @@
+symbol represents: Free Fall Mass
@@ Property / in defining formula @@
+ $g$ 
g
@@ Property / in defining formula: $g$ / rank @@
+Normal rank
@@ Property / in defining formula: $g$ / qualifier @@
+symbol represents: Gravitational Acceleration
@@ Property / in defining formula @@
+ $\rho$ 
\rho
@@ Property / in defining formula: $\rho$ / rank @@
+Normal rank
@@ Property / in defining formula: $\rho$ / qualifier @@
+symbol represents: Density of Air
@@ Property / in defining formula @@
+ $C_{D}$ 
C_D
@@ Property / in defining formula: $C_{D}$ / rank @@
+Normal rank
@@ Property / in defining formula: $C_{D}$ / qualifier @@
+symbol represents: Drag Coefficient
@@ Property / in defining formula @@
+ $A$ 
A
@@ Property / in defining formula: $A$ / rank @@
+Normal rank
@@ Property / in defining formula: $A$ / qualifier @@
+symbol represents: Cross Section
@@ Property / in defining formula @@
+ $v_{0}$ 
v_0
@@ Property / in defining formula: $v_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: $v_{0}$ / qualifier @@
+symbol represents: Free Fall Initial Velocity
@@ Property / in defining formula @@
+ $v_{\infty }$ 
v_\infty
@@ Property / in defining formula: $v_{\infty }$ / rank @@
+Normal rank
@@ Property / in defining formula: $v_{\infty }$ / qualifier @@
+symbol represents: Free Fall Terminal Velocity
@@ 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 @@
+ $y$ 
y
@@ Property / in defining formula: $y$ / rank @@
+Normal rank
@@ Property / in defining formula: $y$ / qualifier @@
+symbol represents: Free Fall Height
@@ 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 / community @@
+MathModDB
@@ Property / community: MathModDB / rank @@
+Normal rank
@@ Property / Is Linear @@
+Amount 0
Unit 1
 Amount
 Unit
@@ Property / Is Linear: 0 / rank @@
+Normal rank
@@ 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

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.