dear friends
i am sorry i have to write in english as i don't have the ability to rite in arabic
about the airplanes which stop sound for more than 2 minutes i think cause it's super sonic planes which means the plane is faster than sound speed so u see it before u hear its sound ,about how the plain move??
air plane contain some kind of michanism (internal compusion engine)same like cars and each fan has its own engine ,fan is important to preduce drag force which responsable for flying
this is article about drag force i wish it's usful for u
Aerodynamic drag is proportional to velocity squared. Terminal velocity is
the velocity where the aerodynamic drag force exactly cancels out the
gravitational force acting on an object. The tough part of this problem
comes in when you consider that a penny will tumble as it falls. This
tumbling will result in the profile presented to the relative wind changing
with time. This unsteady problem would be quite difficult to model.
This material would be covered in any fluids/aerodynamics text. An online
aerodynamics text, including an online standard atmosphere calculator, can
be found at:
http://www.desktopaero.com/appliedaero/appliedaero.html
Consider a penny falling normal to the flow field.
(While this is obviously the most unstable orientation for our penny, it
also presents the most conservative steady state calculation we can
perform.)
The airflow will reliably separate around the circumference of the disk, and
as a consequence, the drag coefficient will be nearly invariant with respect
to Reynolds number. (This is a very handy simplifying condition for this
problem.)
The drag coefficient (C_d) for a disk oriented normal to the flow is
approximately 1.18.
Drag (D) is equal to one half the product of the drag coefficient, cross
sectional area (S), local density (rho), and velocity squared (V^2).
The density of air at sea level on a standard day is 2.37e-3 slug/ft^3
The area of a penny is 3.068e-3ft^2
(http://www.usmint.gov/circulating/specifications.cfm)
The force due to gravity on the penny is equal to its mass (m) times the
acceleration due to gravity (g)
F=m*g
The mass of a penny is 1.713044e-4 slug
Acceleration due to gravity is 32.2 ft/s^2
Equating the drag force and the weight of the penny, we can solve for its
terminal velocity.
A simple matlab code follows:
C_d=1.18; % Drag coefficient
rho=0.00237; % Sea level density (slug/ft^3)
r=0.5*0.750/12; % Radius of a penny (ft)
m=2.5*6.58217e-5; % Mass of a penny (slug)
g=32.2; % Accel due to gravity (ft/s^2)
S=pi*r^2; % Area of the penny
W=m*g; % Weight of the penny
V=(W/(0.5*rho*S*C_d))^0.5
Our penny would fall at 35 ft/s.
An expression for the acceleration of our penny is:
a=g-0.5*(rho/m)*S*C_D*V^2
Numerically integrating this expression for 100 seconds in Matlab,
[t, x]=ode45('xprm',[0, 100],[0, 0]);
where the file 'xprm.m' exists and contains:
**********************************
function xprime=xprm(t,x)
C_D=1.18; % Drag coefficient
rho=0.00237; % Sea level density (slug/ft^3)
r=0.5*0.750/12; % Radius of a penny (ft)
m=2.5*6.58217e-5; % Mass of a penny (slug)
g=32.2; % Accel due to gravity (ft/s^2)
S=pi*r^2; % Area of the penny
V=x(2);
a=g-0.5*(rho/m)*S*C_D*V^2;
xprime=[V; a];
% x=[x xdot]
% xprime=[xdot xdbldot]
********************* EOF*****
You will see the penny reaches its terminal velocity after about 3.5
seconds, and about 100 ft of freefall. Dropping a penny from any higher
would not increase its velocity.
Repeating this exercise for a penny falling edge on would bound the problem
in question.
Drag coefficient for this orientation is a bit more tricky to determine, but
a conservative estimate follows.
The new drag coefficient:
C_D=2.0
The new planform area:
S=3.1783e-4 ft^2
All other aspects of the problem remain the same.
The edge on terminal velocity would be about 84 ft/s (57mph), requiring
about eight seconds of acceleration in about 500 ft.
The momentum of these two pennies can be calculated as
p=m*V
0.0057 slug*ft/s (face on)
0.0138 slug*ft/s (edge on)
Assuming an impulsive collision with a pedestrian, with the time of
interaction taken as 0.015 seconds (approximately the time a baseball is in
contact with the bat)
The impulsive force is
p=F*dt
0.3855 lbf (face on)
0.9200 lbf (edge on)
Spread over an area as pressure
P=F/S
18096 psi (face on)
416870 psi (edge on)
Looking up the ultimate compressive strength of some common materials,
(ksi=1000psi)
Oak 7ksi
Granite 15-26 ksi
Steel 30-60 ksi
So unless I have slipped up somewhere along the way, I sure wouldn't want to
be under that penny.....
Sorry for the jumbled, rambling responce.
Rob
> Discussing projectile motion in a calculus class, I was asked if it were
true
> that
> a penny, if dropped from a significantly high location, would achieve a
> velocity
> such that it could do "serious damage" to someone's skull.
>
> I explained how, in reality, air resistance would reduce the acceleration
to
> the point where the velocity would remain relatively constant (terminal
> velocity).
>
> Does anyone have an idea as to the terminal velocity of a penny? That is,
> is it dangerous (or just plain stupid) to throw coins off of the Empire
State
> Bldg?
================================================== ============================
From: "Rob McDonald" <rmcdo*engineer.com>
Subject: Re: Terminal Velocity of a Penny
Date: Thu, 16 Sep 1999 02:06:05 -0400
Newsgroups: sci.math
Oops,
I spread the force of the edge on penny over its projected area. It would
actually impart its force over the VVsmall(ideally infnitesimal) area of the
curved edge of the penny. This would drive the pressure WAY up.
> Spread over an area as pressure
>
> P=F/S
>
> 18096 psi (face on)
> 416870 psi (edge on)