Re: A question for those interested in physics...

Jonas M�ller wrote:

> Edwin <zer...@aiur.org> wrote in message news:<a7q95c$n6or0$1...@ID-56786.news.dfncis.de>...
> 
>>"Robert Bowmaker" <rob...@dse.gen.nz> wrote in
>>news:x7Vn8.1094$sO2...@news.xtra.co.nz: 
>>
>>
> 
>>>The question is: What actually happens to the bullet? Does it go into
>>>space? Does it fall back down? Does it burn up? None of the above?
>>>
> 
> I got a bit interested in this problem so I tried to solve it, at
> first mathematically but thats a bit difficult.
> I came up to this differential equation
> 
> V(t) = V(0) -g*t -cw*A*rho*t/2/M*(V(t))^2
> 

This is the correct equation for one way only, but you handled it 
appropriately in your program with a while statement.


> which is to difficult to solve, so I wrote a programm to solve this
> problem.
> Here is it:
> 
> ------
> import java.io.*;
> public class Physik {
> 
> // this Programm assumes constant gravity. START_VELOCITY should not 
> // be to close to escape velocity
>     public static final double START_VELOCITY=600.; //meters per
> second
>     public static final double BULLET_MASS=.0059367; // kg 
>     public static final double BULLET_RADIUS=0.005; //m
>     public static final double SPHERE_CW_VALUE=0.43; 
>     public static final double EARTH_ACCELERATION=9.81; // m/s^2
>     public static final double AIR_DENSITY=1.29; //kg*m^-3
> 
>     public static void main(String[] args) {
>  double velocity = START_VELOCITY;
>  double altitude=0.1;
>  long time=0; // milliseconds
> 
>  while(altitude>0) {
>      time++;
>      if(time%1000==0) { // Output every second
>   System.out.println("Time: "+(int)(time/1000)+
>   " sec.  Velocity: "+velocity+" Altitude:"+altitude+"m");
>      }
>      if(velocity>0) {
>   velocity -= (0.001*EARTH_ACCELERATION); // effects of gravity
>   velocity -= 0.0005*SPHERE_CW_VALUE*Math.PI*BULLET_RADIUS*
>   BULLET_RADIUS*AIR_DENSITY*velocity*
>   velocity/BULLET_MASS;// effects of air resistance
>      }
>      else {
>   velocity -= (0.001*EARTH_ACCELERATION); // effects of gravity
>   velocity += 0.0005*SPHERE_CW_VALUE*Math.PI*BULLET_RADIUS*
>   BULLET_RADIUS*AIR_DENSITY*velocity*
>   velocity/BULLET_MASS;// effects of air resistance
>      }
>      altitude += 0.001*velocity;
>  }
>  System.out.println("End");
>  System.out.println("Time: "+time+" msec.  Velocity: "
>  +velocity+" Altitude:"+altitude+"m");
>     }
> }
> -------
> And here is the output:
> Time: 1 sec.  Velocity: 182.767329315557 Altitude:313.9889103484415m
> Time: 2 sec.  Velocity: 102.93655324264626
> Altitude:450.19204386384945m
> Time: 3 sec.  Velocity: 67.28102752697508 Altitude:533.4695325824632m
> Time: 4 sec.  Velocity: 45.885623795788625 Altitude:589.3113694914061m
> Time: 5 sec.  Velocity: 30.721468003701805 Altitude:627.2551712330571m
> Time: 6 sec.  Velocity: 18.66332461450972 Altitude:651.7606345423462m
> Time: 7 sec.  Velocity: 8.168188312246363 Altitude:665.085517850534m
> Time: 8 sec.  Velocity:-1.708012596526278 Altitude:668.2907108883071m
> Time: 9 sec.  Velocity:-11.331565958315913 Altitude:661.7275295391529m
> Time: 10 sec. Velocity:-20.19517275872547 Altitude:645.8738977444464m
> Time: 11 sec. Velocity:-27.848887324834912 Altitude:621.7352040884126m
> Time: 12 sec. Velocity:-34.09827745002394 Altitude:590.6398258126908m
> Time: 13 sec. Velocity:-38.972018448610804 Altitude:553.9931841438874m
> Time: 14 sec. Velocity:-42.63856531226591 Altitude:513.0945060604246m
> Time: 15 sec. Velocity:-45.32292568279939 Altitude:469.040225796333m
> Time: 16 sec. Velocity:-47.24932123874531 Altitude:422.69864533895m
> Time: 17 sec. Velocity:-48.61203334409702 Altitude:374.7273849964622m
> Time: 18 sec. Velocity:-49.56622374124049 Altitude:325.60917279345995m
> Time: 19 sec. Velocity:-50.2296014059005 Altitude:275.6907170908416m
> Time: 20 sec. Velocity:-50.68850928763151 Altitude:225.2172953804121m
> Time: 21 sec. Velocity:-51.00487835669808 Altitude:174.36062359164038m
> Time: 22 sec. Velocity:-51.22246413502058 Altitude:123.2400549298544m
> Time: 23 sec. Velocity:-51.371866322071526 Altitude:71.93813718527623m
> Time: 24 sec. Velocity:-51.47433608682388 Altitude:20.511768627818906m
> End
> Time: 24398 msec.  Velocity: -51.50557167546148
> Altitude:-0.032895169707768394m
> 
> As you should see its not really important how fast the bullet is
> shot, because air resistance evens the earth acceleration out. If the
> bullet falls a distance of about 490 meters(after it has reached the
> highest point) it gets a speed of about 50 m/s (180 km/h) which is
> probably enough to be very dangerous.
> 
> This program simulates a direct vertical shot of a spherical lead
> bullet started with a 600 m/s (2160km/h). The bullet has a diameter of
> 5mm and weigths 5.9376g (I do not know if this is realistic). A bullet
> with a different size would probably reach an other velocity. If
> there's no wind, this bullet will reach its starting place 24 seconds
> after it was shot.(if there is wind, it will reach an other place in
> the same time with the same horizontal speed)
> 
> 
> I hop I brought some clarity into this discussion.
> 
> 
> If you want to test this program you need an installed Java SDK
> 
> Paste the programm into an editor
> save as 'Physik.java'
> compile: 'javac Physik.java'
> run: 'java Physik'
> 

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