Timeline for Calculating the theoretical velocity of a projectile
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2016 at 0:36 | comment | added | CuriousOne | The acceleration is very high... but the barrel is short. If you use $s=at^2/2$ and $v=at$, then you can substitute $t=v/a$ in the first equation, which gets you $s=a(v^2/a^2)/2=v^2/2a$. It follows that $v=\sqrt{2as}$, which is dimensionally correct, if you check the units. If we insert an acceleration of $a=70,000m/s^2$ and a barrel length of $s=0.5m$, then we get $v=\sqrt{2*70000m/s^2*0.5m}=265m/s. And now I have to apologize because I got it wrong by a factor of 2 the first time (I had it in the denominator instead of the numerator under the square root). | |
| Jan 12, 2016 at 0:17 | comment | added | Ryan | I calculated the acceleration actually, since my units are in m/s^{-2}. With my force of 28N and mass of .0002kg (.2g), I basically used f=ma to solve for a. @CuriousOne | |
| Jan 12, 2016 at 0:13 | history | edited | Qmechanic♦ |
edited tags
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| Jan 12, 2016 at 0:11 | history | edited | Ryan | CC BY-SA 3.0 |
Corrected math mistake
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| Jan 12, 2016 at 0:09 | comment | added | CuriousOne | Ah... did you use the area of a half sphere? OK. While tempting it's only the circular cross section that counts. The pressure does act on the normals of the sphere, but the components of that force that are not pointing in the direction of the barrel do not accelerate the bb. All of this is minor, though. How did you calculate the total velocity? I think that's where the major problem in your estimate is. | |
| Jan 12, 2016 at 0:02 | comment | added | Ryan | Ah good call. I used 6 as the radius instead of three. But your surface area equation is for a circle not a sphere. I will update my question :) @CuriousOne | |
| Jan 11, 2016 at 22:32 | comment | added | CuriousOne | The area of a round 6mm bb comes out to about $\pi r^2\approx 3*3*3.14 mm^2 \approx 28mm^2$. How did you get the $250mm^2$? That's 14N of force and an initial acceleration of 7000g. For a 50cm long barrel that gives me 132m/s as velocity. Sounds about right, no? It couldn't go much faster than that, anyway, otherwise one would have to understand sonic and even hypersonic airflow in the gun and that's not so easy (and not happening here). | |
| Jan 11, 2016 at 22:09 | history | asked | Ryan | CC BY-SA 3.0 |