# Long and short barreled guns

Projectiles containing delicate elecrtronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not from guns with short barrels. -Explain why a projectile fired from a long-barreled gun is subject to less acceleration than a projectile fired from a short-barrelled gun if the range is the same in both cases. This question has been a nightmare for me when i was in highschool and until now i cant have a good answer your help would be appreciated.

• An idea would be to say that long-barreled guns = more friction thus less force and thus less acceleration and vice versa Feb 19, 2016 at 0:46
• A really good answer to this question was posted by Scott Manley on Youtube, but with a slightly different premise. Why can't we fire humans into space?
– Aron
Feb 19, 2016 at 0:47
• Take down your comment, it has nothing to do with friction. Its simply due to the equation E = Fdx. Given a longer barrel (dx), the required Force (F) is smaller for the same Muzzle Energy (E).
– Aron
Feb 19, 2016 at 0:50
• I would not think a projectile fired from a long-barreled gun is subject to less acceleration than a projectile fired from a short-barrelled gun. Are you sure this is true? Feb 19, 2016 at 1:21
• If you say so then proove it. :/ Feb 19, 2016 at 2:21

Energy is force times distance. So if you want your projectile to have a kinetic energy of, for example, $E=1250 \text{ J}$, which, since $E=M\cdot v^2/2$, corresponds to a velocity of $v=500 \text{ m/s}$ if the weight of the bullet is $M=0.01 \text{ kg}$, you can either accelerate it with a force of $F=1250 \text{ N}$ for a distance of $x=1 \text{ m}$, or with a force of $F=125 \text{ N}$ for a distance of $x=10 \text{ m}$, or any other combination that gives you your required kinetic energy and therefore speed and range.

The longer barrelled gun can contain the pressure of the explosive charge over a greater period of time than the short barrel, for the same initial charge, so the acceleration can be effectively reduced but produces an equal range for both guns.

• Why would the bullet leave the two guns with the same velocity? If I drop a marble down a short slide and a long slide, wouldn't it be going faster at the bottom of the long slide? Feb 19, 2016 at 3:09
• @user1717828 your thinking is correct, but the statement 'they have the same range' automatically induces the fact/assumption that they have the same initial velocity and obviously the same angle of elevation. So one can easily assume that they are launched with the same initial energy E. Feb 19, 2016 at 6:41
• @user1717828 Sorry i cant modify my previous post but what i wanted to say is that your thinking is wrong,as they have the same potential energy at the beginning and it is gradually converted to K.E , so the corresponding velocity is only dependent on the height covered thus independent of the path taken. :/ Feb 19, 2016 at 7:13

The short barrel gun has a high force because $$F=GmM/r^2$$ for the long barrel has a long radius thus less force but short barrel gun has a small radius thus large force.

But $F=ma$ so $F$ varies directly as acceleration. The smaller the force the smaller the acceleration and the greater the force the greater the acceleration accounting for the high velocity.

• Would you care so specify what are $G$, $M$ and $m$ in your answer? Mar 5, 2017 at 22:09