What is the maximum velocity of a bullet at the instant it leaves the barrel?

[stvsxm]

hi, my high school physics is letting me down here and I just have to get an explanation...

when you talk to gun guys, they say that the maximum velocity that a bullet reaches is the muzzle velocity ... i.e. the absolute velocity of the bullet at the instant that it clears the barrel. their assertion is that , once the gases stop pushing the bullet, that everything after that is " slowing down.

I understand the logic and science of their position but I can't get it to make sense to me. I certainly remember f=ma ... a given force imparted to a given mass results in a given acceleration... fine. then any unbalanced force acts to offset that acceleration. fair enough... so the bullet is immediately subjected to a drag force as a function of air versus its instantaneous velocity and gravity pulling it down...

I did that calculation a hundred times in school... " someone throws a rock of x mass with a force of y lbs off a cliff z feet high in a vacuum . how far does it travel before it hits the ground ? " that was all linear... time to ground etc... but in the real world it just seems , just like the guy throwing the rock, that the bullet accelerates for some period of time AFTER it leaves the barrel before it reaches an equilibrium with the drag and starts slowing down... i.e. max v occurs not at the muzzle but somewhere down range.

just like a pitcher throwing a 100 mph fast ball... the pitchers arm isn't moving at 100 mph when the ball leaves his hand ( is it ? ) so the ball accelerates to max v and then slows down... the velocity is a curve... of distance vs time rather than a straight line ... starting at max and ending at zero... so... somebody please remind me what the truth is , please...

 

[phyzguy]

Your intuition is wrong and your gun friends are right. As soon as the bullet leaves the barrel and the hot gasses stop pushing on it, the bullet begins slowing down. This is a simple consequence of F=ma. Also, a pitcher's hand is moving at 100 mph when the ball leaves his hand.

 

[Drakkith]

just like a pitcher throwing a 100 mph fast ball... the pitchers arm isn't moving at 100 mph when the ball leaves his hand ( is it ? )

Of course not. It's moving faster since the ball slows down between release and catch.

so the bullet is immediately subjected to a drag force as a function of air versus its instantaneous velocity and gravity pulling it down...

Note that the bullet immediately begins to experience drag at the moment the cartridge is fired since there is air inside the barrel. The drag force increases as the bullet accelerates down the barrel and once out of the barrel the force from the expanding gas that propels it is lost and it begins to decelerate because of this drag.

 

[stvsxm]

Of course not. It's moving faster since the ball slows down between release and catch.
Note that the bullet immediately begins to experience drag at the moment the cartridge is fired since there is air inside the barrel. The drag force increases as the bullet accelerates down the barrel and once out of the barrel the force from the expanding gas that propels it is lost and it begins to decelerate because of this drag.

ok. I get it. thanks for reminding me .

 

[stvsxm]

ok. I get it. thanks for reminding me .

on second thought,... let's talk about this for a minute... take the example of a baseball bat hitting a pitched baseball...

ignore , for the sake of discussion, the compressibility of the ball and the coefficient of restitution of the bat...

so the ball approaches the bat at some given velocity. the bat of a given mass makes contact with the ball in the opposite direction and imparts some given force ... now... at the instant of impact the ball has zero velocity. then the ball accelerates in the other direction to some terminal V before it slows down and begins to fall.

ignoring the vector analysis of the trajectory and just discussing the velocity/acceleration question, there can be no way that the ball achieves max V in the other direction instantaneously as it leaves the bat. it has to go from 0 velocity in the outgoing direction to some max v over some distance and time... so it has to accelerate.

now... I suppose this could be a conservation of momentum deal... where once the bat contact the ball and that system has a given momentum so once the ball leaves the bat ( like a hub cap falling off a moving car ) the ball has the same system momentum and being of substantially less mass , now much achieve a higher speed and therefore accelerates...

and I am thinking that's what happens to the pitched ball as well... there is no way a pitchers hand is moving at a 141 fps to thor a 100 mph fast ball all you have to do is watch it with a stop watch and the time it takes for a full forward movement vs the linear distance isn't even close to that... and I can't help but think the same thing happens with the bullet... that's why long barrel guns have higher velocity than short barrel ones... because the bullet has a longer time exposed to the propellant gas pressure... so it becomes a momentum issue the gas+the bullet vs the bullet alone...

and that's why I am talking to you guys because you are , presumably , far better educated than I and can rationalize the observed data vs the theoretical... I m not arguing... I am trying to understand.

 

[russ_watters]

...there can be no way that the ball achieves max V in the other direction instantaneously as it leaves the bat. it has to go from 0 velocity in the outgoing direction to some max v over some distance and time... so it has to accelerate.

Here's your distance and time:



The universe looks a lot different if you zoom in or zoom out a lot in distance or time. What looks instantaneous to our eyes is in fact a process that takes time, during which the baseball covers a distance and accelerates due to an applied force.

... there is no way a pitchers hand is moving at a 141 fps to thor a 100 mph fast ball

I don't quite agree with what you were told before. Because the ball is rolling off the pitcher's fingertips, there is a mechanical advantage due to the changing angle of the hand and changing point of contact. The ball and therefore the point of contact with the hand moves at 100mph, but the hand itself (fingertips) doesn't have to.

It is important not to underestimate the impact of technique in sports. I read somewhere that a pro golfer has a substantially lower peak head acceleration than a typical amateur, it's just that their body mechanics enable them to maintain the acceleration more consistently throughout the swing. Pitching is similar, where you have multiple pivot points (waist, shoulder elbow, wrist) rotating in sync to achieve progressively faster motion at the end of each lever.

and I can't help but think the same thing happens with the bullet... that's why long barrel guns have higher velocity than short barrel ones... because the bullet has a longer time exposed to the propellant gas pressure...

That's true, but aren't you arguing against your point?

[Go Phillies!]