It’s not that I disagree with Cecil’s description of the
facts (that firing a bullet from a gun will produce a longer
drop time than dropping a bullet directly). I just think
it’s amusing that he specifically mentions that we are
taking for granted that we are experimenting in a vacuum,
and later points out the curvature of the Earth. Really,
in any practical sense, you are far less likely to be
firing bullets in a vacuum than you are to be firing a gun
that, while firing horizontally, has any chance to be
affected by the Earth curving away from the bullet’s path.
We are either firing bullets in the real world or we aren’t.
The question searches for the effect of gravity on
horizontally moving objects. To assume the unreality of
a vacuum and not to assume the unreality of a flat plane is
kind of silly.
Welcome to the SDMB, and thank you for posting your comment.
Please include a link to Cecil’s column if it’s on the straight dope web site.
To include a link, it can be as simple as including the web page location in your post (make sure there is a space before and after the text of the URL).
The column can also be found on page 201 of Cecil Adams’ book “Triumph of the Straight Dope”.
I personally don’t think it’s silly to make those assumptions. When I was studying high school physics (the highest level at which most people probably study physics), those kind of assumptions were routinely made. So in his first (simple) answer, Cecil made those assumptions, but then pointed out that the real answer was more complicated. I fail to see what is insufficient with the way he chose to answer the question.
The fired bullet would hit the ground last as it has to bend over the earth’s surface. Cecil said if the fired bullet only travelled a small distance then both bullets would hit the ground at the same time. WRONG. The fired bullet would hit later, even if it barely makes it out of the barrel.
Also, in a vacuum, combustion can’t occur and the gun wouldn’t fire.
I’m not sure this is absolutely accurate. I thought that smokeless powders “made” their own oxygen as part of the combustion process (ie., one of the chemicals in the powder gives up oxygen as it burns). Trying to remember my time working in the gun shop in high school…ouch, my old brain hurts. I know that smokeless powders burn faster as the pressure increases (which is why they only burn when you light a pile of the stuff in the open, as opposed to black powder, which will explode in the same situation).
Now, whether the primer would work in a vacuum is another question.
Of course, gunpowder will explode in a vacuum. Ditto for the primer.
Consider, the powder and primer are tightly packed in a brass cylinder with both ends sealed. There’s only minuscule amounts of air in there with it. Yet, in a fraction of a second, it explodes. Note that this explosion happens before the bullet is expelled, letting air into the cartridge. It should be obvious that this explosion does not require the presence of air to happen.
And don’t pick the obvious nit about the tiny amounts of air in the cartridge. They aren’t enough to make any difference.
Hmph. No contest. Fire the bullet straight down, that avoids the curvature of the earth problem, the vacuum problem, and any thing else that might stand in the way. The fired bullet with then hit the ground first, by a considerable time difference, I might add.
Actually, that is not Cecil’s description, and it is wrong. The fired bullet will NOT take longer to drop. It just travels a lot farther away.
I agree with the principle you mentioned that curvature is less likely to be noticed than atmosphere, so it seems arbitrary to make one assumption and not make the other. But I think it’s fair that Cecil picked the assumptions he wanted to make his point (there have to be simplifications), and as long as he lists the assumptions, it’s fair. The reason for assuming a vacuum is simply to remove turbulence and wind effects. He could have said a perfectly windless day instead.
With the added bonus that, if the gun is aimed at your foot, you can visually demonstrate the origin of a well-know proverb, thus killing two birds with one stone.
First, even if you maintain that the earth is curved and the bullet goes in a straight line, is the curvature significant enough to matter? The earth is approximately 40,000 km in circumference. A bullet (as close as I can figure it using muzzle velocities for a .22 and a height of 2 meters for the initial firing) would travel about 1.5 km. One degree would be around 110 km, so you are looking at just over .01 degree of arc.
But the second thing is that in my muzzy memory of physics, is that unless the bullet is traveling fast enough to escape from the earths gravitational pull, it will also travel in an arc, that would be parallel to the center of the earth. The same thing would apply to an airplane for example. If you take a plane to 35000 feet and set it level, you can fly completely around the world. I hope I didn’t muddle this up and make a fool of myself, it has been a long time since I took physics.
PUNdit, bullets do travel in an arc. This is because of the gravitational pull. It will not be parallel to the surface of the earth unless it reaches orbit. Otherwise, it will fall in a parabolic path approaching the surface at whatever course is determined by the combination of initial velocity, drag, and gravity. For a REALLY fast bullet that is not quite escape speed, it could curve a significant distance around the earth and hit the far side.
The reason why planes fly in a level path is because they generate lift as they fly. That’s what the wings are for - to counteract gravity. The amount of lift is balanced so the altitude stays constant above the surface, not to produce a straight line path.
A gun firing off a sphere with no gravity field would produce the straight path away from the barrel that diverges from the sphere.
wait wait wait. if the bullet in question is
from a smoothbore firearm, and we assume a flat
plane, vacuum and uniform gravity, then they both hit the
ground at the same time, right?
but what if it’s a rifled barrel? won’t the
gyroscopic force generated by the spinning bullet slow
its downward fall?
No. The gyroscopic effect just maintains the orientation of the bullet, not it’s altitude. It will prevent tumbling, but the gravity is perpendicular to the axis of spin, anyway.
Get out your toy gyroscope and try it out. There’s no resistance when you move the gyroscope, just when you try to reorient it’s axis.