Galileo revived

C

cdoc42

New member
Galileo described gravity and postulated that any object falling to earth would fall at the same rate. He believed that a cannonball and a feather, if dropped from the same height, will touch the ground at the same time provided there is no air resistance.

This has been proven true in a room devoid of air, dropping a bowling ball and feathers at the same time (somewhere on the internet).

Which created a discussion between me and an engineer friend who insists it is impossible for a 150gr bullet (example) dropped from a height of 6 feet, would hit the ground at the same time as the bullet being fired, the only difference being distance traveled.

I agree, given air resistance from the front or wind acceleration from the rear, would prevent both bullets from simultaneously hitting the ground.
The situation would have to be the same as the bowling ball and feathers- an environment devoid of air, AND it would depend on the trajectory of the bullet -the muzzle would have to be 6 feet from the ground over absolutely flat terrain.

What say the physicists among us?
 
Let's add a few factors to those in your last sentence.
1) The rifle bore must be absolutely parallel to the plane over which it is fired.

2) The still bullet will have to start its fall at the instant the fired bullet leaves the muzzle, or at least when they are parallel to each other at the same height above the plane.

3) Gravity must be constant over the entire length of the bullet's trajectory. (Contrary to popular belief, gravity is not a constant at all locations on earth at sea level. It can vary a little even at points a few meters apart.)

Given all that (and that's a whole lot of "given"), the two bullets will hit the surface of that fictional plane at the same time.
 
If rifle barrel were exactly level and terrain also exactly level and zero recoil, absolutely true. The difficulty would be to drop the bullet at exactly the same time as the fired bullet left the muzzle.

Bob
WB8NQW
 
cdoc42 said:
Which created a discussion between me and an engineer friend who insists it is impossible for a 150gr bullet (example) dropped from a height of 6 feet, would hit the ground at the same time as the bullet being fired, the only difference being distance traveled.

I agree, given air resistance from the front or wind acceleration from the rear, would prevent both bullets from simultaneously hitting the ground.
The situation would have to be the same as the bowling ball and feathers- an environment devoid of air, AND it would depend on the trajectory of the bullet -the muzzle would have to be 6 feet from the ground over absolutely flat terrain.
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You are postulating a hypothetical situation that cannot effectively be tested in the real world. In addition to comments before my post, I will add that headwind or tailwind are of no consequence, unless the projectile has a shape that in some way generates aerodynamic lift. Absent an aerodynamic lift component, headwind or tailwind wouldn't matter any more than varying the muzzle velocity of the projectile. Assuming a perfectly level barrel, firing over perfectly level ground, the time the projectile takes to drop 6 feet will always be the same -- what will change is how far it travels horizontally before striking the ground.
 
IF the barrel bore is parallel to the ground and the ground, over the distance, is perfectly flat and there is no wind and if the bullet is released to fall at the same time the bullet leaves the muzzle,, the dropped bullet will hit slightly before the fired bullet due to aerodynamic jump and ground effects.

IF those things are the same, but in a vacuum, both will hit at the same time.
 
they will hit the ground at the same time, as far as any human observer can tell.

In my high school science (50 years ago) there was a neat gadget to illustrate this. It was a fixture that held two steel ball bearings (1 inch so students could easily see them) and released them at the same time. One of the ball bearings dropped straight down, the other was "fired" by a spring, horizontally.

Placed on top of a 6ft stand, when tripped, BOTH balls hit the ground at the same time, one right under the device and the other half way across the room.

Special equipment capable of measuring in milli / micro seconds could probably detect a very tiny difference in time of impact, but the human eye and ear, could not.

Your engineer friend is sort of right, on Earth (in atmosphere) they will not hit at EXACTLY the same time, external factors will affect the fired bullet more than the dropped one to a very, very, very, very TINY amount.

Factors in your measuring system will also have an effect on the readings, such as the length of wire between the sensor and the measuring unit, for one. Those kinds of factors are known and can be compensated for. What the atmosphere does is more random and not as fully predictable.
 
Aguila mentioned it, this has always been a question in my head

Given the shape of most bullets I feel like Bernoulli has to come into effect at some point but being a Political Science major it is way out of my realm.
 
Mal H said:
Rob228 said:
Given the shape of most bullets I feel like Bernoulli has to come into effect at some point ...
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Not in a vacuum, which is one of the original stipulations.
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And being in a vacuum would also eliminate any aerodynamic lift effects. It would also mean no aerodynamic drag, so I hope the experiment has a very LOOOOOOOOOOOOOOONG test range ...
 
Right. I had started to stipulate that the bullets had to have a ballistic coefficient of infinity (in other words, zero drag) otherwise all bets are off. But, then I remembered that this (highly unlikely and almost impossible on earth) experiment was being carried out in a vacuum.
 
Dredging up fuzzy math from high school physics, v = at and d = at^2/2.

If d is 6 feet, and acceleration due to gravity is 32 feet/second/second, then the time for anything to drop 6 feet is the square root of 6/16, or .612 seconds.

If we assume a muzzle velocity of 3,000 feet-per-second with zero drag (in a vacuum), the time to drop times the velocity is .612 x 3000 = 1,836 feet. That's how far the projectile would travel if this experiment could be conducted in a vacuum, with the barrel and the ground perfectly flat and level.
 
they will hit the ground at the same time, as far as any human observer can tell.
Click to expand...

Yep. I've actually done the calcs on a test in Grad school exterior ballistics. The difference was on the order of 30 milliseconds for a .30-06 fired in STP atmospheric conditions. That is a number that was almost impossible to measure 100 years ago and still takes some pretty high end equipment today.
 
Mythbusters did it with a 1911 in 45ACp.
The difference was in milliseconds, which was well within the best accuracy of the equipment used.
 
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