Question about bullet energy

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herbloob

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I was reading and noticed someone said

"In order to equal the impact of a 9mm bullet at its muzzle velocity, a one pound weight must be dropped from a height of 5.96 feet, achieving a velocity of 19.6 fps. To equal the impact of a .45ACP bullet, the one pound weight needs a velocity of 27.1 fps and must be dropped from a height of 11.4 feet." (source)

I'm not sure i'm understanding this right because I did the math and one pound moving a 19.6 fps only equals 5.96 ft lbs and a 9mm hits with at minimum 300 ft lbs. Can someone explain this? It seems to come from a pretty legitimate source and I've heard a doctor quote it, am I misunderstanding something? Thanks!
 
The comparison seems to be about momentums (mass*velocity), not energies. I did the math too, 19.6 lbs*ft/s and 27.1 lbs*ft/s are quite typical momentums of 9mm and 45ACP bullets.
 
I'm a little out of my depth here, but the classic kinetic energy formula (mv^2)/2 does not yield foot-pounds. The units will be in pounds-(feet-per-second)squared.

I've found two on-line calculators that will handle the unit conversions:

http://www.1728.org/energy.htm

and

http://www.reloadammo.com/footpound2.htm

Both yield an answer of SIX foot-pounds for a one-pound weight at 19.6 ft/sec.

So I think everybody is confused, including myself.
 
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I think I'd just as soon get shot with a 9mm as get hit with a 1 pound weight going 95 miles an hour!

That right there would leave a mark!

rc
 
Now I want a one-pound lead rod with a 9mm diameter that I can drop into ballistic gel from 300 feet up.
 
Hi All,

Don't confuse weight and mass. K.E. does not = 1/2 w * v^2. The English unit of mass is the slug. The pound is the unit of weight.

The formula K.E. =1/2*m*v^2 does yield a unit of ft.-lbs. if the English system is used.

At first glance it looks like it should yield lb*ft^2/s^2 but remember that we need to use mass, m, not weight, w. Weight is the force of gravity pulling on a mass. F = m * g where g is the local acceleration due to gravity, in ft/s^2 in English units. Rearranging the equation we have m = F/g. Now substitute F/g, in lb/(ft/s^2) into the K.E. formula.

K.E. = 1/2 * lb/(ft/s^2) * ft^2/s^2. The lb. is left alone, the "single" ft cancels one of the "squared" ft and the two s^2 's cancel leaving K.E. to be measured in lb * ft which we customarily write as ft-lbs.

Dan
 
Dan,

You clearly are much less confused about this than I am.

Can you explain why the on-line calculators are coming up with 6 ft/pounds when our own math comes up with 192?
 
Yes, I can explain.

The calculations yielding 192 ft-lbs. used 1 lb. as the mass. That is incorrect. The mass is 1/32.2 (that is m=F/g; F is the force of gravity pulling on the object, in this case 1 lb.; g is the acceleration due to gravity, 32.2 ft/s^2 at the Earth's surface).

1/32.2 = 0.031.

K.E. = 1/2 *0.031 *19.6 *19.6 = 5.96 ft.-lbs..

Weight and mass are very easy to confuse and that is what happened in the incorrect calculations.

Dan
 
dan the farmer,

that is some highpowered ciphering for a farmer, you musta had some learning ta the university??? I hadn't been around no farmers could cipher near as good as that!!

Bull
 
I think I'd just as soon get shot with a 9mm as get hit with a 1 pound weight going 95 miles an hour!
Click to expand...

One of these things is quite deadly, the other is about .355 inches in diameter :D

Barring headshots, of course.....
 
DanTheFarmer you are absolutely correct, it *is* an easy mistake, as I have just demonstrated...although my excuse is that I am old and didn't have my coffee yet when I typed that :)

The easy way to sanity check this particular example, without fretting over conversion to slugs, is to recognize that the kinetic energy at the ground = the potential energy at the top, which equals the work required to move the mass from ground to 5.96 ft:

W=F*d=1lb*5.96ft = 5.96 ft-lb
 
Yes, I can explain.

The calculations yielding 192 ft-lbs. used 1 lb. as the mass. That is incorrect. The mass is 1/32.2 (that is m=F/g; F is the force of gravity pulling on the object, in this case 1 lb.; g is the acceleration due to gravity, 32.2 ft/s^2 at the Earth's surface).

1/32.2 = 0.031.

K.E. = 1/2 *0.031 *19.6 *19.6 = 5.96 ft.-lbs..

Weight and mass are very easy to confuse and that is what happened in the incorrect calculations.

Dan
Click to expand...

<Best Foghorn Leghorn voice>
I, I say, son, what DO you farm?


:)

Larry
 
Energy is relevant in highpower rifle rounds where energy levels above 1200 ft-lbs produce permanent cavitation and hydrostatic shock.

Self defense handgun calibers do not produce enough energy for either of those things to happen. So, for handgun calibers, look for what penetrates the most with the largest hole. They work by tearing up tissue and causing blood loss.

Energy is relevant for highpower rifle rounds. Energy is irrelevant for self-defense handgun rounds.
 
Energy, momentum, and force are all just different faces of the same thing. If you know how one of them unfolds in time, you know them all.

Force is mass x acceleration, and acceleration is the rate of change of velocity, so force = m x rate of change of acceleration.

If you perform an integration on force, it becomes momentum, m x v.

If you perform an integration on m x v, it becomes .5 x m x v^2, which is kinetic energy.

So statements like, "It's momentum that matters, not kinetic energy" fail to take into account that these things are intimately connected, and you don't have just one or the other.

Momentum is one particularly useful way to look at things because momentum is conserved. Force and kinetic energy are not.
 
While it is important to separate force from "amount of substance", calling one "mass" and another "weight" is a modern pedegogical invention. It is ahistorical and those who do not observe it are not "wrong".

The English words weigh and weight are about 700 years old. People have been comparing "masses" on a balance for over 3000 years and calling it weight or the equivilent word at the time. The spring scale measuring force "weight" directly was only invented about 240 years ago.. Bow draw force has been called weight for at least 500 years.

Mike

PS. A lot of people know the recent history of "Ms." and "gay" but few people know that the word flammable (meaning inflammable) was made up in the 1920s and promoted by the National Fire Protection Association or that the word "niacin" for the vitamin nicotinic acid was made up to disguise the chemical relationship to nicotine.
 
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arizona mike said:
While it is important to separate force from "amount of substance", calling one "mass" and another "weight" is a modern pedegogical invention. It is ahistorical and those who do not observe it are not "wrong".
Click to expand...

Nope, the ones who do not observe it ARE wrong.

Newton's Second Law (F=MA, Force = Mass x Acceleration) has been around since about 1687. People who don't know the difference are just as wrong as people who think that the earth is flat.

Luckily for most people it won't make any difference.

You can easily see just how "wrong" they are by the results on this thread of people trying to plug weight into the basic kinetic energy formula which requires mass for the correct computation.

Try to do about any kind of engineering without distinguishing between weight and mass and you'll quickly discover just how wrong you are when the new car airbags you designed don't work, or your satellite doesn't make it to orbit, or the spaceship you're trying to land on Mars either misses the planet completely or crashes into the surface at about a zillion miles per hour.
 
45_auto said:
Nope, the ones who do not observe it ARE wrong.
Click to expand...
Of course you are wrong if you ignore the difference between inertia and gravitational force. I made that point at the beginning of my post. My point is that it is not necessary to enforce a false dichotomy between two English words which is a recent invention to do so. A strict linguistic separation appeared in the latter half of the 20th Century. Mass in that sense did not appear in writing at all until 1704, so Newton didn't need to observe it either.

Mutationem motus proportionalem esse
vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur

A change in motion is proportional to the motive force impressed and takes place along the
straight line in which that force is impressed.
Click to expand...

Mike
 
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