Correct my Paper

When I was in 9th grade, we had an assigned problem set from our book to do. We were doing problems with physics, and we had one question about kinetic energy. Without giving us any numbers, the book asked us "Which has more kinetic energy, a battleship moving at full speed or a bullet being fired?" Aside from the semantic arguments you could make about the bullet not moving since it was 'being' fired, it is an interesting question. It was supposed to make you think about how velocity is squared in the kinetic energy equation ( KE = (m * V²)/2 ) and thus if two things have the same product of mass and velocity the one moving faster will have greater kinetic energy. However, I thought about this, and though the bullet is moving much faster, it is exceedingly lighter. I think the publisher didn't realize just how much a battleship weighs. So, I put down the battleship, knowing that the gross displacement of the USS Missouri is over 50,000 tons. I got my paper back, and found that it was marked wrong. I looked it over, then talked to the teacher. She showed me the answer in the book, and sure enough, it said that since the bullet was moving faster, it had greater kinetic energy despite its lower weight. I argued for a minute, but then gave up, as my teacher was only as smart as the book. This was before the heyday of the internet, so I didn't have ready access to the facts and figures necessary to calculate this sort of thing. This was just a gut feeling I had, that the Missouri at top speed had more kinetic energy than a bullet.

Today, I do have internet access. This question arose in my head this afternoon and I decided to put a 12 year old question to rest.

First, since we are assuming the use of the USS Missouri, an Iowa class battleship (the largest of the US fleet), we must assume that we are talking about a rifle bullet, not some wimpy handgun round. We will further assume that we're not talking about some light and slow subsonic .22LR round, but rather about a rifle with some punch, the .308 Winchester round. Further, we will also compare to the most powerful commercial round on the market, the .50 BMG.

First, we take a look at the kinetic energy of the .308 Winchester round. The bullet weights vary from 110 grains to 190 grains for the most part. The muzzle velocity on these is 3100 ft/s and 2395 ft/s, respectively. Converting to SI units and keeping in mind significant figures, we come up with a kinetic energy of 3170 J for the 110 grain bullet and 3197 J for the 190 grain bullet. Already, the velocity conception of the book's problem is falling flat, as the weight difference between bullets is outweighing the velocity.

Second, we look at the .50 BMG. This is a little more exciting. With a bullet weight of about 662 grains and a velocity of 2912 ft/s, we come up with 16,954 J of kinetic energy at the muzzle. I was impressed by this.

Then I went to www.ussmissouri.com and looked up the ship's details. It can do about 35 knots (highest declassified speed--it could probably do 37 or 40 knots) when fully loaded. Since we're comparing to the .50 BMG, we'll assume the ship is fully loaded. The ship, fully loaded, weighs 53,000,000 kg. Yes, that's right, fifty-three million kilos. Right here I was already thinking that we're orders of magnitude above the bullets, but I kept going anyway. After converting to proper units and calculating the kinetic energy, it comes out to 8,586,000,000 J. Eight point six billion joules. No shit. Hmm. Let's see... the physical science book I studied from was only wrong by five orders of magnitude.

If someone asked you where your house was, and you told them "On the moon", even at its apogee (farthest distance) from Earth, you would still be correct according to my 9th grade physical science book. I think I deserve a point back for that one.