# Hi, engineers!

April 11, 2012

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Q) How big of an explosion would you get from having a grain of sand going the speed of light?

A) Nice! A question with some good math-y meat to it! In order to calculate this, we are going to have to make a few assumptions.

We will assume that your grain of sand is about 1.57 milligrams (which seems reasonable based on what I found on the Internet). Secondly, nothing can EVER, EVER go the speed of light, so we will instead assume more like 95% the speed of light (which is still 285,000,000 meters per second or 637,085,798 miles per hour).

Normally we could use our normal equation of Kinetic Energy = ½ * mass * velocity^2, but unfortunately this equation breaks down as objects start approaching the speed of light. You see, as you approach the speed of light your mass begins to increase, continuing to increase up to infinity as you approach the speed of light. This is one of the main reasons that it is impossible to go faster than the speed of light, because once you weight infinity it takes infinite additional power to make you go even the tiniest bit faster, so it is physically impossible to go any faster.

Anyway, back to the question: we will have to use the much less-used relativistic Kinetic Energy (K.E. from now on because I am lazy) equation to figure out how much force our grain of sand will have on impact. This equation is K.E. = mass * speed of light ^ 2 * (gamma-1). First thing you should notice is that everything except the gamma part is K.E. = mc^2. (Thanks Einstein!) This means that the energy you will be getting out of this object is almost the entirety of the energy that exists inside of the object, multiplied by some other number gamma. Gamma is defined as gamma= 1/ SquareRoot(1-(velocity/speed of light)^2). This is a little less friendly of an equation, but it helps us find out how much extra energy our grain of sand will get because of the mass increase due to the excessive speed. I will spare you the full calculations, but after solving for gamma and then K.E. we can see that the total Kinetic Energy of this little speedy death-bomb is 3 * 10^11 joules (for the non-math people out there this is a 3 with 11 zeroes after it). If we convert this to the much more awesome scale of equivalent Tons of TNT, we get 74.5 tons. This means that our tiny little grain of sand going 95% the speed of light will have as big of an explosion as a huge pile of 74.5 tons of TNT. To put that in perspective that is about 5 dump trucks full of TNT. If we increase our speed to 99.9% the speed of light (ludicrous speed), then it equals out to 722 tons of TNT.

Both of these, however, would be tiny on the scale of nuclear weapons, so we need to step it up to perhaps a golf ball(45.93 grams). If we can get this bundle of joy up to 99.9% of the speed of light, we get 21,108,987 tons of TNT (21 megatons). Now that is a good explosion!

This is much higher than a typical U.S. nuclear missile (which is usually only half of a megaton or less). The only bomb on earth larger than that was the Cold War era Tsar Bomba from Russia, which was 50 megatons. Because I don’t like being showed up by the Commies, lets go ahead and take that dump truck full of TNT from earlier (about 15 tons) and get it going at 99.9% the speed of light. This gives us an explosion of 4,741,873 Megatons or about 5 Teratons. This should be able to handle anybody you really want to get rid of (and their town, and their city, and their country, and around half of their continent).

The moral of the story is that if you see something going the speed of light, get out of the way! Of course, if there was an object passing by Pluto at 99% the speed of light, by the time the light from it got to us so we would see it coming, we would have about six minutes of warning to try to save the world. So, you know, sweet dreams!

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