You’re asking how you release that equivalent amount of energy, and thinking that you maybe have to have the pencil (or whatever) moving at the speed of light. But it doesn’t work like that. To accelerate a pencil to the speed of light would require an infinite amount of energy.
You’d release the equivalent energy of that pencil if you annhilated it with anti-matter having the same mass. Annihilated it with an anti-pencil of the same size.
as for the literal question you asked – people do such odd things with units all the time. How do you "divide’ a meter by one “second”. You do that all the time when you measure velocity. Sometimes these units combine in unexpected ways.
Don’t think of it as a meter divided by a second so much as a meter per second, if that helps. Every second, you go one meter.
If you’re still having trouble grasping the concept of multiplying and dividing units…well, I don’t know what to tell you. That’s how different physical qualities are related. Mass is kg, distance is m, time is s. A speed/velocity is meters per second, or m/s. A momentum is kilogram meters per seoond, or kg*m/2.
Maybe this will help:
The speed you’re walking is meters per second, or m/s.
The acceleration is going to be an increase (or decrease) in that speed (well, technically velocity, but that part’s not important right now.) That aceleration is a change in the speed. This acceleration is measured in meters per second, per second, or m/s/s. This can also be written as meters per second squared (if you don’t get why m/s/s is also m/s[sup]2[/sup], well…it’s a property of fractions, so go talk to a mathematician, :p)
Now, this still might not make sense, but think of it this way: when you speed up, you are increasing your meters per second. How do you measure this increase? Well, you say that every second, you will note how much the speed increases. So in other words, every second, you measure the increase in meters per second, so it comes out to meters per second per second…that first meters per second is the speed, and the other second is the unit of time you are measung that increase in, so it’s (speed increase) per second.
It can then also be written as m/s/s, or most commonly m/s[sup]2[/sup], which are the SI units of acceleration.
I think what’s frustrating the nerds here is that you do this kind of thing yourself every day. I guess most people just don’t think about it explicitly.
Examples:
miles/hour
dollars/doughnut
dollars/gallon
candies/dollar
kids/classroom
strings/guitar * guitars * dollars/string = dollars I need to spend on guitar strings.
On the literal face of it, none of these make much sense (“HOW are you dividing candies by dollars?”), but it’s the only way to get practical answers.
Remember that a meter or a kilogram aren’t physical things, they’re just arbitrary measurements. You can multiply a kilogram by a meter because they are just abstract concepts, you can do whatever you want with them. You can’t multiply a pencil by c[sup]2[/sup], but you can multiply the pencil’s mass in kilograms by c[sup]2[/sup]. The mass is just a number, expressed in units of our choosing based on convenience. The mass can be 1 kilogram, 0.7 pounds, 155 hoozawhatsits, 99.7 hoobajoobs, whatever. Typically, kilograms are used because the common unit for energy is expressed in kilograms times (meters per second) squared.
Why do these units together in that combination yield something we call energy? Well, it goes back to basic physics concepts you can find in any intro physics textbook, but this hijack has probably gone on far enough…
Or to try my “practical explanation method” that I try in physics class:
Your car will get up to 80 mph. Any car will. The difference is that a Camaro will do it in about 8 seconds, and your minivan will probably take 16. So the difference isn’t the speed, but the acceleration: the rate of change in speed.
So, the change in speed from 0 to 80 is the same, but the time taken will be different. If the time taken is smaller, then the acceleration is greater. So if I went from 0-80 in 8 seconds, my average acceleration is 10 miles/hoursecond. If you take 16 seconds, yours is 5 miles/hoursecond. My acceleration was faster than yours, but to show it, we needed to divide by the time it took to do it. When we divide by a smaller number (seconds) we get a bigger answer (acceleration). My answer is bigger than yours, in terms of acceleration.
If both times were measured in seconds, then we have s*s on the bottom of the fraction, which is s^2.
Oh, I had another thought about your objection to dividing by another unit.
Don’t think of it as dividing by this other unit, but as rating one in terms of another. You don’t usually think of dividing your dollars by a gallon of gas, but everyone rates a gallon of gas in dollars. The one that you want to emphasize is on the bottom of the fraction: the one that is a constant. The size of a gallon of gas doesn’t change, so I put the variable dollars on top. At least most people like it that way.
To keep it simple, we’ll use a mass of one gram. In keeping with the basic metric theme, we’ll calculate c in terms of meters per second: 299,792,458. C2 therefore is 89,875,517,873,681,764. We multiply this by our mass of 1 gram and find that E = 89,875,517,873,681,764 units. Now is the unit in question a gram/meter2/second2? In other words the amount of energy acting on a mass of one gram which is being accelerated at a speed of one meter per second in a time of one second over a distance of one meter (ie one thousandth of a joule).
So the energy equivalent of a mass of one gram is 89,875,517,873,681.764 joules?
Assuming you’ve done the calculator punching right, it seems so. You’re right to notice that using grams means you have to move the decimal smaller by three places, as you’ve been using grams instead of kg.
Interesting, because I was told “on the internet” that the Hiroshima bomb destroyed about a gram of uranium, but wiki says the yield was 6.3 E13 Joules, which is off “one gram” by over 10x, the official estimate being smaller. Curse you, internet!!!
In any case, it means that if you could totally destroy a paper clip over New York, pretty much the whole place would be burned or blown over. There’s a lot of energy in matter. It’s a conundrum, a mystery, and a weird duck.
Found an online energy converter. Rounding my figure off to 89,875,518 megajoules, I convert this into 24,965,422 kilowatt hours. So I have enough energy to run a 100 watt lightbulb for 10,402,259 days. Which is the approximate equivalent of running 285 such bulbs for a century.
After having spent four years in the OTC, due to transfer to a proper TA unit as a Potential Officer, I’ve given lots of order for various encounters - including detailed map briefs.
Get me on the spot, however, and tell me that something is east or west and I have to roll my eyes back a bit, put my hand out in front of me and recite “Never Eat Shredded Wheat” to work out that West is left and East is right. I almost know it instinctively, and know that I live in the West-End of my City so can figure it out, but it’s always fastest and easiest if I do the stupid rhyme.
Think it might come and bite me in the ass when I go for commission - sure way to lose peoples’ confidence in my abilities, I think!
I don’t know how electricity works. I mean, I got an A in physics A level, and I can tell you what will happen if you connect up such-and-such a circuit, and know that Power equals Ivy Watts and all that stuff, but … how does it actually work?
I mean, the electricity comes into my house from the power station, and it goes out of my house to the power station again, as it’s a complete circuit, and it does useful stuff in my house, but how? There’s not “less” electricity flowing out of the house than there is flowing in, is there? And in any case, it’s AC, so the electricity is actually flowing into my house then out of my house in the same direction and back again, 50 times a second. How the hell does it do anything useful?
Thank me only if I got it right. Bouv was saying that’s not the way the equation works. Which I don’t understand because I though all equations worked the same.
Oh, here’s something. I wasn’t aware that condoms apparently have a proper inside and outside. Honestly, besides lubrication and spermicide, I’m not quite sure what it matters, nor do I know how to tell right from wrong.