Math Help

[TheDarkestOfAngels]

Hello everyone. I've been busy at work on a writing project and I've run into a bit of a snag.
I've been having a difficult time finding the right equation to describe a physics problem of mine.
This problem is exasperating because as far as math goes, I'm still much of a layperson with a lot of schooling yet to do on the subject. So.. here goes:

I need to find out the amount of energy required to accelerate an object.
Specifically, something to the tick of about 5 billion kilogram object to about a ten gravity acceleration to the tick of about 100 meters/second in a vacuum.

I've also had a difficult time researching magnetism. I can easily find information on things that are magnetic, but I'm interested in finding out the effects of extremely powerful magnetic fields on a patch of space-time. Also, I would like to know how much energy it takes to generate a magnetic field - especially powerful ones.
For example, if there's some correlation to energy imput to a ferromagnetic item (such as iron or nickel) or any item to the magnetic output in teslas.
Specifically, I'm trying to find out how much energy I would generally need to generate a magnetic field of about 800 petateslas or even something significantly weaker, like a Magnetar.

Anything you can tell me on either of these things would be greatly appreciated.

[Autumnlicious]

If one could divert an amount of energy completely to kinetic, then it is just .5 m v^2. The integral of energy over time must be equal to that energy. So in essence, it does not matter if I throw a ball as fast as I can or as slow as I can with respect to energy.

Look on wikipedia for the following: Electromagnetism, Inductors, Voltage, Current, Magnetic fields, Induced Emf, magnetic permittivity.

Energy is a term used to describe work - however it is affected, differs.

[TheDarkestOfAngels]

I believe I may have found my answer to my first issue. I now almost feel silly for asking it, because from the look of it, I learned this in middle school. It's amazing all the stuff I've forgotten over the years.
Like Newton's Second Law:

f = ma or force equals mass times the acceleration of the object

So my massive object (a space ship) would be somewhere between 2 and 2.25 billion kilograms depending on how much stuff is in it - including its nearly one million kilograms of compressed fuel.
Assuming 2.2 billion kilograms, it would be (converted to grams)

2,200,000,000,000 grams x 100 meters per second = 220,000,000,000,000 newtons of force

So, I believe this means that a constant influx of 220 trillion newtons of force is required to keep an object at an acceleration of 100 m/s. If I'm not mistaken, this also means that 220 trillion joules of energy is required to fuel this amount of force per second of acceleration.

Am I getting this right? Because it feels like I'm missing something, particularly in the newtons to joules conversion.

(Then again, I do tend to overcomplicate sometimes amazingly simple math).

In regards to magnetism, I've looked up a lot of the sources you've recommended, but I'm having difficulty understanding the material and what a lot of the math involved represents. I suppose it means perhaps there are dynamics to the problem that I'm unaware of, but now I'm not even sure what I'm looking for. Wikipedia isn't helping at all - it doesn't appear to explain what all the jargon actually means. It seems to just throw informaiton at me and I'm having trouble deciphering a lot of it into something I can use.

[Tiberius]

You are slightly wrong in your calculation. The standard measurement for mass is the kilogram, so if you convert to grams you will have to divide the answer by 1000.

The easiest way for you (since you are starting out with kilograms) is just to use them, so the calculation becomes:

2,200,000,000 kg x 100 m/s2 = 220,000,000,000 N

Or 220 billion Newtons.

You also used the wrong measurement for acceleration. Remember, velocity is measured in m/s (metres per second); acceleration is measured in m/s2 (metres per second squared).

For the second part, Joules is a measurement of work done by a force over a specific distance. It is therefore calculated by multiplying the force by the distance traveled.

So you first need to know the distance your spaceship needs to travel (in metres) and then multiply that value by 220 billion Newtons to get the correct amount in Joules.

[TheDarkestOfAngels]

So you first need to know the distance your spaceship needs to travel (in metres) and then multiply that value by 220 billion Newtons to get the correct amount in Joules.

That's another thing I keep having trouble with that's gotten a great deal of my data wrong in the past. I keep forgetting to convert a number on one order of power in the SI scale for another. Thanks, this actually changes a number of measurements I needed to have. Turns out my ship apparently doesn't need to generate nearly as much power as I thought it did.

Full disclosure:
My story is about the first faster-than-light travel to a nearby solar system - Epsilon Eridani in this case. Other than breaking the 'light barrier' I'm trying to keep everything as Kosher with actual science as possible. No resolving overheating by letting in the "space air" or anything like that.

So I figure this ship can easily generate enough power (10 fusion generators and a matter-anti-matter reactor) as most of the ship's mass is dedicated to power generation, thrust, and it's enormously powerful magnetic field - which protects the ship and bends space/time around the ship enough to allow the ship go faster than light (essentially a modified alcubierre drive that manages to stifle the mass-increase that going relativistic speeds would bring, essentially raising the light speed limit over a local area).

So, given the above and a few other calculations I've already done, I've figured out that a 100 meters/second acceleration would only need to be done for 52 days and 2 hours over 1,012,500,000 kilometers exactly four times for a round trip between acceleration and deceleration with almost no adjustment needed for the journey when it's just cruising near it's maximum speed of 450,000 km/second (92% speed of light, locally.)

In any case, I only really needed to know how much energy per second I need, which I think is already done for me since the 220 billion joules is per second (since it's figured in kilometers/second) so I could understand how much power the ship needs to generate per second so I can start assigning numbers to the power generators, which is why I'm still working to solve my other problem of the magnetic field.

I'm reasonably certain that a magnetic field as powerful as the one I'm using in the story is going to consume at least as much energy as the engines assuming that a human-made device could even withstand the forces necessary to maintain a field strength of 800 petateslas continuously for a 14~15 year round trip space flight @ 1.5c.

Interestingly, when I assumed the ship needed to generate 220 trillion joules of power, the ship actually needed far less fuel than I anticipated by several orders of magntitude. So... good on me and a neat prospect for human space travel in the future, assuming we can get off our asses and perfect fusion and later matter/antimatter generators.

EDIT: Well, I multiplied the distance by the 220 billion joules and divided the result by the amount of time in seconds it takes to cross that distance to get the joules requirement every second: 49,500,000,000,000.000000000000000003 joules/second.