General Physics Help - Questions on E=mc^2 & Train Mass at Light Speed

[LT72884]

Ello all, new to the forums here. I just did a quick google search and wound up here. Figured i could get some answers to some of me questions i have about physics. A lil history real fast bout me. I was working on a network engineering degree, but after hating the IT field so much and not enjoying it, i went with something that i have always enjoyed... science. I am finishing up my generals and then i will be going into Mechanical Engineering since i like physics and science.


Any way i have a question or two i would like to understand a bit more. I watched a nova special called Einsteins big idea. It explained somewhat about the E=mc^2. What i would like to know is this..

If light is the fastest thing we know of and nothing can go faster than light, why is it squared? You can't go faster than light so why square it?

second, if a train is moving at the speed of light and it can't go anywhere faster, and we keep pushing it to go faster, all that energy has to go somewhere, that somewhere is the trains mass. So does the mass of the train square? IE, train weighs 10 tons, when it can't go any faster than light and that energy is converted to mass, does the train become 100 tons?

thanx guys.

 

[mgb_phys]

If light is the fastest thing we know of and nothing can go faster than light, why is it squared? You can't go faster than light so why square it?

Check the units, they need to balance both sides of the equation.
One way to derive e=mc^2 is here http://www.adamauton.com/warp/emc2.html

second, if a train is moving at the speed of light and it can't go anywhere faster, and we keep pushing it to go faster, all that energy has to go somewhere, that somewhere is the trains mass

correct.

So does the mass of the train square? IE, train weighs 10 tons, when it can't go any faster than light and that energy is converted to mass, does the train become 100 tons?

The mass increases by 1 / sqrt( 1 - v^2/c^2)

So as your speed V gets nearer to c the term (1-v^2/c^2) get closer to zero, so 1/this get larger.
The train also gets shorter by this factor, and time slows down by the same amount.

 

[LT72884]

Check the units, they need to balance both sides of the equation.

Thanx for the links. I read over the paper but still have a question. Oh and who and how figured the equation for how much mass is gained?

I don't have any units to work with. haha.. I am not trying to solve something with that equation. I am just trying to figure out why the speed of light is squared. Since nothing can go faster than the speed of light, why do they square it? I mean, if the speed of light is 299 792 458 m / s, and nothing can go faster than that, if you square it you get 89875517873681764 m/s.. So if nothing can go faster than 299 792 458 m / s there is no need to square it.. that's where i am lost.

thanx

 

[NeoDevin]

If light is the fastest thing we know of and nothing can go faster than light, why is it squared? You can't go faster than light so why square it?

In this equation, you can think of $c^2$ as a conversion factor, to convert between units of mass and units of energy. Kind of like how you would multiply a distance in miles by a conversion factor to get a distance in kilometers.

second, if a train is moving at the speed of light and it can't go anywhere faster, and we keep pushing it to go faster, all that energy has to go somewhere, that somewhere is the trains mass. So does the mass of the train square? IE, train weighs 10 tons, when it can't go any faster than light and that energy is converted to mass, does the train become 100 tons?

One way to think of this is that as the train speeds up, it gains energy. By the equation $E = mc^2$, it gains mass as well. As it becomes more massive, it takes more energy to speed it up the next little bit. Because of this, you can never actually accelerate a massive object to the speed of light, because the closer you get to it, the more energy it takes to go faster. For a massive object to actually reach the speed of light would require infinite energy, since the mass increases unboundedly.

 

[LT72884]

Sorry for such a late reply. i was not ignorin you guys. haha. Just slammed with homework. Ok so squaring the speed of light is a conversion factor somehow. Please forgive me, its been a while since i have done conversions. we bit more explanation would be much appreciated.

My school of thought is that if i am running at 17 mph, somehow my mass is increasing. How does E=mc^2 work in our every day lives? what are some examples? Does a car or a person get heavier because they are moving faster? i hope that makes sense. ahaha

thanx guys

Matt

 

[NeoDevin]

My school of thought is that if i am running at 17 mph, somehow my mass is increasing. How does E=mc^2 work in our every day lives? what are some examples? Does a car or a person get heavier because they are moving faster? i hope that makes sense. ahaha

Yes, but the amount is so small that you won't ever notice it.

 

[Superstring]

Sorry for such a late reply. i was not ignorin you guys. haha. Just slammed with homework. Ok so squaring the speed of light is a conversion factor somehow. Please forgive me, its been a while since i have done conversions. we bit more explanation would be much appreciated.

It's simply the number you have to multiply by to balance the mass with the energy. The equation doesn't infer that something is moving at c².

For example, take an equation like F=ma. In order for the force and the mass to be balanced, the mass must be multiplied by an acceleration.

My school of thought is that if i am running at 17 mph, somehow my mass is increasing. How does E=mc^2 work in our every day lives? what are some examples?

GPS systems take into account time dilation.

Does a car or a person get heavier because they are moving faster? i hope that makes sense.

Yes they do increase in mass, but so slightly that it is completely negligible. Only at speeds close to c do you really see a significant change.

 

[LT72884]

It's simply the number you have to multiply by to balance the mass with the energy. The equation doesn't infer that something is moving at c².

For example, take an equation like F=ma. In order for the force and the mass to be balanced, the mass must be multiplied by an acceleration.



GPS systems take into account time dilation.



Yes they do increase in mass, but so slightly that it is completely negligible. Only at speeds close to c do you really see a significant change.

dude, if i could buy you dinner, i would... Thanx for the help. i have not takin math since 2002 and so my math is soooo bad right now its sad. I am still trying to decipher what you ment by saying, " to ballance force and mass you must multiply by acceleration." LOL. I am so embaresed. Haha. Thanx for being paitenet with me.

 

[mgb_phys]

When you move you get shorter (in the direction of travel), heavier and time goes more slowly.
All by the same factor sqrt(1 - v^2/c^2)

So if you go across the atlantic by 747 (10hours at 600mph)
Time goes slower by sqrt( 1 - 270^2/300E6^2) or about 1 part in 1E14
So you end up about 0.3ns younger!

 

[LT72884]

When you move you get shorter (in the direction of travel), heavier and time goes more slowly.
All by the same factor sqrt(1 - v^2/c^2)

So if you go across the atlantic by 747 (10hours at 600mph)
Time goes slower by sqrt( 1 - 270^2/300E6^2) or about 1 part in 1E14
So you end up about 0.3ns younger!

lol, i just read a paper on this literally 4 minutes ago. I just got off of work and saw it sitting on the table at home. So what's V messured in? it went from 600mph to 270? is that 270Km?

and is E6 mean the same as 10^6?

thanx guys with all the help.

 

[mgb_phys]

So what's V messured in? it went from 600mph to 270? is that 270Km?

Doesn't matter as long as its the same as c is measured in - because it's a ratio

270 is 270 m/s = roughly 600mph, I just happened to know this as the speed of a plane
and all scientists remember that c is 300,000,000 m/s 300x10^6m/s = 3E8m/s
I don't know what c is in mph (apparently it's 670 616 629 mph - a bit harder to memorize)

So, 270^2/3E8^2 = 600^2/670616629^2

and is E6 mean the same as 10^6

Yes, just easier to type