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MMarroquin1024
2008-Oct-02, 05:36 AM
Is there anything on the web (Something like a Graph) that shows how you need infinite power (energy) to accelerate to the speed of light?
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Jens
2008-Oct-02, 05:50 AM
Is there anything on the web (Something like a Graph) that shows how you need infinite power (energy) to accelerate to the speed of light?
____

Obviously, the whole thing couldn't be displayed as a graph, because you can't show infinity. I'm guessing you're looking for a graph that shows how the curve changes, like how much energy you need to get to 0.5C and 0.9C and 0.99C, etc.?

tony873004
2008-Oct-02, 05:52 AM
You can make one yourself with Excel.
In cell A1, start with 1. A2=A1+1000. Drag this column down until it equals 300000, which is the speed of light in km/s.

In cell B1, put the gamma function: =1/SQRT(1-A1^2/(300000)^2)

Extend this column down by double clicking the square black box in the bottom right corner of cell B1.

Now graph column B. You'll notice that it starts out at 1, rises very slowly, and then explodes to infinity as you approach c.

timb
2008-Oct-02, 05:57 AM
Obvious homework problem.

John Mendenhall
2008-Oct-02, 05:03 PM
Obvious homework problem.

Well, OP? If so, the Excel reply should give you more than enough info.

Extra credit: Do it for the apparent mass also.

MMarroquin1024
2008-Oct-02, 07:56 PM
Obvious homework problem.

I'm not in school anymore, It was just out of curiosity. Thanks for the reply though.

MMarroquin1024
2008-Oct-02, 08:08 PM
You can make one yourself with Excel.
In cell A1, start with 1. A2=A1+1000. Drag this column down until it equals 300000, which is the speed of light in km/s.

In cell B1, put the gamma function: =1/SQRT(1-A1^2/(300000)^2)

Extend this column down by double clicking the square black box in the bottom right corner of cell B1.

Now graph column B. You'll notice that it starts out at 1, rises very slowly, and then explodes to infinity as you approach c.

I get #NUM! I guess that means ∞ or at least something of that nature...Wait, Is this the reason why astronomers use Newton's formulas instead of Einstein's?
Seeing as Einstein's formulas only become relevant as objects (bodies) get close to the speed of light.

MMarroquin1024
2008-Oct-02, 08:14 PM
Obviously, the whole thing couldn't be displayed as a graph, because you can't show infinity. I'm guessing you're looking for a graph that shows how the curve changes, like how much energy you need to get to 0.5C and 0.9C and 0.99C, etc.?

You're right! the whole thing can't be shown, but at least to 299000 Km/s it sort of makes sense, If you went to, let's say, 295000, the graph would look really weird. I believe 299000 km/s is enough to get the main idea.

Sam5
2008-Oct-02, 10:25 PM
Obviously, the whole thing couldn't be displayed as a graph, because you can't show infinity.

Oh sure we could. All we would need is an infinitely large computer monitor screen. :)

Cougar
2008-Oct-02, 10:36 PM
I believe 299000 km/s is enough to get the main idea.

Yeah. If you don't look too closely, it looks like a step function that stays on "1" until very close to 300000, then it jumps to infinity. :surprised

[ETA: Well, that's if you put in 999 into cell A1, so at 299,999 you get 387.2986574]

cjameshuff
2008-Oct-02, 11:42 PM
Relativistic kinetic energy:
E = m*c^2/sqrt(1 - v^2/c^2) - m*c^2
Newtonian kinetic energy:
E = 0.5*m*v^2

For comparing the two, the common parts can be divided out. Pull out mass and c^2:
E/m = c^2/sqrt(1 - v^2/c^2) - c^2
E/m = 0.5*v^2

E/m/c^2 = 1/sqrt(1 - v^2/c^2) - 1 = 1/sqrt(1 - (v/c)^2) - 1
E/m/c^2 = 0.5*v^2/c^2 = 0.5*(v/c)^2

Now graph with x = velocity as fraction of the speed of light: v/c:

E/m/c^2 = 1/sqrt(1 - x^2) - 1
E/m/c^2 = 0.5*x^2

Just plug:
1/sqrt(1 - x^2) - 1;
0.5*x^2;

into this web-based graphing calculator (or the equivalent into your favorite alternative):
http://www.walterzorn.com/grapher/grapher_e.htm

Use x minimum 0, maximum 1, y minimum 0, maximum from 0.5-50 gives a good idea of the difference between Newtonian and relativistic kinetic energy.

nauthiz
2008-Oct-03, 12:44 AM
Here, I graphed it and took a screenshot.

Red line is 0.5x2
Blue line is 0.5(sqrt(1-x2)) - 1

phunk
2008-Oct-03, 03:40 AM
I get #NUM! I guess that means ∞ or at least something of that nature...Wait, Is this the reason why astronomers use Newton's formulas instead of Einstein's?
Seeing as Einstein's formulas only become relevant as objects (bodies) get close to the speed of light.

Not just close to the speed of light. The orbit of mercury couldn't be properly explained until general relativity was applied.

MMarroquin1024
2008-Oct-03, 05:44 AM
Not just close to the speed of light. The orbit of mercury couldn't be properly explained until general relativity was applied.
So what's up with mercury that made it so complicated to explain with Newtonian Physics?

MMarroquin1024
2008-Oct-03, 05:47 AM
Here, I graphed it and took a screenshot.

Red line is 0.5x2
Blue line is 0.5(sqrt(1-x2)) - 1

Thanks, I did one on excel and it looked like this one. Thank so much. You know, we all understand things better when we see them on a graph rather than just seeing the numbers.

01101001
2008-Oct-03, 06:04 AM
So what's up with mercury that made it so complicated to explain with Newtonian Physics?

More mass close by.

Wikipedia: Tests of general relativity (http://en.wikipedia.org/wiki/Tests_of_general_relativity)

Careful observations of Mercury showed that the actual value of the precession disagreed with that calculated from Newton's theory by 43 seconds of arc per century. [...] Einstein showed that general relativity predicts exactly the observed amount of perihelion shift.
[...] All other planets experience perihelion shifts as well, but, since they are further away from the Sun and have lower speeds, their shifts are lower and harder to observe. For example, the perihelion shift of Earth's orbit due to general relativity effects is about 5 seconds of arc per century.

mugaliens
2008-Oct-03, 08:18 AM
Oh sure we could. All we would need is an infinitely large computer monitor screen. :)

And what might the area under the curve be?

timb
2008-Oct-11, 11:15 AM
I'm not in school anymore, It was just out of curiosity. Thanks for the reply though.

Sorry if I got the OP wrong. One time posters asking for a nice graph of X or formula for Y are often taken for students not wanting to do their own homework.

alainprice
2008-Oct-12, 11:12 PM
Is there anything on the web (Something like a Graph) that shows how you need infinite power (energy) to accelerate to the speed of light?
____