small question on space travel (1 Viewer)

[metalicarulez]

In terms of the energy required, accelerating a spacecraft to the speed of light is an impossibility. Explain why this is so

ok all i can think of this is... the cost involved

i don't know wot else to write coz im given 3-4 lines to answer

 

[Ragerunner]

Because your moving at the speed of light, mass will increase as a result of relativity.

As mass increases, the energy required by the spaceshuttle would need to increase in order to keep the shuttle moving as shown by einstein's famous equation E = MC^2

Which means an extreme amount of fuel is required that is impossible to get at this present time, which leads to the high costs involved.

 

[Constip8edSkunk]

consider the mass dilation function:

m_v = m_o / sqrt [ 1 - (v/c)^2 ]

as you can see, when v approaches c; the relativistic mass, 'm_v', approaches infinity. this would therefor require an energy input of infinty (E=mc^2), which is clearly impossible. Hence, one can never reach the velocity of c.

 

[:: ck ::]

wot ?! theres a mass dilation equation

or is that supposed to be time dilation?

edit : nvm found it
http://www.utdallas.edu/~parr/chm5414/54140903.html

is mass dilation in our syllabus?

 

[Xayma]

Originally posted by Ragerunner
Which means an extreme amount of fuel is required that is impossible to get at this present time, which leads to the high costs involved.

Actually its more then just an extreme amount of fuel, since as you travel faster you need more fuel which therefore requires a greater mass, which will never reach the speed of light because the mass of fuel will then become infinite. It will become asymptotic to that line though. Of course there are theories of a "warp bubble" star trek style idea.

 

[Xayma]

Originally posted by :: ryan.cck ::
is mass dilation in our syllabus?

Yeah it is in the same dot point as time dilation and length dilation.

 

[:: ck ::]

ohh so ur rite =)

damn its not even in jacaranda

 

[Xayma]

Originally posted by :: ryan.cck ::
ohh so ur rite =)

damn its not even in jacaranda

Well the formulas exactly the same as time dilation so the questions should be interchangable.

 

[Ragerunner]

And it's also in the formula sheet =)

 

[zeropoint]

Originally posted by Ragerunner
Because your moving at the speed of light, mass will increase as a result of relativity.

Not exactly. This notion of ``relativistic mass'' increasing with velocity was rejected by Einstein and subsequently by all modern physicists. The fictitious relativistic mass m<sub>r</sub> was first introduced so that one could write the equations of motion of relativistic particles in Newtonian form using f<sup>i</sup> = m<sub>r</sub>a<sup>i</sup> where m<sub>r</sub> increases with velocity and i runs values of 1,2,3. Later study found that m<sub>r</sub> was an absolutely useless quantity that plays no role in any physical equation. The correct form is F = dP<sup>u</sup>/dt<sub>0</sub> where P<sup>u</sup> = m<sub>0</sub>U<sup>u</sup> is the 4-momentum, U<sup>u</sup> = dx<sup>u</sup>/dt<sub>0</sub> is the 4-velocity, x<sup>u</sup> = (cx<sup>0</sup>, x<sup>1</sup>, x<sup>2</sup>, x<sup>3</sup>) is 4-position, m<sub>0</sub> is the ``invariant'' rest mass, d/dt₀ denotes the derivative with respect to proper time and u runs values of 0,1,2,3 with time being the 0th dimension. The relativistic analog of Newton's second law is thus F^u = m₀A^u, A^u = dU^u/dt₀ is the 4-acceleration. It can be seen from this derivation that ``relativistic mass'' varying with velocity is not the correct reason why accelerating a spacecraft to the speed of light is an impossibility. The correct explanation is that a given force produces a diminishing coordinate acceleration as the speed approaches c.

Edit: It occured to me that my previous explanation wasn't as clear as it could be, so I have revised it.

 

[Rahul]

when i called up the hsc advice line, and asked about mass dilation. they said you just need to know its effect.
in other words, the 'what' and not the 'why'...

 

[Ragerunner]

Originally posted by zeropoint
Not exactly. This notion of ``relativistic mass'' increasing with velocity was rejected by Einstein and subsequently by all modern physicists. The fictitious relativistic mass m<sub>r</sub> was first introduced so that one could write the equations of motion of relativistic particles in Newtonian form using F = m<sub>r</sub>a where m<sub>r</sub> increases with velocity. Later study found that m<sub>r</sub> was an absolutely useless quantity that plays no role in any physical equation. The correct form is F = dp/dt<sub>0</sub> where p = m<sub>0</sub>u is the 4-momentum, u = dx/dt<sub>0</sub> is the 4-velocity, x = (cx<sup>t</sup>, x<sup>x</sup>, x<sup>y</sup>, x<sup>z</sup>) is 4-position, m<sub>0</sub> is the ``invariant'' rest mass, and d/dt₀ denotes the derivative with respect to proper time. Therefore we may define F = m₀ d²x/dt₀², where F is the 4-force and d²x/dt₀² the 4-acceleration (second derivative of 4-position wrt proper time). Noting that dt/dt₀ = 1/(1− v²/c²)^1/2 (relativistic gamma) we obtain F = m₀d²x/dt² 1/(1− v²/c²). As such it would require an infinite force and thus infinite power to accelerate to the speed of light.

What the gay? I didn't understand that but oh well

 

[Xayma]

Originally posted by Ragerunner
What the gay? I didn't understand that but oh well

The mass of any object traveling at the speed of light is undefined because you are dividing by 0.

 

[Ragerunner]

But that is not required by the syllabus?

 

[...]

Originally posted by Xayma
The mass of any object traveling at the speed of light is undefined because you are dividing by 0.

in this case, its not undefined rather infinity

thats one rule of dividng by 0..either undefine or infinity

 

[Xayma]

Originally posted by ...
in this case, its not undefined rather infinity

thats one rule of dividng by 0..either undefine or infinity

It doesnt really matter since you arent going to reach it anyway. If you do limits it does approach infinity though.

Of course there is a way to avoid travelling at the speed of light and thats through wormholes etc. http://omnis.if.ufrj.br/~mbr/warp/ but this is outside the scope of the syllabus but interesting to know.

 

[zeropoint]

Please note however that relativistically increasing mass is not a real physical phenomena, merely a mathematical tool used to make certain equations of motion look more Newtonian. It is an entirely obsolete and useless quantity in light of the modern 4-space approach in which mass is invariant. The fact that relativistic mass is a mandatory part of the HSC syllabus indicates a deep-rooted problem with the physics department of the board of studies.

 

[Xayma]

Originally posted by zeropoint
Please note however that relativistically increasing mass is not a real physical phenomena, merely a mathematical tool used to make certain equations of motion look more Newtonian.

Then why cant we reacht he speed of light, if mass doesnt not increase to the point of infinity, then any continuous application of force will eventually bring the object to above the speed of light.

 

[...]

dunno if this is true

the mass is increased to infinity..hence u need infinite amount of energy to make the object reach the speed of light..hence u can never get to speed of light, or else :\

 

[Xayma]

Originally posted by ...
the mass is increased to infinity..hence u need infinite amount of energy to make the object reach the speed of light..hence u can never get to speed of light, or else :\

Why bother getting to the speed of light, just change the amount of space you have to cover.