small question on space travel (1 Viewer)

metalicarulez

New Member
Joined
Dec 9, 2003
Messages
9
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 :(
 
Last edited:

Ragerunner

Your friendly HSC guide
Joined
Apr 12, 2003
Messages
5,472
Location
UNSW
Gender
Male
HSC
2003
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

Joga Bonito
Joined
Apr 15, 2003
Messages
2,397
Location
Maroubra
Gender
Male
HSC
2003
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.
 

Xayma

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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 ::

Actuarial Boy
Joined
Jan 1, 2003
Messages
2,414
Gender
Male
HSC
2004
ohh so ur rite =)

damn its not even in jacaranda :(
 

Xayma

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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.
 

zeropoint

Member
Joined
Dec 10, 2003
Messages
243
Location
Sydney
Gender
Male
HSC
2004
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/dt<sub>0</sub> 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<sup>u</sup> = m<sub>0</sub>A<sup>u</sup>, A<sup>u</sup> = dU<sup>u</sup>/dt<sub>0</sub> 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.
 
Last edited:

Rahul

Dead Member
Joined
Dec 14, 2002
Messages
3,647
Location
shadowy shadows
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

Your friendly HSC guide
Joined
Apr 12, 2003
Messages
5,472
Location
UNSW
Gender
Male
HSC
2003
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/dt<sub>0</sub> denotes the derivative with respect to proper time. Therefore we may define F = m<sub>0</sub> d<sup>2</sup>x/dt<sub>0</sub><sup>2</sup>, where F is the 4-force and d<sup>2</sup>x/dt<sub>0</sub><sup>2</sup> the 4-acceleration (second derivative of 4-position wrt proper time). Noting that dt/dt<sub>0</sub> = 1/(1− v<sup>2</sup>/c<sup>2</sup>)<sup>1/2</sup> (relativistic gamma) we obtain F = m<sub>0</sub>d<sup>2</sup>x/dt<sup>2</sup> 1/(1− v<sup>2</sup>/c<sup>2</sup>). 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 :D
 

Xayma

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
Originally posted by Ragerunner
What the gay? I didn't understand that but oh well :D
The mass of any object traveling at the speed of light is undefined because you are dividing by 0.
 

...

^___^
Joined
May 21, 2003
Messages
7,723
Location
somewhere inside E6A
Gender
Male
HSC
1998
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

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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.
 
Last edited:

zeropoint

Member
Joined
Dec 10, 2003
Messages
243
Location
Sydney
Gender
Male
HSC
2004
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

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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.
 

...

^___^
Joined
May 21, 2003
Messages
7,723
Location
somewhere inside E6A
Gender
Male
HSC
1998
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

Lacking creativity
Joined
Sep 6, 2003
Messages
5,953
Gender
Undisclosed
HSC
N/A
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.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top