MC question (2 Viewers)

[ohexploitable]

But you're entirely disregarding the problem of mass dilation and how no matter how much fuel you have, if you are applying a force at a relativistic speed, it will be converted into mass, not kinetic energy, if the force is insufficient...

If an object is already travelling near 'c' and kinetic energy is added, most will be converted into mass but some into more kinetic energy in such a way that:

velocity will still mathematically increase asymptotically to c

 

[mirakon]

But you're entirely disregarding the problem of mass dilation and how no matter how much fuel you have, if you are applying a force at a relativistic speed, it will be converted into mass, not kinetic energy, if the force is insufficient...

*facepalm* ok quite clearly you're missing the point entirely. All your assumptions are based on the force being insufficient. Let me say it as simply as possible.

F=ma
if infinite fuel therefore there must be a continuous force and therefore continuous acceleration. Relativity is irrelvant at this point.

Now assuming relativity, you would agree that v cannot exceed c. However, this is due to mass dilation etc.

so for a function of v, it will be asymptotic to c, that is it will never reach it.

However, this does not mean that v cannot get infinitely close to c, that is there is no limit to how close it can get.

With continuous acceleration resulting from infinite fuel, v can get steadily closer and will never stop at a maximum speed. The line follows the asymptote forever.

Only if there was limited fuel would there be limited acceleration. Therefore A is the answer. Speed at which gases are ejected only impacts on the force if other variables such as time and therefore accelration are known, so B is incorrect.

 

[khfreakau]

F=ma
if infinite fuel therefore there must be a continuous force and therefore continuous acceleration. Relativity is irrelvant at this point.

Now assuming relativity, you would agree that v cannot exceed c. However, this is due to mass dilation etc.

so for a function of v, it will be asymptotic to c, that is it will never reach it.

However, this does not mean that v cannot get infinitely close to c, that is there is no limit to how close it can get.

With continuous acceleration resulting from infinite fuel, v can get steadily closer and will never stop at a maximum speed. The line follows the asymptote forever.

NO. If you were to do this, every single bit of acceleration would require an ever greater force due to the increased mass.

F=ma
If you are approaching c, then the mass is approaching infinity. In other words, F would either have to be VERY VERY VERY large or a would have to be VERY VERY VERY VERY small. Problem is, F is constant (in most cases anyway). If mass were to reach an indeterminate value, then it'd be hard to say F was constant anymore. Sigh.

I'm not assuming the force is insufficient, it IS insufficient. You're assuming that it IS sufficient. I can see where you're coming from, but I can't agree that that the velocity would steadily get closer to c and never stop if there isn't a greater force applied.

 

[ohexploitable]

NO. If you were to do this, every single bit of acceleration would require an ever greater force due to the increased mass.

F=ma
If you are approaching c, then the mass is approaching infinity. In other words, F would either have to be VERY VERY VERY large or a would have to be VERY VERY VERY VERY small. Problem is, F is constant (in most cases anyway). If mass were to reach an indeterminate value, then it'd be hard to say F was constant anymore. Sigh.

I'm not assuming the force is insufficient, it IS insufficient. You're assuming that it IS sufficient. I can see where you're coming from, but I can't agree that that the velocity would steadily get closer to c and never stop if there isn't a greater force applied.

Not B. If I was in a rocket where the propulsion system is me blowing air out of a straw, I would eventually get close to the speed of light if a) I had enough air (fuel supply) and b) if I could live that long lol.

If I were to continue blowing forever (infinite fuel), I would get closer and closer to the speed of light. Whilst the thrust generated per second in very low, if I were to blow continually for zillions of years the total force over that time is very large.

 

[khfreakau]

If I were to continue blowing forever (infinite fuel), I would get closer and closer to the speed of light. Whilst the thrust generated per second in very low, if I were to blow continually for zillions of years the total force over that time is very large.

So? You would reach a certain velocity and get stuck there because the force being applied is not enough to overcome the mass, and the thrust per second is being converted into mass, not kinetic energy.

 

[ohexploitable]

So? You would reach a certain velocity and get stuck there because the force being applied is not enough to overcome the mass, and the thrust per second is being converted into mass, not kinetic energy.

So... you're saying if there was a large mass in space suspended in a state of equilibrium and a tiny minuscule external net force is applied to it, the equilbrium wouldn't be disturbed at all?

 

[FCB]

Let me clear up the tension. Had khfreakau said that he put 'a' then i reckon at least one person in this thread (merely suggesting and not aiming at anyone) would have said it is dead obvious that it is 'b'
i'll be 100% upfront, i would have said 'b' and i understand why you lot would put 'a' but in an exam situation, i highly doubt that would be the case.

 

[khfreakau]

So... you're saying if there was a large mass in space suspended in a state of equilibrium and a tiny minuscule external net force is applied to it, the equilbrium wouldn't be disturbed at all?

No... if it was stationary it would obviously move off in another direction and if it wasn't stationary then depending on how fast the large mass is moving, there would be either an acceleration or increase in mass of the object.

 

[ohexploitable]

No... if it was stationary it would obviously move off in another direction and if it wasn't stationary then depending on how fast the large mass is moving, there would be either an acceleration or increase in mass of the object.

Refer to my previous post.

If an object is already travelling near 'c' and kinetic energy is added, most will be converted into mass but some into more kinetic energy in such a way that:

velocity will still mathematically increase asymptotically to c

 

[jamesfirst]

As far as I'm concerned. The thrust stays constant.

 

[hscishard]

I bet you all would agree d is incorrect. Lol
Too ambiguous but...
I would've picked a)
for c) and b) you could say that an infinite amount fuel is required to make it go faster forever. Though a fixed max speed is never really achieved as it can only approach c, and never be c. Think someone said that the force turns into purely mass and no kinetic energy, I don't think that's right because this can only happen when the mass has reached infinity and this can only happen when there is an infinite amount of fuel (not possible)
So a) I think would be correct

 

[MikeK]

No, only if there is an INFINITE FORCE being applied. Hence why I believe B is also a correct answer.

Incorrect. Any force will always increase your speed towards c regardless of your current velocity, but by smaller and smaller amounts. There isn't some sort of threshold at which you can't accelerate further, it just becomes less effective.

 

[MikeK]

without an increasing or constant acceleration (if a is not >= 0 ), velocity will not be increasing

Incorrect. Velocity will increase as long as a is positive.

Even if a is approaching zero, it will not actually equal zero until time equals infinity, or the fuel runs out. Even our ideal rocket must have a finite fuel supply, or the answer would be that all four cases reach c after an infinite amount of time and hence the answer would be none of them.

 

[mirakon]

NO. If you were to do this, every single bit of acceleration would require an ever greater force due to the increased mass.

F=ma
If you are approaching c, then the mass is approaching infinity. In other words, F would either have to be VERY VERY VERY large or a would have to be VERY VERY VERY VERY small. Problem is, F is constant (in most cases anyway). If mass were to reach an indeterminate value, then it'd be hard to say F was constant anymore. Sigh.

I'm not assuming the force is insufficient, it IS insufficient. You're assuming that it IS sufficient. I can see where you're coming from, but I can't agree that that the velocity would steadily get closer to c and never stop if there isn't a greater force applied.

which is the flaw ohexploitable and I have tried to make you understand. Regardless of how small a force is, it will have an effect. You are right in saaying the force is infinitesimal as it approaches the speed of light, but then by F=ma the acceleration is also small BUT STILL THERE. You can't just discount the effect of a force because ti is too small because scientifically it is still applying a net acceleration and therefore increasing the velocity, meaning there is no max velocity reached unless a force is not applied. so A is the answer because only limiting the fuel will limit the force.

 

[hscishard]

You are right in saaying the force is infinitesimal as it approaches the speed of light

Thrust is constant...? The effect the force has on the object/rocket/w/e will be infinitesimal.

Hmm now that I've read more of the thread, OP is confused with force on heavy masses. So long as the NET force is >0, the mass will accelerate (i.e. go faster). For this situation, we neglect gravity. I'm pretty sure you do because it's only a MC question (if we consider gravity, several problems arise anyway). So thrust is the only force, it will accelerate F=ma, F is constant (considering only thrust), m is huge, "a" is very small.
BTW you don't need to think of all this in the exam. You should've just thought of what I wrote before

 

[jyu]

Hey guys, this is a question from my half yearly where I disagree with the given answer, was wondering what you guys thought.

Ultimately, the factor limiting the maximum speed of a rocket is:
a) the amount of fuel it carries
b) the speed of ejection of the gases
c) the mass of the rocket
d) the length of the rocket

simple and easy to understand answer by considering energy:
more fuel, greater height reached, greater kinetic energy when the rocket falls back to earth, .: greater speed.

 

[Riproot]

If b was true, would c be true too?

 

[mattyr1]

the answer is A,, why do u think it is B

 

[khfreakau]

If b was true, would c be true too?

They accepted C in the end, so I don't see why they can't accept B as well -_-

Also after a bit of research, I have discovered a little formula which is quite nice. http://j.mp/keJnZL

 

[jamesfirst]

A and C is similar...

So both are technically correct. Why do you think B is the answer?