HSC Physics Space Questions! (1 Viewer)

[x.Exhaust.x]

1. With developing technologies, human have been able to travel at ever increasing speeds. This has led many to believe that there is now a greater potential to travel greater distances in the universe.

a) Propose the restrictions that Einstein's theory of relativity has imposed on space travel.
b) Evaluate potential benefits that Einstein's theory of relativity have had on space travel.

2. The average life span in Australia is about 70 years. Does this mean it is impossible for an average person to travel at a distance greater than 70 light years away from the Earth? (Note that a light year is the distance light travels in a year). Explain your answer (Assume that the person will live to the age of 70).

Lol I can only think of stupid things for this e.g. the guy will run out of food, GG. Or time will be dilated (increased) in the travellers reference point compared to an observer on Earth, and so it is possible for the average person to travel 70 light years due to this increase in time (he ages less). What do you guys think?

3. Describe one method that could be used to investigate the effects of relativity.

The relativity of simultaneity experiment? The train one?

4. Draw a graph of energy vs. velocity, for the non relativistic case (KE=1/2mv^2) and the relativistic case (KE=mvc^2-m0c^2, where m0c^2 is the rest energy). Explain why the non relativistic case doesnot hold for large velocities.

And finally, a calculation:

5. Alan is on a spacecraft travelling at 0.600c that is flying past Betty who is on Earth (as usual). at the instant he passes her they both start timers.

a) When Betty measures that Alan has moved 9.00x10^7m what does Alan's timer read?

tv=t0/sqrt.(1-v^2/c^2).
tv=9.00x10^7/sqrt.(1-(0.600)^2)
tv=112,500,000

I don't think the above is right...If it is, what would be the units?

b) At that instant when Alan reads 0.400s on his timer, what does Betty read on timer?

tv=t0/sqrt.(1-v^2/c^2)
t0=tv.sqrt.(1-v^2/c^2) <- Rearranged
t0=0.400.sqrt.(1-(0.600)^2)
t0=0.32

Same as above.

Tee why ^^.

 

[Aerath]

Units would be in seconds wouldn't it?

 

[Lucid Scintilla]

I'm not entirely sure what the premise of this thread was, but ... are you expecting someone to answer your questions - quite possibly doing your working, without at least explaining?

Edit: never mind.

1. With developing technologies, human have been able to travel at ever increasing speeds. This has led many to believe that there is now a greater potential to travel greater distances in the universe.

a) Propose the restrictions that Einstein's theory of relativity has imposed on space travel.
b) Evaluate potential benefits that Einstein's theory of relativity have had on space travel.

a&b) Mass increase shows that as speed increases towards c, mass increases up to 'infinity'. What this means, is that as a spacecraft gets faster, its mass will increase and its acceleration will progressively decreases.

While acceleration will never become 0, because mass increases and approaches infinity, and F=ma (Newton's second law of motion), a spacecraft will never travel at the speed of light.

This is a limitation (energy limitation) as to how much such a technology that humanity has created can travel.

Einstein's ToSR, however, has beneficial applications, namely in time dilation and length contraction. Astronauts will age slower, and the distance to objects ahead of it decreases, allowing for more 'coverage' of space.

2. The average life span in Australia is about 70 years. Does this mean it is impossible for an average person to travel at a distance greater than 70 light years away from the Earth? (Note that a light year is the distance light travels in a year). Explain your answer (Assume that the person will live to the age of 70).

Lol I can only think of stupid things for this e.g. the guy will run out of food, GG. Or time will be dilated (increased) in the travellers reference point compared to an observer on Earth, and so it is possible for the average person to travel 70 light years due to this increase in time (he ages less). What do you guys think?

My bad in not answering you straight-up.

What's the frame of reference, who is moving, and what are the effects of special relativity here?

Spoiler

Ans: No; it isn't impossible.
1. Time dilates for person, and thus he ages less.
2. Further, distance decreases, due to length contraction.

3. Describe one method that could be used to investigate the effects of relativity.

The relativity of simultaneity experiment? The train one?

Think difference in time displayed on atomic clocks, the dilated lifespan of muons, etc.

(Einstein's gedanken regarding the simultaneity observed by a person on a train, and another outside of it, led to the posulates and statement of relativity.)

4. Draw a graph of energy vs. velocity, for the non relativistic case (KE=1/2mv^2) and the relativistic case (KE=mvc^2-m0c^2, where m0c^2 is the rest energy). Explain why the non relativistic case doesnot hold for large velocities.

Violates law of conservation of energy.

And finally, a calculation:

5. Alan is on a spacecraft travelling at 0.600c that is flying past Betty who is on Earth (as usual). at the instant he passes her they both start timers.

a) When Betty measures that Alan has moved 9.00x10^7m what does Alan's timer read?

tv=t0/sqrt.(1-v^2/c^2).
tv=9.00x10^7/sqrt.(1-(0.600)^2)
tv=112,500,000

I don't think the above is right...If it is, what would be the units?

It is/should be (by inspection).

Meters.

b) At that instant when Alan reads 0.400s on his timer, what does Betty read on timer?

tv=t0/sqrt.(1-v^2/c^2)
t0=tv.sqrt.(1-v^2/c^2) <- Rearranged
t0=0.400.sqrt.(1-(0.600)^2)
t0=0.32

Same as above.

Tee why ^^.

Moving clocks appear to run slow; Alan is moving here.
Shouldn't Alan have the lesser time? (Yes.)

Units would be in seconds wouldn't it?

Answers should be in SI units, unless otherwise specified.

Oh, I've re-read; Aerath, re-read, too.
My answers are meters and seconds.

Exhaust, check the bold, please. Timers, AFAIK, don't measure distance.

 

[x.Exhaust.x]

I'm not entirely sure what the premise of this thread was, but ... are you expecting someone to answer your questions - quite possibly doing your working, without at least explaining?

Edit: never mind.

Ah! I apologise if I sound lazy and want someone to do my work for me. But I'm struggling with the relativity of simulataneity and the questions of time dilation, length contraction, mass contraction .

But thanks for the detailed help Lucid! Much appreciated.

 

[cutemouse]

(From the other thread...)

I apologise if I sound lazy and want someone to do my work for me. But I'm struggling with the relativity of simulataneity and the questions of time dilation, length contraction, mass contraction

I question the validity and the truth of that statement. Maybe you do want others to do your work for you?

IOW: Don't comment on stuff you have no clue about especially when you can't even get the (IMO) simple concept of special relativity under your belt!

Ladies and Gentlemen, we have the case of the pot calling the kettle black here.

 

[x.Exhaust.x]

(From the other thread...)

I question the validity and the truth of that statement. Maybe you do want others to do your work for you?

IOW: Don't comment on stuff you have no clue about especially when you can't even get the (IMO) simple concept of special relativity under your belt!

Ladies and Gentlemen, we have the case of the pot calling the kettle black here.

Firstly, this is a HSC forum where others help people who are struggling within a certain topic or subject. You have a shit argument placed above. So please, stfu and gtfo, kthxbai.

And lol, so you decide to come into my thread and backfire at me since you were clearly wrong .

Note that this stuff isn't examined much so I personally wouldn't worry about it.

It isn't examined much? Source?
And you're a HSC 2009 student man. I question the validity of your post

So I had a fair statement of implying that cube roots of unity may be in the exam, for the sake of others (if they don't revise through the concepts). I don't want them to be mislead by a BOS'er who clearly hasn't completed the HSC for 4U mathematics. Don't be vague.

Alright then, why don't you go through 30 trial papers (from various years) and other HSC papers, like I did, and count how many times they've asked you to prove expressions using these results.

Fair argument, but look below towards your reply (from past 4U students):

Roots of unity are actually not that uncommon.
p.s i did my maths in 2008, so i do know.

yeah they do tend to pop up quite a bit
and its what most people struggle with the most in complex numbers.
that or vectors

Don't be so obscure next time. Oh, and cry somewhere else, thanks .

 

[cutemouse]

Firstly, this is a HSC forum where others help people who are struggling within a certain topic or subject. You have a shit argument placed above. So please, stfu and gtfo, kthxbai.

And lol, so you decide to come into my thread and backfire at me since you were clearly wrong .

So I had a fair statement of implying that cube roots of unity may be in the exam, for the sake of others (if they don't revise through the concepts). I don't want them to be mislead by a BOS'er who clearly hasn't completed the HSC for 4U mathematics. Don't be vague.

Yes but I don't appreciate you immediately jumping to the conclusion that I was deliberately posting something misleading. You could've easily posted something less sinister, but no you had to arrogantly try and look like the tough one.

Fair argument, but look below towards your reply (from past 4U students):

I was referring to the type of questions where you are asked the PROVE expressions using the forementioned results.

Don't be so obscure next time. Oh, and cry somewhere else, thanks .

Did you intend offend me there? Don't think it worked