# Oxbridge Physics Prelims Revision

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So hold on....is it as follows:

Given a sample of a population, with standard deviation: s...

the standard deviation of the whole population = s/root(n)
the standard error in the mean is the standard deviation of the whole population divided by root(n-1)

is that right?

What about when the error is just the standard deviation? Is that ever the case?
HELP!

I'm getting thoroughly frustrated at a question here, please please someone help I really cant see how to keep this simple:

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By considering the zero momentum frame for a collision between a mass m1, at speed v (in the lab frame) and a stationary (in the lab frame) mass m2, calculate the fraction of initial kinetic energy transferred to the mass m2.
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It's driving me crazy cos I just get stuck in a mess of algebra. Someone please help!
Willa
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By considering the zero momentum frame for a collision between a mass m1, at speed v (in the lab frame) and a stationary (in the lab frame) mass m2, calculate the fraction of initial kinetic energy transferred to the mass m2.
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In the ZMF (zero-momentum...), particle 1 has speed $u_1=v-\frac{m_1v}{m_1+m_2}=\frac{m_2v}{m_1+m_2}$, and particle 2 has speed $u_2=-\frac{m_1 u_1}{m_2}=-\frac{m_1v}{m_1+m_2}$.

Now use the energy and linear momentum conservation equations:

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$
$m_1u_1^2+m_2u_2^2=m_1v_1^2+m_2v_2^2$

You know u_2 in terms of u_1, so you can eliminate v_1 and v_2 from the 2 equations. The algebra is generally a bit messy, but just plough through the working, making sure that your main aim is to eliminate variables, convert back into lab frame, and calculate kinetic energies, as required.

What I say may be obvious, but the key thing is not to mess around with variables, just try and eliminate them! Keep track of which variables are known, and which ones you are trying to determine in terms of these known variables.
LennonMcCartney
In the ZMF (zero-momentum...), particle 1 has speed $u_1=v-\frac{m_1v}{m_1+m_2}=\frac{m_2v}{m_1+m_2}$, and particle 2 has speed $u_2=-u_1$.

but they're different masses so u2 doesn't equal -u1 - you need no momentum so doesn't $m_1 u_1 = -m_2 u_2\ so\ u_2 = -\frac{m_1 u_1}{m_2}$
Bezza
but they're different masses so u2 doesn't equal -u1 - you need no momentum so doesn't $m_1 u_1 = -m_2 u_2\ so\ u_2 = -\frac{m_1 u_1}{m_2}$

Sorry, yes, me being silly. He is correct of course, but the point is that u_2 can be written as a known function of u_1.
grrr I have tried doing it but i always end up with a nasty square root part which just is really pissing me off! Cos I have to find v2, which is the square root of something horrid, and add something to it...and it just isnt working! ARGH this is driving me crazy!
yay i finally did it. I hope to god a question like that doesnt come up in the exam!!
That is the problem with mechanics, you can never really tell if you're doing it right or not. But if the velocities fit the equations, then it must be correct.
Quick relativity question, just to check i've got things the right way round:

If an event occurs at a distance x' (as seen by the S' observer) at t'=0, then this means that a stationary observer determines that the event happened at t = gamma * vx'/c^2

that right?
Yes. I tend to remember that

$x'=\gamma(x-\beta ct)$ and
$ct'=\gamma(ct-\beta x)$

for the symmetry of it and the easier application to energy and momentum. And to switch the dashes, just replace $\beta$ with $- \beta$.
OK I'm trying to analyse a situation in two different ways which should give the same answers but arent!

I have a rocket moving at speed 2c/3 and it emits a photon from x' which travels to the origin and then back to x' again. This obviously means t' = 2x'/c
So I want to see what time the stationary observer records, and using the standrd equation: t = gamma(t' + vx'/c^2) I obtain 4t'/root(5)

Now I wanted to check that this corresponded to length contraction, so I imagined the stationary observer seeing the rocket to be length x. That means that the first leg of the photon journey is t=x/(c+v) because it the photons relative speed to the rocket is c+v. And then adding on the return journey, t=x/(c+v) + x/(c-v)
substitute in the value for v above, to get: t=3x/5c + 3x/c = 18x/5c
But that should equal the previous calculated t, so 18x/5c = 4t'/root(5) = 8x'/croot(5)
so x = x' * (40/18root(5))

but using the standard transformation, that factor should be gamma = 3/root(5)

so where's my mistake!?
Anyone know of a good website that explains phasor diagrams well, I cant find any which help me understand how to use them. We seemed to cover them in lectures really quickly but they pop up everywhere and I dont think I can do them v well. Can anyone help?
Try hyperphysics. Look that up in google, and it should give you some ideas.
LennonMcCartney
Try hyperphysics. Look that up in google, and it should give you some ideas.

No that hasnt really helped me, I'm still confused. I can't do this subject damn it, why is nothing going right for me.....I couldnt do chemistry and computing, physics was my one strength, and now I can't even do that
And my rowing coach this week seems to be picking on me which makes me feel like I can't row either....and these new blades (shiny as they are) are causing a whole set of new blisters. Hmmmmpth nothing is going right for me

And with my first exam on monday, I am so underprepared that I'm gonna barely be able to answer any of the questions. This sucks, and it's all my fault!
Aww! Will, chill out! OK so this is a fairly tense time of the year. Worry a little bit, but not too much. Make sure to take plenty of breaks, just for yourself, where you don't worry, don't revise, don't do anything stressful.
I dont have time to take breaks, I've taken too many breaks already! I dont have the time to revise enough to get a good mark in these exams - well at least a mark which represents what I think I can achieve. I'm only just getting the hang of some modules, and I reckon I dont have time to learn entire chunks of some of them!
GOOD LUCK ALL THE OXFORD PHYSICISTS IN THEIR EXAMS WHICH START TOMORROW (sorry Will, don't know when yours start but Good Luck to you too!!!).

No doubt I'll have lots of questions in the morning.
i start exams tomorrow morning as well, but my physics paper isnt until saturday. I have compsci tomorrow....oh woe is me
Willa
i start exams tomorrow morning as well, but my physics paper isnt until saturday. I have compsci tomorrow....oh woe is me

Good luck!
Ok last minute panic time! I have two questions that I'd really appreciate answering:

1) Rotational Dynamics: How do I prove that L = Lcm + c^p. I've seen the proof, but don't understand why some terms are zero and can thus be ignored.

2) "Show the quantity x^2 - (ct)^2 is a Lorentz invariant" [Q7. Physics1 1999]

Thanks guys! Hopen your compsci is going well Will....we're thinking of you!