# Oxbridge Physics Prelims Revision

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LennonMcCartney
OK, from my analysis, I get:
$F=m \frac{dv}{dt} + \omega \frac{dm}{dt}$.
Do you agree with this?

Almost, except I would have thought it would be $m_{o}$ on the first term on the RHS
LennonMcCartney

We know that $\alpha=dm/dt$, and that $m=m_0-\alpha t$

If you differentiate m you get alpha should be -dm/dt, but you've got the right sign in your expression from somewhere!

Chloe, you don't get m0 in the first term because you're looking at a general time t when the mass is m.
Hoofbeat
Thanks for trying Will. I'm still not 100% convinced as the method I was using was the same as we've been taught to use (with a small edit that my tutor insists on) and I don't see why it just won't work!!! <sighs> I guess I'll just have to wait til next week when my tutor's back from Canada and pester him instead.

i dont understand what your "general method" is then? To me I thought this method was deriving an expression for change in momentum, and then taking the derivative! That seemed like what you were trying to do, but you looked like you were getting confused with what was a function of time and what is a constant through time. For example, m is a function of time: m = m0 - at. but a and m0 are the constants.
Hoofbeat
Almost, except I would have thought it would be $m_{o}$ on the first term on the RHS

In our whole analysis, we assume that p(t)=m(t)v(t) so until we susbtitute $m(t)=m_0-\alpha t$ m is always a function of time, and at no point is it m0 (except for t=0, of course), since our analysis of momentum change does not occur only at the start, but we check for change in momentum at any time t and a short time t+dt after.
As I said, you don't stick in init conds until the end
shiny
As I said, you don't stick in init conds until the end

The irony.
can someone help me with this question please (i'm finding it hard to focus with my poor back...cursed rowing!!!):

I need to show that for an oscillator that it's probability that it is found in a region of space: x -> x+dx is given by:

p(x)dx = |dx|/Tv(x)

where T = time period of oscillation and v I presume is the velocity function

And then I must calculate the probability distribution p(x) (as above) for an oscillator with potential energy = .5ax^2

help!?

argh my back...anyone a physio by any chance?
Willa
argh my back...anyone a physio by any chance?

I got a spanner?!
shiny
I got a spanner?!

is it made of painkillers? Argh jesus christ the past hour it's got seriously painful! I'm so bloody annoyed at my captain he doesnt seem to care at all about how i am, he's far more concerned about whether i can get a decent sub or not. I've already had to row in two outings with my back injured, and now I think i've done it. I can't even focus on my work! I think I need to go to the doctors if it's like this tomorrow!
Willa
I need to show that for an oscillator that it's probability that it is found in a region of space: x -> x+dx is given by:

p(x)dx = |dx|/Tv(x)

where T = time period of oscillation and v I presume is the velocity function?

what you want is dt/dx = 1/v(x) which tells you how long it stays in this bit of space x to x+dx and then you want to normalise to get the probability.
use a topical heat treatment and also take some codafen...and don't do anthing afterwards because you might not be able to tell that you are ****ing it up further because of the pain relief...doesn't the boat team have physios or anything?
shiny
what you want is dt/dx = 1/v(x) which tells you how long it stays in this bit of space x to x+dx and then you want to normalise to get the probability.

but u dont know what the function v(x) is do you?
Willa
but u dont know what the function v(x) is do you?

v(x) = dx/dt ? What d'ya mean?

Also, did you make a typo? Your LHS and RHS don't match in terms of dimensions!
shiny
v(x) = dx/dt ?

Also, did you make a typo? Your LHS and RHS don't match in terms of dimensions!

well we dont know what v(x) is though! and i didnt make a typo unless the question makes a mistake itself, i copied it straight out!
Willa
well we dont know what v(x) is though! and i didnt make a typo unless the question makes a mistake itself, i copied it straight out!

Do you mean needing v(x) in order to do the normalising? If so, then if you think about it, you are just integrating all the ickle dt's so the normalising constant is just T the period of the oscillation.

Well, if v(x) is speed then the LHS has units of length and the right hand side has no units?
shiny
Do you mean needing v(x) in order to do the normalising? If so, then if you think about it, you are just integrating all the ickle dt's so the normalising constant is just T the period of the oscillation.

Well, if v(x) is speed then the LHS has units of length and the right hand side has no units?

no cos p(x) is a probability distribution, so it's unit's are length-1

and i'll give the integration a go after my backs had a rest!
~Raphael~
doesn't the boat team have physios or anything?

Will is just rowing for his college and unfortunately the colleges certainly don't have physios Anyways, I agree, you need to rest Will and just ignore your coach if he's being an arse. I screwed up my wrist when I was younger and didn't rest it enough at the time....6mnths later I was haunted by it and I ended up having to rest it for 12mnths and even now it's not completely recovered.

Afraid I can't help with your question either However, I too have one on it's way (Raphael you'll be pleased to hear that it is a maths question!!! )
Willa
no cos p(x) is a probability distribution, so it's unit's are length-1 and i'll give the integration a go after my backs had a rest!

oh yeah, der! i work with dimensionless stuff too much
Willa
can someone help me with this question please (i'm finding it hard to focus with my poor back...cursed rowing!!!):

I need to show that for an oscillator that it's probability that it is found in a region of space: x -> x+dx is given by:

p(x)dx = |dx|/Tv(x)

where T = time period of oscillation and v I presume is the velocity function

I may well be talking rot, but isn't the probability of it being found in that interval

dt/T = dx/(dx/dt * T) = dx/(T v(x))

given that the probabilty of it being somewhere at any time can be modelled by looking at a single period of the oscillation.
RichE
I may well be talking rot, but isn't the probability of it being found in that interval is

dt/T = dx/(dx/dt * T) = dx/(T v(x))

given that the probabilty of it being somewhere at any time can be modelled by looking at a single period of the oscillation.

yup, thats essentially what i dids