Oxbridge Physics Prelims Revision

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

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

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.

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

As I said, you don't stick in init conds until the end

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

I got a spanner?!

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.

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

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!

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?

doesn't the boat team have physios or anything?

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!

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 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.