PAT - November 6th 2014

It's just one of the small-angle approximations, like sinx~x when x is small etc... I think it's arrived at using the Taylor series or smt (because you can neglect terms w/ of higher degree, as they get so small, you get the neat form used)

No but for that question we needn't do this approximation. For one thing the angles doesn't come here at all

The question (c) is actually asking about the assumptions we make to model the pendulum as an 1)ideal pendulum and then as a 2)rod pendulum.

1) We assume that the mass of the rod is negligible. Mr -> 0. When we do this the equation appears the same as in (a)

2) We assume that the mass of the bob is negligible. Mb -> 0. So then the equations appears as in (b)

Came across these the other day trying to find out a way to work a question out. Never covered those at school, would never have known them if it wasn't for coming across that question. It seems some things on these papers rely on you being lucky enough to have looked into the right things in the past.

I just always get stuck on the shape ratio questions. Apart form that not too bad except the odd question here and there, finding the physics section better on most papers barring 2012

It's just one of the small-angle approximations, like sinx~x when x is small etc... I think it's arrived at using the Taylor series or smt (because you can neglect terms w/ of higher degree, as they get so small, you get the neat form used)

The simultaneous equations question form 2011 on large, medium and small boxes was bloody annoying; too many equations and variables

I skipped over that one to go back to at a later date, still haven't gone back to it hahaha. Just did the 2008 paper and got the macaw question right though so now might be the time. Questions like the macaw one, the box one, the space ship freight one, and so on, I could never get my head around them but I figured it out on the macaw question so I'm gonna go back and try the others I skipped over?

I skipped over that one to go back to at a later date, still haven't gone back to it hahaha. Just did the 2008 paper and got the macaw question right though so now might be the time. Questions like the macaw one, the box one, the space ship freight one, and so on, I could never get my head around them but I figured it out on the macaw question so I'm gonna go back and try the others I skipped over?

I don't think so. We know dy/dx is simply the posh way of saying the change in y divided by the change in x (I won't insult your intelligence, you know this). So when we represent velocity, it's the distance over time. dt=s/v, acceleration is equal to dv/dt, but dt=ds/dv, substitute means a=dv/(ds/dv)or dv^2/ds). Or simply put, the first differential of displacement with respect to time is v, hence dy/dx=(dx/dt)=v (where the x's ARE NOT THE SAME). Second differential, (d2y/dx^2=dv/dt)=a, the acceleration. You should also be aware of the third differential, d3y/dx^3=da/dt=jerk, rate of change of acceleration. I think this answers your question.

If anyone is running out of pat material to go through I have found the physics Olympiad questions (set by Oxford) to be really useful! The As questions are most similar to the majority of the pat, but the the A2 ones are really like the long 20 mark questions. Hope this helps!


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Huh? No pendulums in that question... The person I responded to was referring not to that question, but another, namely the one on the planet Oceana of whatever

Thanks for answering, and i understand your comments. However I still have 2 queries unanswered.

1) It cannot be legitimate to use 'constant acceleration' formulae in answering this question, when the acceleration is defined as NOT constant, but is variable, relating to displacement.

2) Having derived a simple expression for KE, displacement in part a... by calculus... has anyone got the idea how to change the function in relation to displacement to functions relating to time?? I'd be grateful for suggestions.. not only because of PAT, but of curiosity, because I can't see how to do it!!

Update on the materials science, for those with no As or A2 chemistry:

"Dear 42000,

This is something which will be taken into account along with your full application. If your application shows an interest in Physics related to Materials Science and you meet our minimum entry requirements, it may be the case that you are invited to interview. If Materials Science is something you are seriously considering alongside Physics, I would advise you to read around some of the A level Chemistry related to materials.

I hope this is helpful.
If you have any further questions do not hesitate to contact me.
Kind regards
Jayne"

Have you covered second order differential equations as in Edexcel FP2? If not just go through that chapter and then it'll become clear how to do it. Its applied in M4 for SHM.

Just use d^2x/dt^2 for acceleration and then continue.

Thanks so much for that, it was really annoying me.
I've now solved using the calculus route, and find that velocity/time is indeed like a sine wave (with origin at t=pi), and acceleration as a cosine curve same origin.
Now I know this wouldn't be expected in the actual PAT, but I feel satisfied now!