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Applied Maths - Proofs

PurpleFistMixer

... Are there any?

Well, I know there's proving the moment of inertia of a rod, a disc, a square and a triangle, but do we need to be able to prove the parallel axis theorem and all that?

Also, are there any proofs that aren't in the Rigid Body Rotation question? Do we need to be able to derive the equations of motion? (Though that's kinda simple and I've already it revised for physics, but still.)

As great and all as that brown book is, it's really bad at explaining what you need to know for the exam. (Maybe because 150 years ago when it was written, it wasn't all about exams.)

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Parsley

I wonder too! I really do... I'll ask my tutor tomorrow and get back cha!

raah!

I think any of the proofs in apt maths can be worked out on the spot anyway, as far as questions 1-5 +10 and 9 go anyway. From 1989-2007 there has never been any proofs that have to be learned off. There have been a few dfininitions earlier on though. I doubt he would ask them nowadays though

Cokehead Mother

http://www.education.ie/servlet/blobservlet/lc_applied_maths_sy.pdf?language=EN

The only time the word 'proof' is used in the very old and vague syllabus is in reference to the parallel and perpendicular theorems, and it says they need to be "done as classwork"... I think the implication is that they don't expect us to actually remember the proofs of the theorems and be able to reproduce them in the exam.

Outside of RBR, I don't think we need to know any of the proofs. I'm guessing they're only in the book because Mr. M doesn't want us using formulae pulled out of nowhere. I mean if I was writing an Applied Maths book, I probably wouldn't feel comfortable writing "So then we use this random formulae to find x...".

I can't see any Applied Maths teachers being happy if we were suddenly asked to prove that T = 2pi.root(l/g)

Decerto

need to derive I(omega)^2 = 1/2mv^2 and know some definitions like impulse and shm but nothing major except for rigid body proofs, btw for OP do we need to prove triangle i dont think its on the syllabus?

turgon

How do you do the equations of motion? I dont do physics!!!!

Cokehead Mother

turgon wrote: »

How do you do the equations of motion? I dont do physics!!!!

They're pretty simple and you don't really neeeeeed to know them.

Acceleration is defined as the rate of change of velocity.

So (v - u)/t = a. From that we get v = u + at.

Displacement = average velocity x time.

From that we get s = 1/2(u + v)t

But v = u + at

So s = 1/2(u + u + at) t

Simplify that so s = ut + 1/2 at^2

If v = u + at

Then v^2 = u^2 + 2uat + a^2.t^2

so v^2 = u^2 + 2a(ut + 1/2 at^2)

But ut + 1/2 at^2 = s

so v^2 = u^2 + 2as

raah!

They're in brownsy I think

Speaking of brownsy, it has no formula for the area of a trapezium, I had it written somewhere but i can't find it. I could just look it up on google, but while I'm larkin' about here I may as well ask. Does anyone know this formula.

As far as the equations of motion go you just take a=v-u/t and use that to get v=u+at
And s=t(v+u)/2 for s=ut+ 1/2 at (you sub in u+at for v). If you jsut remember that the two arbitray formulae are the definition of acceleration, and how to find the distance using the average speed you can tittor tot your way to whatever it asks you for

hahahahaha, damn, that trickster cockhead mother beat me too it

alan4cult

raah! wrote: »

They're in brownsy I think

Speaking of brownsy, it has no formula for the area of a trapezium, I had it written somewhere but i can't find it. I could just look it up on google, but while I'm larkin' about here I may as well ask. Does anyone know this formula.

As far as the equations of motion go you just take a=v-u/t and use that to get v=u+at
And s=t(v+u)/2 for s=ut+ 1/2 at (you sub in u+at for v). If you jsut remember that the two arbitray formulae are the definition of acceleration, and how to find the distance using the average speed you can tittor tot your way to whatever it asks you for

hahahahaha, damn, that trickster cockhead mother beat me too it

Trapezium = Half the sum of the parallel sides times the distance between them

PurpleFistMixer

... Has that ever come up? o.O

And as far as the triangle thing goes.. I'm not sure. Went through my papers today, hasn't come up in the last 13 years or so, but I had it in a list of Rigid Body proofs for some reason... It seems somewhat unlikely to come up.

Peleus

you defo need to know the period of a pendulum proof. my applied maths teacher told us. it's quite easy.

Cokehead Mother

Really? Did they tell you of any other proofs that need to be known?

Peleus

he might have, cant remember. the only ones he went over with us are the moment of inertia proofs, the linear motion proofs and the pendulum one. he told us you need to know em but to be honest, i cant see them asking a whole question on a proof. thats more of a regular maths thing to do. I'll check the past papers after economics 2moro to see if they ask proofs.

Decerto

any chance you can post the pendulum proof

Cokehead Mother

Call x the lenght of the arc the particle has displaced since being vertical, and l the radius of the circle.

The force acting on the particle is the weight.

We're worried about the acceration that exists in the direction of the displacment, so we resolve the weight vector.

F = -MgSinA (since it's acting in the opposite direction of the displacement)

In maths we learned that as A tends to 0, SinA/A tends to 1. So for small angles, A is about equal to SinA.

Ma = -MgSinA
a = -gA

A = x/l (definition of a radian)

a = -(g/l)x

a = - w^2 x

So w^2 = g/l and then w = root(g/l)

v = s/t

wl = 2pil/t

w = 2pi/t

T = 2pi/w

T = 2pi/root(g/l)

T = 2pi.root(l/g)

Decerto

tvym, do you need to get T=2(pi)root I/mgh from that for rigid body motion by any chance?

Cokehead Mother

They definitely won't ask that.

You'd need to derive a formula the for the centre of oscillation which is a little too nasty for LC applied maths.