Quiz me, please!

Stargate

Can three people here post one hard physics problem for me to solve??!
(That's one person per problem)

arildno

1) Give a rigourous derivation of the Yang-Mills equations
2) Prove, that under smooth initial conditions, the Navier-Stokes equations will not blow up in finite time.
3) Determine the range of initial conditions three bodies solely attacted by mutual gravity can have in order to exhibit periodic motion.

Good luck!

dextercioby

That's not fair,Arildno,you took all three of them...

Here are my three:
1.Derive the effective action of QED in the first order of perturbation theory (i had this problem at the QFT exam,last year).
2.Derive the Poisseuille-Hagen formula (1839) starting from the Navier-Stokes equations.
3.Prove that Abraham-Lorentz equations are violating the principle of causality.

Daniel.

rachmaninoff

He only wanted one problem per person, arildno.

arildno

Well, but I gave him CHOICES, didn't I?
He can pick the easiest one if he likes.

Stargate

arildno and dextercioby, pick one problem that you want me to solve.

arildno

A bit more serious, I'll pick Daniel's 2.
(It's at least doable, and not too difficult)

dextercioby

The first in the most interesting.Pick the first.Pay attention with your calculation,though.

Daniel.

Stargate

I need one more problem from a different person and I'll get back to you by next monday. Ok?

rachmaninoff

You guys,this is a K-12 forum! You can't assume graduate level knowledge here.

Here's my one, HS-level problem:

1) A 53.0kg spherical projectile, 27.0cm in radius, is fired at an angle 38.5 degrees to the horizontal at 12,350 m/s. Find the maximum height by Euler's method approximation (h = 0.0005) without using electronic aids (you'll need a bit of paper for this). Keep in mind the gravitational force will not be constant. Include air resistance.

dextercioby

Hey,man,this is K-12.Air resistance is usually proportional with velocity,somtimes even with its square.Nonhomogenous gravity field+air resistance:that's a horrible diff.eq.he'll be getting.Without air-resistance,maybe he'll have a chance.

Daniel.

Stargate

I'm a 9th grader by the way so I would like 9th grade problems please.

rachmaninoff

I apologize, this whole thread is being quite inconsiderate, myself included.

A solvable problem: What is the altitude of a satellite in geostationary orbit, given that there are 86,400 seconds in a day, and [tex]r_{earth{[/tex] = 6,370km? (fun problem, really)

rachmaninoff

Dextercioby: Actually I sidestepped the D.E. part when I asked him to use Euler's method.

dextercioby

A very short and interesting problem:
Compute the atmosphere's mass.Assume all constants are given (u may use tables of constants and calculators for the numbers).

Daniel.