janvier 2014

Finding the convection of a node in a hot pipe

vendredi 31 janvier 2014

1. The problem statement, all variables and given/known data

I just completed a lab in class where we heated a copper pipe and measured the temperatures at 25 different locations. Each of these locations is called a node. The goal is to find the convection losses by using the First Law (q_c1 + q_c2 + q_c3 + q_c4 + q_rad + q_conv = dE_CV/dt).

Here is the temperature data for the 25 nodes:

Also, the ambient temperature is 22 °C.

Specifically I circled the nodes I would like to analyze - the node at 58.327 °C. So I assumed the system is in steady state and got:

q_c1 + q_c2 + q_c3 + q_c4 + q_rad + q_conv = 0

Conduction heat transfer: q = kA(T2-T1)/t

Convection heat transfer: q = hA(Tw-T∞)

Radiation heat transfer: q = σε(T2⁴-T1⁴)

Looking at the data, we see that the heat transfer by conduction is out of the middle node to the four surrounding nodes. Also, there is radiation out of that node as well. In other words both conduction and radiation is transferring out of the node.

By the First Law, this would imply that the heat transfer by convection is into the node. However, this does not make sense since the ambient temperature is lower than the node temperature so we should expect the heat to transfer out of the node.

Does anyone know what I am doing wrong?

Cubic Bezier Curve Problem

Hello.

I have a program that, given a value for (x), needs to find the corresponding y-value along a cubic Bezier curve. So long as the Bezier does not switch direction in (x), there is always one, and only one, value of (y) for every value of (x).

In solving for (y), I discovered that the solution was a cubic (not surprising, since the very name of this type of Bezier is "cubic"). Now, my experience with quadratics and what cubics I run into rarely, is that the way to find out which solution to use is to just test it...Most often, one will always work while the others will not, or in some rare cases all of them will work...Assuming that the values are always Real.

At any rate, after testing the program, I found that, indeed, none of the three solutions always offered a Real result. Sometimes all three were Real, sometimes a mix of Real and Complex, other times all Complex. So my conundrum is this: I need a scalar (Real) value for (y), but when I move one of the control points of the Bezier, I run into a majority of cases where the result for (y) is complex, and no solution reliably results in a Real, scalar value for it. Therefore, there is no way to test for which solution to use.

My question is, how am I to interpret a Complex result in this situation? It is a vector with an Imaginary component, when I need a scalar value. Proofing my math results suggests that I have the correct solutions, and whenever a Real value results, that (y) value is always correct. As far as I know, a Complex value may indicate that something is going on in a separate dimension, so I assume that since the Bezier I am using is 2-dimensional, that the Complex result is telling me that there is activity in a third, orthogonal direction. But that makes no sense as far as this Bezier is concerned.

I am stumped. :(

Any guidance would be really helpful.

Many thanks!

Attached Images

P24.55.jpg (13.2 KB)

Amanda Knox Acquittal Overturned

Quote:

Appearing stunned and fighting back tears, Amanda Knox said Friday that she “will never go willingly back” to Italy and would fight any effort to extradite her “to the very end.”

“It’s not right, and it’s not fair,” Ms. Knox said in the interview with ABC’s “Good Morning America,” the day after an Italian appeals court upheld her 2009 conviction for the murder two years earlier of Meredith Kercher, with whom she had been sharing a student apartment in Perugia.

The court sentenced her in absentia to 28 ½ years in prison.

This latest decision is likely to set off years more of court battles in Italy and possibly the United States, legal experts said, before Ms. Knox could in theory be arrested and sent to Italy for punishment...

http://ift.tt/1fjltKb

By accident I happen to have run across an account of this case in the afterword to a book about another famous Italian murder case, The Monster of Florence, by Preston/Spezi. The authors included that afterword about Knox in the second edition to underscore the rather unhinged behavior of the Italian prosecutor who was in charge of both cases, Giuliano Mignini. He is a modern day Joe McCarthy who, instead of hunting communists, hunts devil worshippers, a large network of whom, he believes, are at work in the world today, killing innocent people as part of their rituals.

Preston believes Knox is completely innocent:

http://ift.tt/1fjlu0p

and, going beyond the afterword in the other book, has put out a whole separate book in her defense:

http://ift.tt/1nyMcbt

In this article published in The Atlantic in 2006, Preston encapsulates his experiences researching in Italy with Spezi and relates how, when he and Spezi determine Mignini has prosecuted the wrong man in the Monster of Florence murders, they are harrassed and jailed, and Spezi is accused of being the Monster of Florence. This is the kind of guy Mignini is.

http://ift.tt/1nyMeA2

I think it's important for anyone with an opinion about this case to hear what Preston has to say. It's hard to believe such a thing could exist in the modern world, but it looks to me like Knox was outright framed by a mentally unstable person with a medieval witch-hunter's mentality. I don't believe she should be extradited.

Alternative Proof to show any integer multiplied with 0 is 0

In his book, Spivak did the proof by using the distributive property of integer. I am wondering if this, I think, simpler proof will also work. I want to show that ##a \cdot 0 = 0## for all ##a## using only the very basic property (no negative multiplication yet).

For all ##a \in \mathbb{Z}##, ##a+0=a##.

We just multiply ##a## again to get ##a^2+(a \cdot 0) = a^2##. Then it follows ##a \cdot 0 = 0##. (I remove ##a^2## by adding the additive inverse of it on both side)

Measuring electricity passed to ground from an antenna

First of all, excuse me if this question is too basic: I feel like it shouldn't be a struggle to understand, but the fact is it is.

We put up an antenna to play with radio a little, and someone we were working with showed us that there's a reading on the voltmeter without any of the equipment hooked up.

We are in a city, so there is wifi and power lines, and we're doing old-fashion analog testing to try to reduce the voltage before connecting everything.

The interesting part to us is that when we isolate the antenna by laying it on the shingles, then connect it to ground with the voltmeter plugged in in between, we get a reading of ~4Volts AC (it changes as we move it in relation to the power lines or wifi antennas).

However, if we lay it bare on the ground while still connected to the voltmeter, the voltage drops right off.

The question is: Is our test flawed in some way?

And; though it sounds ridiculous as I pose it: should we consider installing the antenna on the ground permanently?

Thanks in advance

Simple circuit for Battery Status indication for 7.4v re-chargable bat

For my MINI PROJECT

I need to get an LED indication for

full battery and

low battery

the circuit must be simple with components such as transistors,resistors..etc

Battery Details: 7.4v 1500mah li-on

Contribution to margin movement

I'm stumped at how to approach this problem and was hoping someone could enlighten me.

If I had sold $100 of a product and made a 20% profit up until a specific day.

The next day, made three sales;

A) $20 making a $5 profit

B) $50 making a $30 profit

C) $30 making a $15 profit.

So now, in total, I've sold $200 worth making a total profit $70 or a margin of 35%.

The margin delta of 1500 bps, is there a way to show what each sale contributed to that. E.g. A) -300bps B)1000 bps and C) 800bps. I've tried isolating each sale but I don't want order to be a factor.

How to charge a mobile phone (5v500mAh) from 6v 1300mAh Ni-Mh battery

i need to use as a portable charger(POWER BANK) for my mobile

can i use LM7805 to deliver my rated output !

please guide me with circuit s !

Planck Black-Body Law

1. The problem statement, all variables and given/known data

Starting from the Planck-Body Law

I[itex]_{λ}[/itex]dλ = [itex]\frac{2\pi c^{2}h}{λ^{5}}[/itex] [itex]\frac{1}{e^{hc/(λkT)} - 1}[/itex]dλ

where λ is the wavelength, c is the speed of light in a vaccuum, T is the temperature, k is Boltzmann’s constant,

and h is Planck’s constant, prove that the total energy density over all wavelengths is given by

I[itex]_{tot}[/itex] = aT[itex]^{4}[/itex]

and express a in terms of pi,k,h,c

2. Relevant equations

λ = c/f

3. The attempt at a solution

Our teacher gives us a hint "think about whether it is better to do the integral in the wavelength or frequency domain" - which in this case means he wants us to switch to the frequency domain. I did try a bunch of things but I am just not sure if my first step is correct. To switch to the frequency domain, all I havr to do is plug in

λ = c/f

and

dλ = -c/f[itex]^{2}[/itex]

correct? Or is this first step wrong

Calcutaing force needed for a "rudder"

Hello everyone, I joined today in an attempt to get some help with a "rudder" im trying to build for remote control purposes.

Montana State University for Physics?

Hello,

I am looking into transferring to Montana State University for physics (undergrad from a 2-year college), they have really good solar physics research going on and the town (Bozeman) is beautiful and inspiring. My only concern is that the classes may be shaky considering that there are only about 8-9 teaching faculty.

If anyone has gone there for physics or knows anyone that has I would greatly appreciate your opinions on the quality of the department and their undergraduate program.

Thank you in advance.

Particle's spin when subject to a constant magnetic field

1. The problem statement, all variables and given/known data

An alkali atom, on it's fundamental state, passes through a Stern-Gerlach apparatum, which will only transmit atoms with their spins aligned along the +z direction. After that the atoms travel, during a finite time τ, through a region of constant magnetic field [itex]\vec{B}=B\vec{e_{x}}[/itex].

After that time τ the atoms pass through a new Stern-Gerlach apparatum, which only allows atoms with spin along -z to pass. What's the probability that they will pass?

2. Relevant equations

Pauli matrices

[itex]\widehat{H}=-\vec{u_{B}}.\widehat{S}[/itex]

[itex]u_{B}=\frac{q}{2m_{e}}[/itex]

3. The attempt at a solution

From the problem it's easy to see that the state of the system at the instant t=0 is:

[itex]|\psi>(t=0)=|+>_{z}[/itex]

Then I assumed that, while being under the influence of the constant magnetic field along the x direction, the state is:

[itex]|\psi>=\alpha (t)|+>_{z} + \beta (t) |->_{z}[/itex]

Next I applied the hamiltonian to my state [itex]|\psi>[/itex]. Since [itex]\vec{B} = B\vec{e_{x}}[/itex]:

[itex]\widehat{H}|\psi>=-\frac{qB}{2m}\widehat{S_{x}}|\psi>[/itex]

[itex]\widehat{H}|\psi>=-\frac{qB}{2m}\widehat{S_{x}}(\alpha (t)|+>_{z}+\beta (t) |->_{z})[/itex]

Since [itex]\widehat{S_{x}}=\hbar \sigma _{x}[/itex], applying it to [itex]|\psi>[/itex] returns:

[itex]\widehat{H}|\psi>=-\frac{qB\hbar}{4m}(\beta (t)|+>_{z}+\alpha (t) |->_{z})[/itex]

Defining [itex]\omega=\frac{qB}{4m}[/itex]:

[itex]\widehat{H}|\psi>=-w\hbar(\beta (t)|+>_{z}+\alpha (t) |->_{z})[/itex]

Now, using Schrodinger's equation we get:

[itex]\widehat{H}|\psi>=i\hbar \frac{d}{dt}|\psi>[/itex]

[itex]\frac{d}{dt}(\alpha (t)|+>_{z} + \beta (t) |->_{z}) = iw(\beta (t)|+>_{z}+\alpha (t) |->_{z})[/itex]

Separating this we get:

[itex]\frac{d}{dt}\alpha (t) = iw\beta (t)[/itex]

[itex]\frac{d}{dt}\beta (t) = iw\alpha (t)[/itex]

Applying another derivative to the first differential equation we get:

[itex]\frac{d^{2}}{dt^{2}}\alpha (t) = iw\frac{d}{dt}\beta (t)[/itex]

[itex]\frac{d^{2}}{dt^{2}}\alpha (t) = -w^{2}\alpha[/itex]

Doing the same to the second achieves a similar result:

[itex]\frac{d^{2}}{dt^{2}}\beta (t) = -w^{2}\beta[/itex]

Solving both I got:

[itex]\alpha (t) = Ae^{iwt} + Be^{-iwt}[/itex]

[itex]\alpha (t) = Ce^{iwt} + De^{-iwt}[/itex]

Now, since I know that [itex]|\psi>(t=0) = |+>_{z}[/itex], I know that:

[itex]A+B=1[/itex]

[itex]C = -D[/itex]

From this I can conclude that:

[itex]\beta (t) = Fsin(wt)[/itex]

This is as far as I can get.. I don't know what to do from here. Am I approaching the problem wrongly? Any help would be appreciated.

Thanks.

Daniel

Force to Lorentz Force

Greetings,

I am trying to to show that the force in this form:

[itex]\dot{P}=e(\vec{∇}\vec{A})\vec{\dot{x}}-e\vec{∇}\phi[/itex]

Is equal to the lorentz force. I have been trying the approach of some sort of vector identity but have not gotten anywhere.

The equation and where I am trying to get with it are posted on wikipedia towards the bottom:

http://ift.tt/Uiq7zu

I appreciate any help!

Height when a ball is thrown vertically at half its velocity

[itex][/itex]1. The problem statement, all variables and given/known data

A baseball is thrown vertically into the air with a velocity, v, and reaches a maximum height, h. At what height was the baseball with one-half its original velocity? Assume no air resistance.

2. Relevant equations

v₂² = v₁² + 2ad ?

3. The attempt at a solution

let 10m/s be the original velocity

d = [itex]\frac{v^{2}_{2} - v^{1}_{2}}{2g}[/itex]

d = [itex]\frac{0 m/s - (10 m/s)^{2}}{2(-9.8 m/s^{2}}[/itex]

d = 5.1

at 5 m/s:

d = [itex]\frac{0 m/s - (5 m/s)^{2}}{2(-9.8 m/s^{2}}[/itex]

d = 1.28

[itex]\frac{1.28}{5.1}[/itex] = 0.25

but the answer is 0.75 of the original height. How to solve this?

Gravitational pull on an object

How much does gravitational pull on an object decrease if the distance is increased 10 fold for example?

If planet x is stationary and part of a binary star system where star y is 1 AU away from it and star z is 1,000 AU's away, but also has 1,0000 times the mass, which star will exert more gravitational pull on planet x?

Physics

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