...but don't fear! Help is HERE.

Hello!
I know to write the equation for a harmonic wave moving along the x axis in a positive direction (with Y(0,0)=0):
Y= A sin (kx - wt)

How do I write it to describe a wave travelling in an x=y direction with z=0?
I guessed:
Y = A sin [kx (i+j) -wt]
... but I suspect that's rubbish.

Thank you.

I've looked through all 3 of my physics textbooks and still don't get how to solve this problem. Please help.

At the highest point in its path, an arrow is traveling at a speed of 10 m/s. Assuming that its acceleration is 9.81 m/s^2 vertically downward, how fast would it be moving .5 s later? .5s earlier?

My attempt: I'm assuming that the 10 m/s is the horizontal vector part, so I did vf=vi + at with vi being 0 m/s but the answer is negative and doesn't match any of the answer choices even if it was positive.. And I can't think of another way to approach this problem..


Then, there are two more problems that are on the same topic, that I also don't know how to work them out:
At the highest point in its path, an arrow is traveling at a speed of 10 m/s. Assuming that its acceleration is 9.81 m/s2 vertically downward and .5 m/s in the horizontal direction opposite its motion, how fast will it be moving 2.0s later? 2.0s earlier?

Thanks!

Hey, I'm somewhat stumped on how to tackle this differential equation. Any advice is really appreciated.

The equation reads

(1/v)*D(C)/Dt - (3/2)*D(C)/Dy = a*D^2(C)/Dy^2,

where v and a are constants, and D^n(C)/Dy^n is the n-th derivative of C with respect to y.

Here y = ln(R).

At t=0, we have C(R,t=0) = B*delta(R-R_o) , where delta() is the dirac delta function. It says setting

X = y + (3/2)*v*t

may also help. The problem also gives that the general solution to

D^2(u)/Dx^2 - D(u)/Dt = 0 is

u(x,t) = (1/sqrt(4pi*t))Integral( u(x,0) exp(-(x-g)^2/(4t) )dg integrated from -infty to infty.

:S

I am attempting a question from a textbook but the wording or perhaps the question itself is confusing me.
*Light falls at perpendicular incidence on a transmission diffraction grating. The second order diffracted light leaving the grating is examined.
The grating has 600 slits per mm, a total width of 10 cm, and is being used to examine spectral features near a wavelength of 450 nm. How close ( in nm) can the wavelength of two spectral lines be, for the two to still be seen as two, rather than blended into a single intensity peak?

Ok so I have done question son diffraction gratings before, but all straightforward, and using the equation d*sin theta =m*lamda
i have worked out theta to be 32.6 degrees, and (not sure if this is right) but used the equation for double-slit diffraction: y=m*lamda*D/d and worked out the spacing between the maximum and the first minimum, y, to be 0.05389m. Is this at all on the right track or am I totally lost?

I fear the latter. Any help much appreciated! 

My requirement for this project was to build an instrument that can produce all the notes in a C scale. The accuracy of the notes is to be judged through Frequency (Hertz). I decided to build an instrument whose design is comprised of eight electrical conduit tubes (metal) that are about 1.5'' inches in diameter. I strike them with a mallet to produce the sound.


My problem is that I solved for the Length of the eight pieces of tubing (below), but when I went to go test them, the notes that I produced don't seem to be right.

Together, they definitely do not produce an even scale, and they are not in tune with my piano. If my ear is correct, I believe the notes are all flat. I'll describe the process I went through below. I'd really appreciate any problem-solving advice and suggestions for what could be wrong/how to possibly tune my instrument.

Wavenumber k=nPi/L, where n is number of particles and L is length of one side of a box.

The part I do not understand is how to get that the number of states with wavevector between k and k+dk is L(dk)/Pi. I think it involves some sort of integral...

Hi, I am embarrassed to have to resort to this, but I have been stuck on these two problems for (literally) two hours.  Can anyone help?

"Suppose that 1.00g of hydrogen is spearated into electrons and protons.  Suppose also that the protons are placed at the Earth's North Pole and the electrons are placed at the South Pole.  What is the resulting compressional force on the Earth?"

I've gotten several answers for this, but none of them correct (5.12x10^5 N).  I suspect my error is in assuming that the q values are related to the masses of the electrons and the masses of the protons?

"Two identical conducting spheres are placed with their centers 0.30m apart.  One is given a charge of 12x10^-9 C, the other a charge of -18x10^-9 C.  The spherers are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached."

I thought this one would be rather straight-forward, but I keep on getting very large numbers instead of the correct one, 9.0x10+-7 N.

I would appreciate any thoughts on this.  We are allowed to consult others on the homework or even go to our learning center, but they are closed for the night.
Thank you ahead of time for at least reading this!  :)
[x-posted all over in hopes of getting a response]

Could you check/help me on these physics problems?

http://dhilbert.wordpress.com/2007…

THanks

I have a question about an oscillation problem.

A 500g block slides along a frictionless surface at a speed of 0.35 m/s. It runs into a horizontal massless spring with spring constant 50 N/m that extends outward from a wall. It compresses the spring, then is pushed back in the opposite direction by the spring, eventually losing contact with the spring. How long does the block remain in contact with the spring?

Using the equation T=2pi sqrt(m/k), I found the period, which is pi/5. However, the correct answer is pi/10, so I am wondering why I have to divide the period by half.

Thank you!

I’m having trouble with this problem. I just don’t see how the expression that I end up with can be reduced to a familiar formula for entropy…

I did the first part of the problem, and it’s the second question that I’m stuck on. Well, let me set it up:

Now, since I don’t know how else to denote it on here, I’ll just denote the summation by SUM. Note that this is the sum over all states s.

The prblm:

Some advanced textbooks define entropy by the formula:

S = -k SUM {P(s) ln P(s) } ,

where the sum runs over all microstates accessible to the system and P(s) is the probability of the system being in microstate s.

First question (which I did do successfully):

For an isolated system, P(s) = 1 / Ω for all accessible states s. Show that in this case the preceding formula reduces to our familiar definition of entropy.

My work here:

I can factor ln (1 / Ω ) out of the sum because it is independent of the state s. SUM { P(s) } = 1, so S = -k ln (1 / Ω ) = k ln Ω . Yay!

Second question (the one I’m stuck on :( ):

For a system in thermal equilibrium with a reservoir at temperature T:

P(s) = ( exp[ -E(s) / kT ] ) / Z .

Show that in this case as well, the preceding formula agrees with what we already know about entropy.

What I have so far:

In this case, the ln factor cannot just be factored out of the sum because it’s dependent on the state s.

S = -k SUM { [ ( exp[ -E(s) / kT ] ) / Z ] ln ( exp[ -E(s) / kT ] ) / Z }
S = -k SUM { [ ( exp[ -E(s) / kT ] ) / Z ] [ ( -E(s) / kT ) – ln Z ] }

Then since the partition function Z = exp[ -F / kT ] and Helmholtz free energy F = -kT ln Z, I can write this expression as so:

S = -k SUM { [ ( exp[ -E(s) / kT ] ) / ( exp [ -F / kT ] ) ] [ ( F – E(s) ) / kT ] }
S = -k SUM { [( F – E(s) ) / kT ] [ exp[( F – E(s) ) / kT ] ] }

…Sorry for all those brackets. Again, I’m not sure what steps to take next to show that this expression is familiar in any way. Any nudges in the right direction would be awesome.

THANK YOU!