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1. Conceptual Question From Stat Mech

Homework Statement [/B] Why does it take longer to cool water in a refrigerator than it takes to cool air, assuming that the inside of the refrigerator is initially at the same temperature as the room it is in? Homework Equations The Attempt at a Solution Quite frankly I don't even know if...
2. Probability Calculation

Homework Statement Suppose you flip 1000 coins, what is the probability of flipping exactly 500 heads and 500 tails. (Hint: First write down the formula for the total number of possible outcomes. Then, to determine the "multiplicity" of the 500-500 macro state, use stirlings...
3. What is a derivation?

That's what I thought... but the equalities and substitutions to derive further results are very well laid out and "easy" to follow. (easy meaning comprehensive)
4. What is a derivation?

Homework Statement This seems like a simple question but I've never asked it and I'm stuck haha For my general relativity course we are asked to derive the change in a vector under parallel transport. My professor references his lecture notes on his course web page in the statement of the...
5. Normalization Calculation

Homework Statement Using the normalization condition, find the constants λ and a of: f(t)=ae^(-λt) Homework Equations integrate from t=-∞ to t=∞ of the function and set it equal to one The Attempt at a Solution I used to be good at these but something is slipping my...
6. GR: Metric, Inverse Metric, Affine Connection Caluculation Help

Homework Statement Consider the Schwarschield Metric in four dimensional spacetime (M is a constant): ds2 = -(1-(2M/r))dt2 + dr2/(1-(2M/r)) + r2(dθ2 + sin2(θ)dø2) a.) Write down the non zero components of the metric tensor, and find the inverse metric tensor. b.) find all the...
7. Probability of electron location in Hydrogen atom

Remember you can check your answer (or compute it entirely if your instructor let's you) with wolframalpha
8. Variational Principle Problem

Homework Statement A particle of mass m is in a potential of V(x) = Kx4 and the wave function is given as ψ(x)= e^-(ax2) use the variational principle to estimate the ground state energy. Part B: The true ground state energy wave function for this potential is a symmetric function of x...
9. Probability of electron location in Hydrogen atom

The probability is the integral of the quantity you squared. The bounds the integral should be 0 to the bohr radius... that will give you the probability of the electron being within the bohr radius. Does this make sense? Check your formula for the probability... seems as if you left off the...
10. QM Spin Function Question

Homework Statement A number of spin 1/2 particles are run through a Stern-Gerlach apparatus and when the emerge they all have the same spin wave function (ψ1, ψ2)τ and 9/25 are in the +z direction and 16/25 are in the -z direction with the normal basis column vectors for +z and -z...
11. Hohmann Transfer Orbit (Simple)

and p^2=a^3 with a in au for period of the transfer orbit
12. Hohmann Transfer Orbit (Simple)

Homework Statement I've been stuck on this problem forever, any help is greatly appreciated. A satellite is in a LEO at h=300km and it is sent to a geosynchronous orbit at 4.224x10^4 km. Calculate velocity at pericenter i.e v_pe Homework Equations v_pe = (2πa_to)/p_to[2a_to/a_leo -1...
13. Hermitian Operators Question

So would I just treat C and C' as separate equations, equate them and show that it equals zero? ie: C'=AB-BA C=(BA)'-(AB)' and just use the fact that all the operators are hermitian?
14. Hermitian Operators Question

Homework Statement [A,B] = C and operators A,B,C are all hermitian show that C=0 Homework Equations The Attempt at a Solution Since it is given that all operators are hermitian I know that A=A' B=B' and C=C' so i expanded it out to AB-BA=C A'B'-B'A'=C (BA)' - (AB)'=C...
15. Laplace Transformation Convolution Integral

My bad it's G(s) which is not explicitly defined
16. Laplace Transformation Convolution Integral

Homework Statement I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2) the answer is y(t)=2e^-2t +te^-2t...
17. Simple Complex Number Question (Roots of 1)

Homework Statement So on one of my homework assignments I had to find the complex fifth roots of one. Because of Euler's equation the arguments are simply 0, 2pi/5,4pi/5,6pi/5,and 8pi/5. It is easy to see that (e^i2pi/5)^5 = (e^i2pi) = cos(2pi) + isin(2pi) = 1 + 0 = 1 but on my paper I wrote...
18. Need help integrating? Format Help?

Homework Statement This may seem like a strange question but I need help putting and integral into wolfram alpha/mathematica. I have to find <x>, <x^2>, <p>, and <p^2> for a given wave function. I know the formulas for all these values but the wave function is ψ(x,t)= Axe^[-x^2...
19. Quantum Wave Function (Determine V(x,t))

Homework Statement A particle is moving in one dimension in a potential V(x,t). The wave function for the particle is... and then the equation is given.. Show that V is independent of t, and determine V(x). Homework Equations The Attempt at a Solution I don't know where to...
20. Simple Complex Number Review Question

Do u mind showing me the cancellation written on?
21. Simple Complex Number Review Question

Do you mind showing me the e^(-i@) + e^(-i@) cancellation?
22. Simple Complex Number Review Question

Homework Statement z=1 + e^(iθ) calculate z^2 and lzl^2 Homework Equations The Attempt at a Solution for z^2 (1+e^(iθ))(1+e^(iθ)) = 1 + 2e^(iθ) + e^(i2θ).. is that the final answer? i expanded it into cosines and sines as well but that doesn't simplify anymore i don't...
23. Laplace Transformation

Homework Statement Find the Laplace transformation of the following function by using iterations of integration by parts: f(t) = tsin(t) Homework Equations The Attempt at a Solution I know how to do integration by parts (as learned in calculus) but have never seen a funtion...
24. Quick Guass's Law of Gravitation Clarification

ahh thank you so much
25. Quick Guass's Law of Gravitation Clarification

Homework Statement The picture attached shows the answer to a sample problem... I don't understand the last step... how does ∇g = C (1/r^2)∂/∂r(r^4) ? where did the r^4 come from and what does the triple dot triangle: "∴" mean? I understand every step except for the last one... thanks...
26. Basic Compton Scattering

ahhh nevermind i figured it out.. thanks for the guidance..it's appreciated!
27. Basic Compton Scattering

Yes i derived that equation but i still don't see the connection to the energy of the electron... I assume that to maximize the energy of the electron the change in wavelength should be largest at an angle of pi correct? that would yield 2h/mc=delta lambda but now how do i find the energy of...
28. Basic Compton Scattering

I know momentumn does too but how do i combine these two to get the total final energy?
29. Basic Compton Scattering

Homework Statement A photon carrying energy of 40keV scatters from an electron initially at rest. what is the maximum energy the electron can have? Homework Equations The Attempt at a Solution I tried using conservation of energy Initial: 40keV (energy of photon) + mc^2...
30. Special Relativity Question

Ugh nevermind lol I don't have it... and it's driving me crazy. V= L/T = L'/T' and I know L and T'. Time dilation says T=T'sqrt(1-A^2) where A is V/c so i plug in V=L/(T'sqrt(1-A^2)) and solve for V but I get (V^2)(T')^2 - ((V^4)(T')^2)/c^2 = c^2 ahhhhhh
31. Special Relativity Question

got it..thanks
32. Special Relativity Question

soo...what relations? I'm still stuck
33. Special Relativity Question

Homework Statement A particle has a rest energy of 1672MeV and a lifetime of 8.2x10^-11 s. It creates a .024m long track in a lab detector. What is the total energy of the particle Homework Equations The Attempt at a Solution Total Energy = mc^2 + mc^2(1 - A) where A is...
34. Simple Harmonic Motion

Homework Statement A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...
35. Rope Sliding Over Friction less Peg

Homework Statement A uniform rope of mass M and length L is hung off a small peg. The rope moves without friction. Obtain an equation for the length of the rope hanging to the right of the peg, which is denoted x(t). Homework Equations The Attempt at a Solution I set up a net...
36. Basic Special Relativity (Time Dilation)

ahhh finally got it.. Thanks a bunch!
37. Basic Special Relativity (Time Dilation)

I don't think you can )easily) solve for T-T' with the expansion... T=T'/1-ax ==> T-Tax=T'...unless I am missing some simply algebra i don't see how to manipulate to solve for T-T'
38. Basic Special Relativity (Time Dilation)

How does this help though? that just makes 1-ax = 1 - (7.8125e-13) which still is very close to 1. Where/how do you produce the 16.7 nanoseconds?
39. Basic Special Relativity (Time Dilation)

Homework Statement The Concorde traveled 8000km between two places with an average speed of 375 m/s. What is the time difference between two atomic clocks, one on the train and one at rest with respect to the train? Homework Equations T=AT' where A is the Lorentz gamma factor The...
40. Potential Function of a Conservative Force

So would it just be U(x,y)=xy^2 + xy^2 = 2xy^2 + c because it's a scalar?
41. Potential Function of a Conservative Force

Homework Statement Given a conservative force with the Force given as F=y^2(i)+2xy(j), what is the potential function related to it. Homework Equations -dU/dx = F The Attempt at a Solution I know I have to integrate the components but I don't know how... since the (i) direction was...
42. Constant Acceleration of a skier Problem

ok thank you!
43. Constant Acceleration of a skier Problem

I understand that I need to find where they intersect but I don't know how get the equations of the parabola and the line. I have the slope of the incline but no point. And I don't know the parabola either...how do I come up with the equations?
44. Constant Acceleration of a skier Problem

Homework Statement A skier travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 28 m/s. The landing falls off with a slope of 32 degrees. a.) How long is the skier airborne? ignoring air resistance b.) How far down the incline does the jumper...
45. Showing nonsingular matrix has a unique solution

correct...The problem says (i think which you are trying to prove) that it has a solution and the solution is unique. So you know that the matrix of the arbitrary nxn matrix will have a pivot and ever row and column. To represent that use the given that it is a linear system with nonsingular...
46. Evaluate a Definite Integral to find Work

Homework Statement Evaluate: from x=0 to x=1 and y=0 to y=1 ∫(y^2 + 2xy(dy/dx))dx and carry the integration out over x Homework Equations The Attempt at a Solution I know how to calculate double integrals with multiple variables but the (dy/dx) throws me off and it says to...