Homework Statement
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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...
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...
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)
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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
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...
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...
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...
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'
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...
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...
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?
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...
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...
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...
Homework Statement
For a hill the elevation in meters is given by z=10 + .5x +.25y + .5xy - .25x^2 -.5y^2, where x is the distance east and y is the distance north of the origin.
a.) How steep is the hill at x=y=1 i.e. what is the angle between a vector perpendicular to the hill and the z...
Homework Statement
expand sinx about the point x=pi/4
Homework Equations
The Attempt at a Solution
I know how to find each individual terms but how do I got about finding the general term for this series?
Homework Statement
A sphere of radius .5m, temperature of 27 deg C, and emissivity = .85 is located in an environment of temperature 77 deg C. At what rate does the sphere (a)emit and (b)absorb thermal radiation? (c)What's the sphere's net rate of energy exchange?
Homework Equations...
Homework Statement
Expand sinx about the point x= pi/4. Hint: Represent the function as sinx= sin(y+pi/4) and assume y to be small
Homework Equations
The Attempt at a Solution
I thought the problem was simply asking to expand sinx with the McLauran expansions about the...