After studying the methods of Lagrange and Hamilton for a bit I still find myself uneasy about the action. I don't even know how to define it other than the integral of the Lagrangian with respect to time:
$$I=\int_{t_1}^{t_2}\mathrm{d}t\, L(q,\dot{q},t)$$
Does the action have any...
Homework Statement
Find the electric field a distance z above the center of a circular loop of radius r that carries a uniform line charge λ.
Homework Equations
$$E=E_r\hat{r}+E_z\hat{z}$$
$$E_r=\frac{\lambda}{4\pi\epsilon_0}\int_0^r\frac{1}{\mathcal{R}^2}\sin{\theta}\,dr$$...
Homework Statement
Consider the wave function $$\Psi(x,t)=Ae^{-\lambda|x|}e^{-i\omega t}$$
Where ##A##, ##\lambda##, and ##\omega## are positive real constants.
(a)Normalize ##\Psi##.
(b)Determine expectation values of ##x## and ##x^2##.
Homework Equations...
Edit: Can someone change the name of the thread somehow? I accidentally posted it without changing the name.
(Moderator note -- title updated.)
Homework Statement
The question is quite long so here is a picture: http://gyazo.com/dc917d1885b6ffebb0a39e2409af4d61
Homework Equations...
Homework Statement
A chain of mass M and length ##\ell## is suspended vertically with its lowest end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of chain, ##x##, has fallen? (Neglect the size of individual links.)...
I've been thinking about this for around 7 months now, which is way too much; Munkres seems like the "typical" introduction to topology book (kind of like how Griffiths is the "typical" E&M text), and various people (from the reviews over at Amazon) make it seem like it is an undergraduate level...
Homework Statement
A mass m whirls around on a string which passes through a ring, as shown. Neglect gravity. Initially the mass is distance r0 from the center and is revolving at angular velocity ω0. The string is pulled with constant velocity V starting at t = 0 so that the radial distance...
From what I've experienced so far, classical mechanics (well, newtonian since I'm still on K&K) is very difficult. It gets even harder because I have no teacher and my next math class is honors algebra 2 (I already know calculus though). I'm able to solve problems (I'm on chapter 3 about...
Homework Statement
A mass m is connected to a vertical revolving axle by two strings of length l, each making an angle of 45 degrees with the axle, as shown. Both the axle and mass are revolving with constant angular velocity ω. Gravity is directed downward.
(a) Draw a clear force diagram for...
What would be a good mechanics book after K&K that includes Lagrangian and Hamiltonian mechanics? Also, would Griffiths' Electrodynamics be suitable after Purcell? What about Griffiths' Quantum Mechanics (ignoring the math pre-reqs)?
Homework Statement
A 45 degree wedge is pushed along a table with constant acceleration A. A block of mass m slides without friction on the wedge. Find the block's acceleration. Gravity is directed down.
Homework Equations
Constraint Equation...
Homework Statement
A painter of mass M stands on a scaffold of mass m and pulls himself up by two ropes which hang over pulleys, as shown. He pulls each rope with a force F and accelerates upwards with a uniform acceleration a. Find a - neglecting the fact that no one could do this for long...
Homework Statement
At t = 0, an elevator departs from the ground with uniform speed. At time T_1 a child drops a marble through the floor. The marble falls with uniform acceleration g = 9.8 m/s2, and hits the ground T_2 seconds later. Find the height of the elevator at time T_1
Homework...
How many problems should a physics student (or self-learner in my case) be able to solve correctly? I assume it's safe to say that all (*) problems should be correct, but what about (**) and (***) problems? How many of them should be done correctly? Is getting the correct answer important...
Homework Statement
A chain with length ℓ is held stretched out on a frictionless horizontal table, with a length y0 hanging down through a hole in the table. The chain is released. As a function of time, find the length that hangs down through the hole (don't bother with t after the chain...
Homework Statement
In most problems in this book, the ropes, cords, or cables have so little mass compared to other objects in the problem that you can safely ignore their mass. But if the rope is the only object in the problem, then clearly you cannot ignore its mass. For example, suppose we...
Homework Statement
Evaluate: \int{xe^{ax}}dx
Homework Equations
Integration by substitution
The Attempt at a Solution
I'm on a phone at the moment. My work: http://postimg.org/image/v4hdr5uqx/ [Broken]
The correct answer was:
\frac{xe^{ax}}{a}-\frac{e^{ax}}{a^2}
What do guys (and girls) think about Halliday-Resnick? Is it better than Sears and Zemansky's? I wouldn't mind too much calculus in an introductory book (I know it's going to be basic). I was thinking of getting Halliday-Resnick as a book to use along side a physics course I'm taking for extra...
Homework Statement
Find the derivative of \frac{Q}{4\pi \epsilon_0 r}
Homework Equations
\frac{d}{dx} \frac{1}{x}=\ln x
The Attempt at a Solution
Assuming Q and the rest of the variables under it are constant, \frac{Q}{4\pi \epsilon_0}\frac{1}{r} then the derivative should be \ln...
Homework Statement
F=-mg-m\alpha vF=m\frac{dv}{dt} =
\int_0^v \frac{dv'}{g+\alpha v'} = -\int_0^t dt'
This equals:
\ln \frac{1+\alpha v}{g} = -\alpha t
I don't understand why it does; I keep getting an incorrect answer. Can anyone tell me what I'm doing wrong?
Homework Equations
The Attempt...
Homework Statement
Evaluate: \int \frac{3x}{x^2+2}
Homework Equations
\int \frac{1}{u} \frac{du}{dx} dx = \ln u + C
The Attempt at a Solution
I got a horribly wrong answer: \frac{1}{2x}\ln (x^2+2)+C
This was done by multiplying \frac{du}{dx} by \frac{3x}{u}
This part is what...
Homework Statement
How would you define a number that is raised to an imaginary power?
Homework Equations
λi= ?
λ = 6+4i
The Attempt at a Solution
eln x = x
Other than that I have absolutely no idea how to go about solving this.
I was arguing today with a friend and the argument seemed pretty pointless because we had nothing to back up our facts with, so I thought about hearing your opinion(s). Do black holes violate laws such as the conservation of matter + conservation of energy? I'm currently leaning towards 'yes'...
Hey all.
I'm a high school freshman; so I'm not exactly 'wise' when it comes to education. I've been self teaching myself physics over the last couple of months from Sears and Zemansky's University Physics, 12th edition, and although I started out very badly, I now have a very good grasp over...
Homework Statement
A mass m = 5.500 kg is suspended from a string of length L = 1.570 m. It revolves in a horizontal circle (see Figure). The tangential speed of the mass is 2.874 m/s. What is the angle theta between the string and the vertical?
PIC OF DIAGRAM...
I understand the Fourier transform conceptually, but I am unable to reproduce it mathematically; I am very familiar with calculus and integration, but I am taking a QM course and I need to know how to apply it. No websites or videos are able to give me a good explanation as to how I can use it...
Homework Statement
A stone is thrown horizontally from a height h above the ground (h > 0). The stone hits the ground after having traveled a horizontal distance x (x > 0). What is the expression for the initial speed v of the stone? Neglect air resistance. (please use the variables x and h...
What are your opinions on infinitely close objects / numbers?
I believe in them, because I can say 3.9 is close to four, but 3.999 is as well, and so is 3.99999999.
I've heard of LOTS of scientists who disagree with this, can anyone prove this wrong (or right)?