Classical mechanics Definition and 1000 Threads

Homework Statement [/B] Consider a half-atwood machine on a cart as below, with mass m_2 attached to M via a frictionless track that keeps it pinned to M but allows it to move vertically. All surfaces (except between the wheels/ground) are frictionless, and the pulley and rope are massless. If...

Homework Statement I need to find the partial derivative of the action S with respect to the generalized coordinate q(tf) and according to my textbook, it should equal the generalized momentum p(tf). How can I derive this? Homework Equations S = integral of L dt, with boundary ti to tf. (ti...

Hello, I have a question about the interaction between particles. Maybe it's a simple question, but it's bothering me. Consider Coulomb's law. From Wikipedia we have a simple definition to illustrate: "The magnitude of the electrostatic force of interaction between two point charges is directly...

Homework Statement A particle in SHM is subject to a driving force F(t)= ma*e^(-jt). Initial position and speed equal 0. Find x(t). Homework Equations F = -kxdx = mvdv F(t) = F(0)*e^(iωt) x(t) = Acos (ωt +φ) The Attempt at a Solution I have no idea how to deal with the exponential term. I...

Homework Statement At a latitude of 50° north a mass is hanged by a massless string. By the means of an angle how much does the mass deviate from the Earth's radius due to rotation of the earth? Consider the Earth as a spherical body. Homework Equations Fcp=mv^2/r w=dθ/dt v=wr The Attempt at a...

Homework Statement This is the solution of Brachistochrone . Homework EquationsThe Attempt at a Solution I am very confused that how the x in equation(6.24) get its value a(1-cosӨ) ? What is the technique behind this solution of x?

Hi guys I'm searching for a good undergraduate physics textbook on classical mechanics that might has an intro to langranzians and Hamiltonians, that I could tackle right now. I'm actually getting through apostol calculus 1 (just reached partial derivatives). I want it to be hard to follow ,but...

Hi, This might sound very basic and but i am just starting to learn physics. I an lecture by prof. walter lewin, he descibes the hunter and monkey scenario. The monkey jumps from the tree as soon as the hunter aims and shoot his gun. the bullet hits the monkey anyway. In calculating the time it...

Homework Statement A truck hauling a big tank of oil starts at position x=D (Chicago) and heads due west (–x direction) toward its destination at x = 0 (Des Moines). At Chicago, the total mass of the loaded truck is M and the mass of oil it is carrying is λM. (Thus M(1–λ) is the "tare" mass =...

Hi, I am learning classical mechanics right now, Particularly Noether's theorem. What I understood was that those kinds of transformations under which the the Hamiltonian framework remains unchanged, were the key to finding constants of motion. But here are my Questions: 1. What is...

Homework Statement Homework Equations W=-ΔU for conservative force. The Attempt at a Solution Let all three forces be conservative. Since particle comes back to where it was, ΔU=0. Hence ΔUAB+ΔUBC+ΔUCA=0 Hence WCA=-WAB-WBC For case A, if both WAB, WBC>0, then WCA<0. Else its greater than...

Homework Statement A particle of mass m is whirled on the end of a string of length R. The motion is in vertical plane in Earth's gravitational field . The instantaneous speed is v when the string makes angle Ө with the horizontal. Find the tension T in the string and the tangential...

Homework Statement At which minimum velocity should you throw the ball horizontally if you are standing on a hemispherical rock of radius R so that it at no point touches the rock and lands at the minimum distance from the rock horizontally. Find the expression that solves for initial velocity...

Hi all! I was directed (on another thread) to professor Leonard Susskind's first lecture on classical mechanics. I learned a lot from it, however he introduced a "rule" for "acceptable" classical fields/equations that I have a little trouble with. He explains classical mechanics as if you know...

Homework Statement A string wraps around a uniform cylinder of mass M, which rests on a fixed plane with angle θ. The string passes up over a massless pulley and is connected to a mass m. Assume that the cylinder rolls without slipping on the plane, and that the string is parallel to the plane...

I want college-level problems books on the following physics topics: 1)Quantum Mechanics 2)Electromagnetism 3)Classical Mechanics 4)Thermodynamics (and Statistical Mechanics) 5)Waves 6)Special Relativity

I have a degree in Electrical Engineering and I want to learn classical mechanics in my free time. I originally planned to just learn out of a textbook, but I saw the university near me has a graduate course in classical mechanics this semester, and I am considering enrolling in the course...

Homework Statement Given the potential energy function V(x,y)=V(ax-by) where a,b is an arbitrary constants differentiate with respect to x and y. Homework Equations Multivariavle differentiation The Attempt at a Solution The answer yields (d/dt)p1=-aV'(ax-by) (d/dt)p2=+bV'(ax-by). The right...

Homework Statement Consider two objects with masses ##m_1## and ##m_2## exerting forces on each other with magnitude ##F##. If no other net forces act on the objects, they obey the equations of motion ##m_1\ddot r_1=F##, ##m_2\ddot r_2=-F## Show that the corresponding equations of...

So I really have a few questions. First, is it wise to take the following classes in the same semester? Quantum Mechanics I - At the level of Griffiths' Intro to Quantum Mechanics, chapters 1-5ish Classical Dynamics - At the level of Thorton and Marion, Chapters 1-12, ends with coupled...

Homework Statement The human beings are standing at equal distances from a big and high wall. Distance between them is 150 m. When one fires the gun the other hears two shots in an interval of 2 seconds, using the speed of sound to be 340.298 m/s calculate their distance to the wall. Homework...

There was an equation I saw before and I think it pertains to Boltzmann and thermodynamics. I think it describes the entropy of a system. From what I can remember, it involves the symbol omega to denote micro states, k for a constant, and a logarithm somewhere. Anyways, hopefully some one knows...

Homework Statement I was wondering that, if you are standing above a bridge with a height h and throw a rock in your hand with mass m and initial velocity v naught of 0, could you calculate how big of a splash said rock makes when it hits the water? Homework Equations Not sure, I'm guessing...

Hi everyone. I'm confused with the balance of energy in this situation (I'm comparing the mechanical energy, initially, at rest, at a height = h, and then, at the end, at height = 0). It doesn't seem to be fine, maybe I missed something. I'd appreciate some help - Everything is in the .jpg...

Homework Statement A person is standing over a well and drops a rock. After 2.4 seconds he hears a rock splashing into the water. Take the speed of sound to be 300m/s and calculate the depth of the well. Homework Equations x=v/t for constant velocity x=1/2at^2 for accelerated motion The...

Hello all. After reading both chapters on rigid body motion both in Kleppner - Kolenkow and Taylor books, I still do not undertand the physical meaning of Euler equations. Let me explain: In Kleppner - Kolenkow, they claim (page 321 - 322) that in Euler equations, Γ1, Γ2 and Γ3 are the...

Homework Statement Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2 Homework Equations L=ř^2/(2w) - wr^2/2 and H=př-L The Attempt at a Solution Notice here ř means first derivative of r. As i...

Homework Statement A string is connected to a box A mass M at its left end and a box B mass 2M at its right end. Boxes A and B start pulling in opposite directions at the same time with forces which are time dependent and described by functions F(t)=Ct for box A and F(t)=Dt for box B. Values of...

Homework Statement I was thinking about different scenarios in circular motion and came to this scenario. Suppose there's a car moving in a circle around some track. Obviously it's the frictional forces between the tyres and the road which provide the centripetal force. Now, suppose there's a...

Dear all, I'd like to know what is the place/use of complex variables (and complex analysis) in classical mechanics. By the way, is there any? Thanks for your help. Best regards!

I'm currently collating my own personal notes and would really appreciate some feedback on my description of the relativity of position and velocity in classical mechanics. Here is what I have written "Position is clearly a relative quantity as two inertial frames S and S' displaced by a...

Homework Statement So in this exercise, two masses m connected by a massless rod with length l are swinging from two springs with constant k and length b. The two springs also make an angle Ө with the vertical. This angle, for this exercise specifically, is very small. (Gravity can also be...

Homework Statement Two identical disks with mass m and radius r are connected via a massless wire of length L which is winded up around both disks. Disk B is connected to the ceiling and is free to rotate around its axis. Disk A is besides disk B and will fall due to the gravitational force...

This is a problem from Mechanics by Kleppner and Kolenkow1. Homework Statement Two identical masses M are pivoted at each end of a massless pole of length L. The pole is held leaning against frictionless surfaces at angle θ, as shown, and then released. Find the initial acceleration of each...

I have studied physics during my undergraduate years but I want to relearn everything as I came to my realization that I'm weak because of the quality of education I got. So far, I want to know if my order of study is good. Classical Mechanics: An Introduction to Mechanics by Kleppner and...

Hello Seniors, I have done BSc in Physics but couldn't take lectures of Classical Mechanics. I am Almost blind in this subject. Since it's a core course in Physics, so i need your help to understand the basics in this course. If anyone of you have any helping material/notes/slides etc which...

Hello all. I have almost finished chapter 4 on energy in Taylor's classical mechanics book. But in the last example in this chapter I got confused. Here it is: "A uniform rigid cylinder of radius R rolls without slipping down a sloping track as shown in Figure 4.23. Use energy conservation to...

I know the definition of the Poisson bracket and how to derive elementary results from it, but I'm struggling to understand intuitively what they are describing physically? For example, the Poisson bracket between position q_{i} and momentum coordinates p_{j} is given by \lbrace...

A question from a classical mechanics past paper described a particle of mass ##m## that had a pair of horizontal identical springs of spring constant ##k## attached on either side and that the mass is free to move horizontally. The mass is also placed on a table that gives rise to an...

Homework Statement A train wagon of mass M moves on a rail with constant velocity V (without friction). It passes a sand hopper which pours sand in the wagon at constant rate C [kg/s]. The sand falls vertically so it does not transfer any horizontal momentum to the wagon. The length of the...

Homework Statement A ball, which is launched in the air with velocity V, has inelastic collisions with the floor: the kinetic energy after each collision is k times the kinetic energy before the collision, where k<1. Assume that the gravitational acceleration is constant: g [m/s^2]. I was asked...

I'm an EE major doing a minor in physics. I have to take a standard intermediate electromagnetism course from the engineering department (which is just a more applied version of the physics department course). To get my minor, I was thinking about getting permission to use this course as a...

question here Hello, this isn't really a homework question as I understand how to solve it. But just out of curiosity, is it possible for this to actually be set up in real life and for the 1 kg mass to be in equilibrium? because when I imagine such a situation I feel that the revolving puck...

Hello, PF, I'm going to be taking graduate CM next semester and the professor uses Landau's textbook instead of Goldstein, which I take is the usual text. What are the appreciable differences between the books and what kind of math will be needed? I have the basics-complex analysis, linear...

This is the link to the relevant paper. I have to show that vector (t', x', y', z') lies on the sphere. But for that to be, V^2 has to be 1 according to the equation in the introductory part of the section 2. That, by definition, means that E=-m/2. What does that mean, and why is this solution...

Suppose I am stationary in space (no velocity). My body is straight. There is a stationary ball right beside me (also no velocity). Then an accelerating platform hit my feet and the ball from under. Now the ball and I are in contact with the platform constantly and accelerate at the same rate as...

I have read some parts of the book but noticed some errors that are to much for me to be uncomfortable for the rest of the book. Anyone encountered such problems with the book? Mainly, encountering too many errors? Even the errata in the publisher's site didn't gave sufficient corrections to the...

Homework Statement Jupiter has a core of liquid metallic hydrogen, with uniform density $\rho_c$, with radius $R_c$. This is surrounded by a gaseous cloud $R_g$, where $R_g>R_c$. Assume the cloud is of uniform density $\rho_g$. The problem also specifies that we are to assume both regions of...

Homework Statement Given a harmonic oscillator with mass m, and spring constant k, is subject to damping force F= cdx/dt and driven by an external force of the form F[ext]= FoSin(wt). A) Find the steady state solution. B) Find the amplitude and the phase. Homework Equations F=-kx the steady...

I don't know very much about quantum mechanics, but if I'm correct, the future can not be predicted with certainty according to quantum mechanics. If this is true, how can we have formulas in classical mechanics that do predict the future with certainty?