Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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Atwood machine problem [closed]

Sorry for the bad drawing, but I hope that this will help you get a hold of the problem. Consider an Atwood Machine with a total of two blocks, a mass less pulley, ideal string. One block rests on ...
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1answer
298 views

What is the tension in the string of a spherical pendulum? [closed]

Can some one solve it by using Lagrange's undetermined multiplier method or any other method that explains the physics in spherical pendulum system? book references: 1) Classical mechanics by ...
3
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1answer
158 views

Classical dynamics with Schrodinger equation

What are some interesting classical systems for which the dynamics can be reduced to a many-body Schrodinger equation, at least in some useful regions of phase space, and in particular, with many ...
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84 views

How to analyze this constraint question

Let $\gamma$ be a smooth curve in the plane, and introduce curvilinear coordinates $q_1,q_2$ on a neighborhood of $\gamma$; $q_1$ is the direction of $\gamma$ and $q_2$ is distance from the curve. ...
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80 views

Attraction of a Bullet due to Gravity in a Perfect Vaccum

I realise that this might be conventially very difficult to answer because there's no KG or Newtons in space, only particles. As far as I understand, every object creates a 'pull' due to the forces ...
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1answer
544 views

What is the maximum mass that the airplane can have and still maintain enough lift to fly? [closed]

A commercial airplane travels at a speed which is 85% of the speed of sound. The wings of the airplane are designed such that the bottoms of the wings are flat and the tops of the wings are curved ...
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1answer
2k views

Problem with Velocity of efflux [closed]

I am stuck in this problem- I need to find the velocity of efflux at the hole of the container. [We can assume that the area of the hole is negligible in comparison with the base area of the ...
3
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1answer
1k views

What is a bilateral constraint?

In the realm of mechanics/rigid body dynamics, can anyone tell me what a bilateral constraint is? Can't seem to find any information on the exact definition, just uses of it such as "considering only ...
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1answer
126 views

Do vortex tubes work with a reversed end plug?

Would a vortex tube still work if instead of a cone plugged into the 'hot' end you had a smaller hole on the 'cold' end? As I understand it, the point of the cone on the hot end is to only allow the ...
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3answers
166 views

What is the meaning of $U''(x)=0$?

Most potentials with a minimum can be described approximately as a harmonic oscillator. So the procedure is to Taylor expand $U(x)$: $$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$ If we suppose ...
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1answer
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Understanding the Eötvös experiment

The aim of the Eötvös experiment was to "prove" that for every (massive) particle, the quotient $\frac{m_g}{m_i}$ is constant, where $m_g$ is the gravitational mass and $m_i$ is the inertial mass. ...
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0answers
517 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$. Everything I've read on the topic (e.g. this ...
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4answers
463 views

Rotation axis of a rigid body

I am confused about a trivial concept. Let the rotation of a rigid body, say with one point fixed, be described by the equation $\vec{x}(t)=R(t)\vec{x}(0)$, with $R(0)=I$. Then, at each instant ...
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3answers
190 views

Classical Wave Equation - Approximations

I don't understand the derivation of the wave equation given below - $$T \sin (\theta _1) - T \sin (\theta ) = T\tan (\theta _1 )-T\tan (\theta ) = T \left. \left(\frac{\partial f}{\partial z} \right|...
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1answer
435 views

Classical Mechanics - Equation of motion, Lagrangian, Newtons 2nd Law [closed]

I really don't even know where to start with this question. A particle with charge $q$ moving in an electromagnetic field is described by the Lagrangian $$L=\frac{m\mathrm v^2}2+\frac qc\mathrm v\...
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1answer
1k views

Partial and total time derivatives of the Hamiltonian

When does the total time derivative of the Hamiltonian equal the partial time derivative of the Hamiltonian? In symbols, when does $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ hold? In Thornton &...
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3answers
323 views

Does Newton's first law state something substantive, or is it merely describing a convention?

Newton's first law is often said to define what an inertial frame is - namely, a reference frame in which a body not acted on by a force will move with constant velocity. In other words, a frame where ...
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287 views

Forces on a helical screw?

The common screws which we use, are right handed helices, the simplest parametric equations of which are:- $$x(s)=\cos(s),y(s)=\sin(s),z(s)=s$$, with $z$-axis as the axis of the helix. My question ...
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2answers
234 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
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3answers
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Explanation of homogeneity of space and time by giving examples?

while reading landau lifshitz i came across these three terms:- homogeneity of space. homogeneity of time. isotropy of time. it will be a great help for me if someone can explain it to me by ...
2
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1answer
294 views

Can the Lagrange Multipliers depend on the coordinates?

When dealing with Lagrange multipliers to solve systems with constraints we usually have two ways if the constraints are holonomic: Differentiate the constraint and add the appropiate term to the ...
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2answers
339 views

Curve object in liquid under pressure [duplicate]

I would like to know how red forces are compensate in this study. A black solid object is put in a liquid (helium or hydrogen for example). It's a curved solid. Solid don't move up or down, imagine it ...
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0answers
63 views

How to interpret the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$?

There is a small area element of size $da$ and normal vector $\hat n$. I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a ...
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2answers
564 views

How can you solve this “paradox”? Central potential

A mass of point performs an effectively 1-dimensional motion in the radial coordinate. If we use the conservation of angular momentum, the centrifugal potential should be added to the original one. ...
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1answer
448 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
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4answers
531 views

Classical Limit in Quantum Mechanics

Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will ...
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1answer
2k views

Internal kinetic energy and center of mass kinetic energy

For a given system, how can you tell which one is kinetic energy for center of mass and which one is internal kientic energy? K = Kcm + K int For example, "A 150 g trick baseball is thrown at 63 km/...
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247 views

A discrete approach to the catenary

I'm trying to work out a model for the system above, that is, $N$ particles of unitary mass subject to the constraints: $$1=\varphi _i(\mathbf r _1,\mathbf {r}_2,...,\mathbf r _n)=|\mathbf r_i-\mathbf ...
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1answer
152 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
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1answer
111 views

Classical mechanical problem

I have two planes, one characterized by equation $$\phi_1=f(x)-z=0$$ and another $$\phi_2=\alpha y-z=0$$ where $\alpha$ is arbitrary. In their line of intersection(we assume it exist and is continous) ...
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593 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= \...
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1answer
2k views

Explicit time dependence of the Lagrangian and Energy Conservation

Why is energy(or in more general terms,the Hamiltonian) not conserved when the Lagrangian has an explicit time dependence? I know that we can derive the identity: $\frac{\partial \mathcal{H}}{\...
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1answer
104 views

Classical mechanics problem for two boxes [closed]

![enter image description here][2] This question is truly annoying, and I have been stuck for an hour on part D, would greatly appreciate if anyone could shed a light on this problem. Why ans for ...
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0answers
56 views

Acceleration of 2 bodies tied with a string [closed]

Find the acceleration of the block of mass M shown in the figure . The co-efficient of friction between the 2 blocks is μ1 and that between the bigger block and ground is μ2. Could someone help ...
3
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1answer
68 views

Virial of a system

I had obtained $$\overline{E_{kin}} = -\frac{1}{2}\overline{\sum_j\mathbf{r}_j\cdot\mathbf{F}_j}$$ and was asked to show that if the forces are conservative then $$\overline{E_{kin}} = \frac{1}{2}\...
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1answer
142 views

Objects falling on Slopes [closed]

An object falls on a slope and then rebounces....and it is known it hits the slope again...how do I calculate it's second point of contact with the slope....how can a projectory equation be used in ...
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2answers
2k views

Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
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2answers
1k views

Conservation of angular momentum experiment

I've learned in that in this experiment: ...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum ...
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3answers
1k views

Block and inclined plane (INPhO Problem)

The figure shows two blocks on an inclined plane of mass 1kg each.The coefficient of static as well as kinetic friction is $0.6$ and angle of inclination is $30^\circ$ . Find the acceleration of the ...
8
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2answers
371 views

Does Hamilton Mechanics give a general phase-space conserving flux?

Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltonian theory like the flux of an ideal fluid, which doesn't change ...
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4answers
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D'Alembert's Principle: Necesssity of virtual displacements

Why is the D'Alembert's Principle $$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$ stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary ...
2
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209 views

N-body forces in classical mechanics

For a system of two interacting particles 1, 2 we get from the conservation of momentum $$ \dot{\bf{p_1}} + \dot{\bf{p_2}} = 0$$ ...
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1answer
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Direction of tension?

If you draw the free body diagram of the frame above, what direction would the tension force acting on the frame be - to the right or down? Because the rope it horizontal at some points but vertical ...
2
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1answer
199 views

Problem Of Lazy Fish [closed]

Fish achieve neutral buoyancy (so they don't have to swim constantly to stay in place) via a swim bladder. A swim bladder is a little internal sack that they can inflate/deflate with air, which ...
4
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1answer
70 views

Problem Of Pumping Rubber [closed]

One can work out by either lifting weights or using a tension band, which is like a big rubber band. If we model the rubber band as a big spring with spring constant $400 N/M$ how far in meters must I ...
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109 views

How to formally write down the Boltzmann equation?

Can someone write down the Boltzmann equation, not neglecting any of the variables of the involved functions and integrals? Specifically, how to concisely capture the "primed" variables in a sensible ...
2
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1answer
114 views

Can all systems be put in equilibrium?

I'm in a first year statics course. We have spent the whole semester solving for forces and moments so that the system is in equilibrium. When we are given a system, we immediately begin solving for ...
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2answers
219 views

Non-uniqueness of solutions in Newtonian mechanics

In The Variational Principles of Mechanics by Lanczos, in section 1 of Chapter 1, Lanczos states that for a complicated situation, the Newtonian approach fails to give a unique answer to the problem, ...
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1answer
599 views

The virial theorem and a delta function potential

So the virial theorem tells us that: $2\langle T\rangle = \langle \textbf{r}\cdot\nabla V\rangle$. Now I was wondering what would happen if V has te form: $V(\textbf{r}-\textbf{r}') = V_0\delta^{(D)...
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3answers
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How much energy does it take to simply run forward?

I'm interested in tracking as much data about my runs as I can in an effort to get faster, and while I can easily estimate energy expenditure during an uphill run due to the change in elevation, I can'...