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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Deriving Snell's law via Lagrangian mechanics

A particle moves with kinetic energy $K_1$ in a region where its potential energy has a constant value $U_1$. After crossing a certain plane, its potential energy changes discontinuously to a new ...
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Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they ...
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39 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
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Chocolate dynamics

Now I have found a possible model on how to describe chocolate when it is chewed. It has to do with geometrical transformations when a curve $\gamma$ intersects a manifold $M$. The chocolate is ...
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1answer
44 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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Will the center of mass of the whole system change when object swims on curved surface?

In the example given here, the object can move on the frictionless surface of the sphere by changing its shape periodically. So will the center of mass of the whole system change after the object ...
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958 views

Connections between classical and quantum mechanics?

I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
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Conceptually, what is negative work?

I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
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34 views

Force in colliding snooker balls

If a snooker ball is traveling at 2m/s and hits another ball, the first ball will stop dead and the second will accelerate instantaneously to 2m/s. F=ma, so this would seem to imply an infinite force. ...
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How to find out whether a transformation is a canonical transformation?

We had a couple of examples where we were supposed to calculate the Canonical Transformation (CT), but we never actually talked about a condition that decides whether a transformation is a canonical ...
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72 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
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46 views

Rheological behavior of chocolate

If someone eats chocolate, the chocolate goes through the following configurations: $\chi_0:$ chocolate is solid and has a smooth Surface everywhere; the Riemann Tensor vanishes on every Point of the ...
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86 views

How was time defined before we knew the speed of light was constant or in classical physics? [closed]

Nowadays, we now about $c$ the universal speed of light. This lets us define the notion of distance in terms of time (despite the fact that it works the opposite way for our common units.) Before ...
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84 views

Why Galilean spacetime is not $\mathbb{E}^4$?

In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
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72 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses ...
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5answers
322 views

Is the polar coordinate system non-inertial or inertial?

Consider a car driving around in a circle lying in the plane and suppose we were interested in determining its acceleration as measured by an observer stationary on the "ground" or whatever. ...
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330 views

Classical Rutherford scattering (partial) derivation

I am having trouble answering the following question, please could you help! Thank you in advance for any assistance you can give. Consider classical Rutherford scattering of a particle with mass $m$ ...
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2answers
110 views

Hockey puck collision [closed]

I have a homework question in which a sticky hockey puck traveling at constant velocity parallel to the side of the rink strikes a stationary puck and sticks to it. The angels between centres at ...
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47 views

Time reversed Abraham-Lorentz reaction force

The Abraham-Lorentz radiation reaction force on a charged particle is given by: $$\mathbf{F_{rad}} = \frac{q^2}{6\pi\epsilon_0c^3}\mathbf{\dot{a}}$$ I understand the situation where one fires a ...
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1answer
64 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
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1answer
114 views

How much force can bolt cutters exert?

What's the mechanical advantage of an ordinary, let's say, 3 feet long bolt cutters? How many pounds can they exert? I'm asking because I have a lock which is apparently immune to over 9 tons of ...
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88 views

A question on Lagrangian dynamics an the velocity phase space

I've struggled in the past with understanding why we can treat position and velocity as independent variables in the Lagrangian, but I think I may have finally become a bit more enlightened on the ...
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41 views

Quantum chaos vs classical chaos

There is this popular conjecture from Bohigas, which says: When the analogeous classical system of a quantum system shows chaotic behaviour then the spacing distribution of the quantum system ...
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1answer
55 views

What is the criterion for a change to be adiabatic?

I'm trying to understand whether the change of a parameter $\lambda$ of a Hamiltonian $H$ is adiabatic. Reading Landau and Lifshitz "Mechanics", I see ... let us suppose that $\lambda$ varies ...
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1answer
65 views

Jumping vs pulling my hair upwards

Why can't I jump or fly if I pull my hair upwards, while I can jump using my legs? The way I see it, when jumping someone lifts its body using the muscles in the legs (while the feet are standing ...
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3answers
144 views

Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
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136 views

Natural Frequency of an object and the phenomenon of resonance!

I have read about the term natural frequency in quite a lot of places. But I haven't found an explanation as to what is vibrating. It was pretty awkward when I couldn't clearly answer my little sister ...
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1answer
118 views

Falling charged objects: energy conservation paradox?

Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$. We raise them both up to a height $h$. In doing so we ...
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28 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
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273 views

Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that ...
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2answers
47 views

Magnetic Field and Flow of Vector Potential

I am sorry, when my question is not really concrete, but here we go. Consider the Hamiltonian function $$H(x, \xi) = \frac{1}{2m}\bigl|\xi - eA(x)\bigr|^2$$ corresponding to a charged particle in a ...
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3answers
79 views

Classical Limit of the Quantum Harmonic Oscillator

The classical harmonic oscillator obeys an arcsine law in that the distribution of positions of the particle over a single time cycle is proportional to $\frac{1}{\sqrt{A^2-x^2}}$, $A$ being the ...
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79 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
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41 views

On the isotropy of materials

Good morning. I am working on Honeycomb structures and first of all I would like to understand whether it is Isotropic or not, and , if the latter holds which kind of anisotropy it has. How to do it? ...
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1answer
64 views

Is Liouville's theorem valid for dimensionally restricted systems?

Liouville's theorem states that the phase space volume of a system is conserved over time. Intuitively, this seems to imply that if a system is at some time constrained to, say, a curve in phase ...
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2answers
74 views

Does sound have a “louder” direction?

I have a question about the propagation of sound waves. We have two TV's in our house that are almost right on top of each other. One is located on the first floor and the other one is located on ...
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3answers
311 views

Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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60 views

Calculating the flex of a solid bar under force

I want to calculate how much a solid bar will flex when force is applied to it. The set up looks like this: The rod (in green) rests on two stationary points, and the force is applied in the center ...
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How was the formula for kinetic energy found, and who found it?

My questions mostly concern the history of physics. Who found the formula for kinetic energy $E_k =\frac{1}{2}mv^{2}$ and how was this formula actually discovered? I've recently watched Leonard ...
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2answers
42 views

Can center of mass move without any force?

For instance, consider a weight on one end of the ring. Assume that the ring has negligible mass compared to the weight. When the weight splits into two, moves around the ring and recombines at the ...
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18 views

How do I calculate the speed of the air particles flowing out of a balloon? [duplicate]

I am trying to find out what kind of force would a leakage in a balloon cause. What i used is F = (mass flow)speed = (air density)(surface of leakage hole)*speed. I don't know how I could calculate ...
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1answer
201 views

Equation for Terminal Velocity on an inclined plane and the time it takes to reach it

Now I'm doing a research on the matter similar to this thread : Terminal Velocity of identical shape/size objects which is very self explanatory and very helpful. However in my case, the objects will ...
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3answers
59 views

What relative masses are required for them to collide n times in this scenario?

Consider two masses, m and M, where M>m. They begin at rest on an infinite frictionless surface that is flat in one direction and sloped in the other direction. Mass m is placed a little bit up the ...
3
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1answer
117 views

Springs at an angle [closed]

I'm trying to find the equation of motion for the following system: This is how I proceeded: Let's call the length of the hypotenuse $s$. Then, $$F = 2 \sin{\theta}\cdot-k(s - l_o) = -2kx ...
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1answer
29 views

Acceleration in a system equal for every body — why?

A 1 kg cart can slide frictionlessly on the table. The black weights each weigh 1 kg. The pulleys are frictionless. The task is to determine the acceleration of the cart. For the left-most ...
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1answer
62 views

Fluids in a U-shaped Tube

One of the users asked a question about the Fluids in U-shaped Tube. I was wondering and I tried to imagine that the membrane is fixed and the left side is filled up until $h_1=h_2$. So my question is ...
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2answers
28 views

What is the equation of motion for a driven spring?

A spring of length $l$ and spring constant $k$ is suspended vertically with an object with mass $m$ attached at the bottom. If you take the top of the spring and oscillate it such that its ...
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24 views

Parametric impulse on driven, damped oscillator

I've been thinking about driven harmonic oscillators recently. I know how to calculate their response to a sinusoidal drive, and their response to an impulse or more generally an arbitrary drive via ...
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38 views

Born-like measuring rule in classical experiments

this 2011 paper "Born's rule from measurements of classical signals by threshold detectors which are properly calibrated" by Khrennikov investigates the theoretical possibility of Born-like ...