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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74 views

Pulling on a weakened rope - where will it tear?

Let's say I have a rope of 10m length and it is weakened in 3 spots: at 2.5m, at 5m and at 7.5m. Weakened means that if enough tension is applied it will tear at these points (all points are equally ...
0
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2answers
97 views

What indicates if an object will bounce back?

If I throw a small rock (m = 1kg) at a big rock (100kg) the small rock rebounds. Let's say my weight is 80kg, if I would jump into a big rock instead of bouncing back I would move in the same ...
1
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1answer
25 views

How do you find the tension in the real world? (Given a rope in a pulley system)

I'm well aware of the formula to calculate tension, however, given a real world situation where you have a closed pulley system. How do you measure the force (i.e., tension) required to pull on the ...
3
votes
2answers
174 views

What's wrong with my calculation of gravitational potential for a uniform sphere?

This is really embarrassing, but I'm not quite sure where I'm going wrong here... Why is this calculation of the gravitational potential inside a sphere with uniform mass distribution incorrect? ...
3
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4answers
218 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
7
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2answers
256 views

Any good resources for Lagrangian and Hamiltonian Dynamics?

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
0
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2answers
44 views

Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?

I am trying to figure out how much force $F$ is needed to push a syringe plunger. The plunger needs to overcome the friction force $F_1$ and (a much smaller) inertia force $F_2=ma$, giving the total ...
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0answers
26 views

Block slides down smooth hemisphere: WHEN will it leave surface? [on hold]

A block is at rest at the top of a frictionless hemisphere of radius r. It is slightly disturbed and starts sliding down. WHEN will it leave the surface of the hemisphere?
3
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3answers
280 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
0
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0answers
31 views

Difficult Atwood's machine problem - Finding $L(t)$ [on hold]

The whole problem was: You have got a turnable disc of mass $m$ and radius $r$. The rope around the disc has mass $M$ and length $l$. At time $t=0$ the disc is not turning. The height difference ...
31
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2answers
2k views

The Impossibility ( or Possibility) of Solving $N$-Body Problem

One can obtain the solution to a $2$-Body problem analytically. However, I understand that obtaining a general solution to a $N$-body problem is impossible. Is there a proof somewhere that shows this ...
5
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3answers
105 views

How do we know that the Fourier transform of space is momentum?

How do we know that the Fourier transform of real space $x$ is the momentum $p$ space or for energy and time, receptively? What's the mathematical process and physical logic?
2
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1answer
44 views

Are there limits to human/devices perception?

As far as i know, measurement devices present measurements based on something that affects the device's particles, for instance, forces, heat, tension, voltage... My question is, given that every ...
0
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0answers
17 views

Time period of a mass around a long wire [on hold]

A particle of mass $m$ is circling an infinitely long wire in a circular motion with radius $r$. The wire's length density is $\rho$ (in meters per kg). Find the the period of one circulation. I am ...
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0answers
18 views

Projectile Motion with uneven ground [duplicate]

I am suppose to find the optimal angle $\theta$ for a stone to be thrown with the initial velocity $u$, from a tower, of height $h$ to obtain a maximum distance (Range) $R$. So I did the some ...
0
votes
1answer
39 views

spinning a water bottle quickly

When we spin a water bottle so quickly, why don't the water inside the bottle come out ? It has to do with the normal force and the apparent weight , i think . but plz someone explain for me how does ...
1
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0answers
28 views

Describing the motion of a point-mass [on hold]

Consider a point-mass moving around a fixed point on a circle with radius $r$ with constant angular velocity $\omega$. At a certain moment of time, the connection is removed, and the point-mass flies ...
1
vote
1answer
90 views

Langevin equations in translational and rotational direction

I want to describe the following system. A bead is connected with a tether. There is a force $\vec{F}_{up}=F_{up}\hat{y}$ that acts on the bead. The tether acts with a force on the bead, this force ...
1
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1answer
26 views

Simulating Phase Space Evolution

I am interested in modeling the time evolution of phase-space $\rho(\vec{q},\vec{p},t)$. I have attempted to use Liouville's theorem $\partial_t\rho=-\sum_{i=1}^{3}(\partial_{q_i}\rho)\dot ...
1
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0answers
25 views

Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth? [duplicate]

Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth? According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 ...
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0answers
27 views

How high can you stack mobile homes? [on hold]

In Ernest Cline's novel Ready Player One, the main character lives in the "stacks" - a dystopian vision of what a trailer park may look like in the future. The "stacks" are primarily composed of ...
0
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3answers
173 views

Interpreting Aristotle's law of motion $\vec F = R\vec v$

The Aristotle's law of motion, which is incorrect, states that The velocity of an object $\vec v$ is directly proportional to the force $\vec F$ acting on it or $\vec F \propto \vec v$ ...
2
votes
1answer
188 views

Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
1
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0answers
113 views

Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth?

According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 Explosive Space Modulator will require $1.711 \cdot 10^{32}~\text{J}$ to shatter the Earth into a gravitationally ...
3
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1answer
109 views

Why is the relationship between velocity and radius curved, in circular motion?

An experiment to model planetary motion: The brown rubber was supposed to model a planet, while we varied the radius $r$ and the mass hanging from the string. Varying the masses was to show ...
0
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3answers
239 views

A few questions about the concept of work

From Wikipedia: The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: $$W = Fd.$$ If I lift some object from a ground, ...
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votes
1answer
263 views

What makes a space a real space?

By "real space" I mean a space in which physical particles move. Consider a color sphere and let a bunch of objects "move" on its surface. "Move" means "change colors". Let there be some rules ...
-8
votes
3answers
289 views

What would happen if an unstoppable force hits an immovable object? [closed]

I realize that the question a rather large paradox, but I do wonder if such a thing were true what would happen, assuming that neither of these "objects" can be destroyed by each other?
0
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1answer
67 views

Gravitational work

As far as I know gravitational work is independent from the path of the object, and I have an object that goes up on a inclined plane to a certain height, and than, after the object reaches the edge ...
0
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0answers
1k views

Studying from “Berkeley Physics Course Volume I - Mechanics” [closed]

I'm a first year physics student and the main source for our Physics I course is "Berkeley Physics Course - Volume I." I'm having a hard time understanding this book because it assumes a pretty high ...
3
votes
1answer
380 views

Hamilton-Jacobi equation with time dependent Hamiltonian

I was struggling with this exercise about Hamilton-Jacobi equation. I have to solve by menas of Hamilton's principal function the system with Hamiltonian: $$\tag{1} H=\frac{p^2}{2m}-mAtx $$ with $A$ ...
0
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2answers
34 views

What's the physical interpretation of an arbitrary normal mode for masses and springs?

Consider the following system consisting of 3 masses and 4 springs : I have learned that this system posseses three normal modes, corresponding to its three natural frequencies, say ...
6
votes
5answers
794 views

Classical Mechanics contradicts Conservation of energy?

Imagine a Stanford torus rotating with 1 rpm so that centripetal/reactive centrifugal acceleration provides about 1.0g of artificial gravitational acceleration inside the ring. The picture below shows ...
0
votes
1answer
41 views

What am i doing wrong here(dynamics)?they should give the same answer [closed]

So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass: First picture so: $$ -mg + T \cos \alpha = ...
4
votes
1answer
145 views

What is the theoretical upper limit on the rigidity of a material?

Take a perfectly rigid metal rod of length $2\ell$ and some uniform linear density. Place one end (‘south’) at $(0,-\ell)$ and the other (‘north’) at $(0, \ell)$. Over some reasonably short time ...
9
votes
1answer
273 views

Understanding Poisson brackets

In quantum mechanics, when two observables commute, it implies that the two can be measured simultaneously without perturbing each other's measurement results. Or in other words, the uncertainty in ...
1
vote
1answer
71 views

Is there an error in Susskinds' derivation of Euler-Lagrange equations?

http://imgur.com/kZO5C0V First, I believe there is a trivial error. The second equation should have another $\Delta t$ multiplying everything on the right. It is divided out later when the equation ...
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0answers
25 views

Equilibrium Points in Lagrangian Mechanics

Suppose we have a one particle system with generalized coordinates $q_i$. In classical mechanics, the corresponding Lagrangian is $L = T - V$. Assume $V(q)$ is time-independent. What additional ...
7
votes
4answers
832 views

Connection between Poisson Brackets and Symplectic Form

Jose and Saletan say the matrix elements of the Poisson Brackets (PB) in the $ {q,p} $ basis are the same as those of the inverse of the symplectic matrix $ \Omega^{-1} $, whereas the matrix elements ...
2
votes
2answers
234 views

Bertrand's theorem

I found in Goldstein's Classical Mechanics that the condition for closed orbits is given by $\frac{d^2 V_{eff}}{dr^2}>0$.(bertrand's theorem). Can somebody explain to me, how this inequality is ...
3
votes
2answers
1k views

How does the speed of an incoming pitch affect the speed of a baseball after it's hit?

Which will go further if a batter manages to hit it with a baseball bat: a baseball thrown to the batter at 90 miles per hour or one thrown at 60 miles per hour?
0
votes
1answer
17 views

Period of swinging incomplete hula-hoop

I was working on a problem where I had to calculate the period of a swinging incomplete hula-hoop given its center of mass and radius. It only swings with very small amplitude so I considered the ...
7
votes
1answer
292 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
5
votes
3answers
149 views

What forces are at work in a loose ball bearing bicycle hub?

I've landed in a physics debate amongst bike mechanics. In a typical bicycle hub you have a simple bearing; the cups are set in the hub, the race (cone) threads onto the axel and there are just loose ...
1
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1answer
64 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
4
votes
2answers
348 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
2
votes
2answers
94 views

Coupled ODEs that model a quad rotor

I am working on modeling the vibrations of a quad rotor. The arms that support the rotors are fixed to a center plate; that is, it is pretty much a cantilever beam with an end load. Since this is the ...
2
votes
1answer
65 views

Why do some objects tend to change their axis of rotation while rotating?

This question struck me a few minutes back, I was at a table with a pear. It was more narrow than round.I proceeded to rotate this pear in one swift movement. It rotated for a few seconds, and ...
2
votes
1answer
116 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
3
votes
1answer
696 views

How do anti-lock brakes know when to brake?

When you come to a stop normally, the brakes don't pulse when you stop. Since the car can only know its speed by the rotation of the wheels, how can it distinguish between the car is stopped normally ...