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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Max & inflection point in the principle of least action [duplicate]

Short question: What is the physics interpretation of max & inflection points in the principle of least action? Long question: If $$L(q_1,q_2;t)=K-V$$ then let $$S = \int^{t_1}_{t_2} ...
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1answer
53 views

Statistical Mechanics problem regarding the enthalpy and the expected value of energy

So I have an assignment(relating to a chapter on Canonical Ensemble) here with $H_E = \langle H\rangle$ where $H_E$ is the enthalpy, and $\langle H\rangle$ is the average of the Hamiltonian, I think. ...
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5answers
311 views

How does constant thrust avoid quadratic kinetic energy accumulation?

I haven't found the right search terms for this question, so if it has been answered, references would be welcome. Suppose we start from experimental station in deep space (interstellar space if need ...
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1answer
78 views

Harmonic oscillator: if $E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s \theta^2$ then $\omega=\sqrt{\frac{s}{q}}$?

Consider an harmonic oscillator. Suppose that I manage to write the mechanical energy as a function of a quantity, like the angle $\theta$ in this way $$E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s ...
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24 views

Moving a Car the quickest path

I have a car, that has a current angle and location, and a destination angle and location. The car has a maximum linear and angular acceleration. Assume the car will always travel in the direction it ...
3
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1answer
84 views

What is the probability of two bullets to get clashed? [closed]

I was surfing on Instagram, and I found this amazing proto whose description is "the probability of such an event to happen is incredibly small, so this is a really curious finding". Well.. I'm ...
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2answers
158 views

I dropped my tissue box on a glass table, the box didn't bounce back, table didn't move nor break, what happened?

I have a box, it drops and thus by moving has Kinetic energy, It doesn't penetrate and impacts however the box doesn't rebound nor breaks the table. Its like when I slam my fist on a table but the ...
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1answer
66 views

Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. \begin{equation} T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}} \end{equation} ...
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1answer
32 views

Initial velocity and time of motion through water

What initial velocity has to have a ball at the height $h=1\ \text{m}$ in order to sink in the water to depth of $s=4\ \text{m}$? How long is the motion of a ball through water? A ball is made of ...
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1answer
146 views

“Principle of least action” and “Principle of conservation of energy”: Which one is fundamental and which one is derived? [closed]

Suppose I throw a ball upwards. First it will rise under gravity and then fall under gravity. During the rising part the kinetic energy gradually decreases and the potential energy increases until ...
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1answer
48 views

Force as a Function of Position

If given a velocity as a function of position, is force as a function of position just it's derivative times the mass? I'm given the following and I am not sure my above logic is correct: The speed ...
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0answers
17 views

Equality of external derivatives in Canonical Transformation implies invariance of Poisson Brackets

For a canonical transformation, we require that the forms $$p'dq'- H'dt$$ and $$pdq -Hdt$$ differ up to a total differential. From this follows the equality of the external derivatives: $$\sum_i ...
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3answers
72 views

How simultaneous information of coordinates and velocities sufficient to completely determine the subsequent motion of a mechanical system?

I somehow could not find the answers to the question in Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system? to ...
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2answers
77 views

Why is a sphere easier to move than a box of the same mass?

Is it only because of the less friction involved or at there other reasons?
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2answers
124 views

How is the Poisson bracket $\{\mathbf{c},\mathbf{l}\cdot\hat{n}\}=(\hat{n}\times \mathbf{c})$, for constant $\mathbf{c}$, and not zero?

The Poissonian formulation of mechanics tells us that for a generating function $g(q,p,t)$, the Poisson bracket of some function/variable $f(q,p,t)$ with the generating function corresponds with an ...
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1answer
62 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has ...
3
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2answers
97 views

Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$

I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
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2answers
57 views

Im learning Work-energy theorem, this question popped into my mind about Force applied and displacement

I know a lot but I'm not sure, I'm guessing if $400J$ of work done on a 800 Newton object, if I'm correct, $400N$ to $800N$..that is $.5 m$ displacement, so by $W=∆KE$ why do I get $200J$? I was ...
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3answers
78 views

Magnitude of Normal Force in Circular Motion

In the above diagram an object is in vertical circular motion. At $T_0$ the object is at pos1, and at that position, I have shown the forces resolved. So $F_n-mg\cos(a)$ is the centripetal force ...
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1answer
55 views

Statistical Physics of a System with Friction inside a Hot Bath

If you have a classical system (i.e obeying Newton's equations of motion) with Hamiltonian $H(x,p) = \frac{p^2}{2m} + U(x)$ then the statistical behaviour of this system is described by the ...
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44 views

Friction in Lagrangian Method [duplicate]

A uniform, flexible chain of length $l$, mass $m$, hangs off a frictionless table-top of height greater than $l$. The length of the part of rope hanging off is $x$. Gravity accelerates the part of the ...
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2answers
75 views

Long and short barreled guns

Projectiles containing delicate elecrtronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not ...
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0answers
21 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
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0answers
56 views

Rolling Resistance Coefficient

I found that rolling resistance can be expressed with this equation: $$F_\mathrm{rr} = \frac{C_\mathrm{rr} W}{r}$$ Where $C_\mathrm{rr} =$ coefficient of rolling resistance $W =$ normalforce $r ...
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2answers
61 views

Can a system be designed that uses no energy to accelerate particles to high velocity?

I have one system in mind. Although I know it is not possible to accelerate a particle to a higher speed without spending energy, I would like to know why the proposed system won't work. The system ...
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1answer
49 views

Confusion with Thomas precession

Suppose an inertial frame $S^\prime$ is moving with a relative velocity $\textbf{v}=v\hat{n}$ w.r.t another intertial frame S with their axes parallel and $\hat{n}$ is an arbitrary direction. In that ...
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1answer
30 views

A Classical/Theoretical problem regarding Friction

I had a rod. I broke it into two. Now I wish to make it one i.e. to join those (not glue or any thing as such) as if the rod was not broken at all. This is our objective! As I broke the rod apart, ...
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2answers
123 views

Work and forces in systems of many particles

I'm reading Goldstein's Classical Mechanics, first chapter, and am confused about what's going on in equations of forces and work in systems of particles. For example, Goldstein calculates work done ...
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1answer
79 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
0
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2answers
48 views

How do you tell whether a force acting on an inclined plane is going up or down in its perpendicular component to the plane?

I'm practicing mechanics, and I had to resolve the following forces perpendicularly to the inclined plane in order to work out the reaction force (plus the weight of the ball) But I cannot tell ...
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1answer
38 views

How to scale variables in a classical Hamiltonian?

So I looked at some research articles where one has a classical Hamiltonian $H(p,q,t) = p^{2}/2 + V(q,t)$. If one introduces the scaling transformation $$t \mapsto t/\sqrt{s}, \quad H \mapsto Hs, ...
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1answer
36 views

Why are the integrability conditions necessary and sufficient for the existence of a canonical transformation's generating function?

Consider a canonical transformation $(p,q) \rightarrow (P,Q)$ under a generating function $F$. The condition for form invariance of Hamiltonian equations of motion looks like : $$\sum_{s}P_s\dot{Q_s} ...
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0answers
34 views

car dashboard problem

I stumbled upon this question while I was driving my car. On my dashboard I have fuel gauge and engine temperature gauge next to each other, look at the pic: http://i.stack.imgur.com/aDgKj.png Fuel ...
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1answer
67 views

How did he find the “lambda” value in this question? [closed]

There is a pdf i found when searching about Lagrangian Multpliers, but i was not able to understand how he derived lambda from two differential equations. If anyone can walk me through it, i would be ...
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0answers
36 views

Maximizing horizontal displacement from projectile motion off of downward slope [closed]

Firstly, I think I should point out that I am a high school student, so please excuse me if my question seems mediocre. What I am doing was seemingly simple, I am doing some research on projectile ...
0
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2answers
19 views

How to determine the friction constants

We know that the friction is formulated in this form $$F=av+bv^2+Nμ$$ I'm working with an object and surface and I want to find $ a, b, μ $ for them. Can you please give me an experimental method ?
2
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0answers
48 views

Origin of spin and direction in the magnus effect

If you solve the Bernoulli equation: $$p=p_0-\rho_0{v^2 \over 2}$$ using a complex flow potential for a flow around a cylinder: $$W(z)=v_0 z + {v_0 R^2 \over z} - {\Gamma \over 2 \pi } \ln(z)$$ you ...
0
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1answer
30 views

Phase Portraits Given Hamiltonian

Given a Hamiltonian say $$ H = 5p^2 $$ What is the correct procedure for producing a phase portrait. My initial thoughts were to solve the system of equations $\frac{dq}{dt} = 0$ and $\frac{dp}{dt} ...
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0answers
22 views

Impulse response of coupled oscillators

The behaviour of a LTI system can be described entirely by it's impulse response. Imagine the following coupled pendulums have no friction losses. They will have 2 resonant frequencies, one for when ...
1
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0answers
29 views

Classical Quantum or Relativistic? [closed]

An ensemble contains free electrons at 10^3 electrons per m^3 at 10^7 K. What can this ensemble be treated as: a Classical Quantum or Relativistic gas or in some overlapping domain?
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1answer
44 views

Energy method to solving equations of motion? Why does this method work and what is it called?

Given the stated system in the photo we are suppose to prove simple harmonic motion when given an initial displacement $x$ I first considered the total energy of the system which we will call $H$ ...
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2answers
63 views

Equivalent spring constant of setup

A mass $M$ is suspended using two springs having spring constant $k_{1}$ & $k_{2}$ with distance from mass as $a$ & $b$ respectively. Find equivalent spring constant of system. So I ...
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1answer
35 views

Can point mass have vibrational motion?

Can a point mass have vibrational motion. I have read that reason for point mass is to ensure that we can idealize translational motion and don't have to worry about rotational and vibrational motion. ...
3
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1answer
27 views

Diagonal of a thin rectangular foil, inertial principal axis?

I'd like to know if the diagonal of a thin foil is an inertial principal axis. I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a ...
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9answers
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Why is it possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand?

It is possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand. Why is this so?
3
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1answer
61 views

1kg mass impacting at half light speed - effects?

Such a mass would have kinetic energy approximating a 1 mega-tonne thermonuclear weapon. So, what would such an object do if it hit the Earth? We know how destructive such an energy release can be, ...
3
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0answers
48 views

Elastic collision / relative velocity problem [closed]

I'm having some trouble with a homework exercise and I'd really appreciate some help! I've done the first part correctly (according to the solution sheet), but I can't seem to get the second part ...
3
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4answers
96 views

Intuitive explanation of $1/2(at^2)$ motion equation?

The full equation $$ Xf = X_o + V_o t + \frac{at^2}{2} $$ is integrated from the velocity function (which was integrated from constant acceleration function), right? The problem is, I can't seem to ...
1
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0answers
30 views

Find the angle of the projectile [closed]

Given: Hmax = 2 * Range Find the angle of the projectile. After using the formula for both Hmax and Range, I got an angle of 74.69 if I am not mistaken. On the math exam teacher said the answer ...
3
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2answers
138 views

How does the Moon influence atmospheric pressure?

I have just read in the Telegraph an article entitled Moon overhead makes rainfall lighter, scientists conclude. In that article there is the following statement: When the moon is overhead, its ...