Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
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Compression of airbags
I am currently creating a simulation of a rover landing on mars. Part of the landing would include the rover being dropped to surface of mars whilst surrounded by airbags.
I understand that using ...
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2answers
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Rocket's momentum
It is well known that to give a liftoff a rocket, we use the momentum principle: The momentum of the gases emitted by a rocket and the rocket's momentum is equal to zero. So why is it not enough to ...
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Block slides down frictionless wedge on frictionless surface. Find accelerations of the blocks
I am working on a physics problem where a small block of mass $m$ slides down a wedge-shaped block of mass $M$ with an angle $\alpha$ to the horizontal that rests on a frictionless horizontal surface. ...
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Does the movement of a passenger change the velocity of an aeroplane?
I encountered a problem in my physics textbook today.
An aeroplane of total mass of 50,000kg is travelling at a speed of 200m/s. If a passenger of mass 100kg then walks toward the front of the ...
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How is momentum conserved in the case of a ballistic pendulum collision?
To my knowledge, momentum is conserved when net external force equals zero.
In the case of a block $m_1$ attached to a string hitting another block $m_2$, there must be a net force on $m_1$, which ...
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Finding symmetry from conserved quantity (reversed Noether's theorem) [duplicate]
Is Noether's theorem reversible? For example, given some conserved quantity, can you find the underlying symmetry which leads to the conserved quantity?
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How does an accelerating mass on a ring interact with the ring?
In outer space, imagine a mass $m$ on a ring with mass $M$. The small mass is given a velocity $v$ after which it moves without friction on the ring. Initially, the velocity of the center of mass (COM)...
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Why can't we use conservation of angular momentum to solve this question since this whole system is isolated?
A solid rubber wheel of radius $R$ and mass $M$ rotates with angular velocity $\omega_0$ about a frictionless pivot. A second rubber wheel of radius $r$ and mass $m$ also mounted on a frictionless ...
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2answers
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If everyone on Earth jumped at the same time, is it possible to steer the Earth?
Newton's third law states that in every action, there is a equal and opposite reaction.
When we jump, we exert a force on the ground and the resultant force upwards propels us up into the air. However,...
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How can Hawking radiation maintain the balance of matter and antimatter?
If hawking radiation simply reduces the mass and emits electromagnetic radiation, how can the balance of matter / antimatter be maintained? Couldn't you use some of that $E = mc^2$ energy you would ...
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How is energy conserved in blueshifting?
I am having trouble understanding the conservation of energy in the scenario below.
A photon of $\lambda_1$ is emitted by a source and then absorbed by object 1 in space. Object 1 can be considered ...
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3answers
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Friction during rolling
I have four doubts regarding friction during rolling.
Does slipping mean zero angular velocity, or is it just the $v$ velocity not being equal to $\omega r$?
If a wheel is initially given the ...
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How to understand the Fresnel relation $1+R=T$? [closed]
From the perspective of energy conservation, we are familiar with the relation $T+R=1$ (Set the incident wave amplitude as 1, $T$ and $R$ are Fresnel transmission and reflection coefficient, supposing ...
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Energy conservation in systems with discrete time
Numerical simulations of classical particle dynamics usually break energy conservation due to discretization of time. Is there any explicit numerical scheme that does not break energy conservation (...
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1answer
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1D Elastic Collision with restitution coefficient
I have an exercise about a 1D collision with a certain restitution coefficient, that is: $$e = \frac{|u_1-u_2|}{|v_1-v_2|}$$ One must calculate the velocities of the 2 colliding masses after the ...
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Conservation of Energy with Chemical and Kinetic Energy of Moving Body
A rocket is moving relative to the earth such that it has $E$ joules of kinetic energy. The rocket contains fuel with $E$ joules of chemical energy. The mass of the fuel is negligible in comparison to ...
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Conservation of momentum: One moving car hitting another stationary one. Does the target always move forward?
Consider an isolated system with two cars of any mass, a ground with friction, and Earth. Both cars are free to move on the ground.
One car (Car #1) is moving towards the other stationary car (Car #2)...
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What is the significance of the term 'isolated system' in law of conservation of charge?
I did not understand why charge can only be conserved in an isolated system. Kindly elucidate.
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Why is angular momentum $mvr$ and not $mvr^2$ or $mvr^3$?
We know angular momentum $L = mvr$, where $v$ is the velocity in the direction perpendicular to the distance from the source to the object whose $L$ we are trying to measure. My question is why $L$ ...
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If electrons can be created and destroyed, then why can't charges be created or destroyed? [duplicate]
I read on Wikipedia that electrons can be created through beta decay of radioactive isotopes and in high-energy collisions, for instance when cosmic rays enter the atmosphere. Also, that they can be ...
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1answer
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Forces in an elastic 1D collision [closed]
Let's say I have block A (5kg, a = 10 $\frac{m}{s^2}$) and block B (20kg, a = 20 $\frac{m}{s^2}$). When they collide together elastically, the forces exerted on each other should be the same by Newton'...
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4answers
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Conservation of Charge
We know that universe is all about charge conservation mass conservation and energy conservation. Charge on a system can be measured by comparing it with charge on a standard body, positive and ...
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How can I show that in an elastic collision i can set $| \vec{v_2} - \vec{v_1} | = | \vec{v_2}' - \vec{v_1}' | $?
I am getting stuck in a really easy problem in Statistical Mechanics that involves elastic collisions, it is really very shameful that I am getting stuck at such a simple thing, but from:
$$\|\vec{v_1}...
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Conservation laws for the collision of two classical particles
In Kleppner and Kolenkow's An Introduction to Mechanics (3rd ed.), the authors state (p. 227) that for the collision of two classical particles with no external forces or torques, with 6 unknowns (the ...
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How to interpret charge continuity equation for conductors that obey Ohm's law?
For conductors, we propose that the free current density is proportional to the applied Electric field and the constant of proportionality is defined as conductivity.
\begin{equation}
\textbf{J}_\...
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Noether's Theorem: There are conserved quantities corresponding to symmetries of position, orientation, and time, but why not velocity?
Noether's Theorem seems to be one of the most fundamental and beautiful results in all of physics. As I understand it, the fact that the laws of physics are the same independent of position, ...
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Why is energy not conserved when the “surface is moving in time”?
Consider a particle moving in the field of a conservative potential $V(\bf{r}$$)$ which is constrained to move on a surface $\sigma(\bf{r},$$t)=0$. Here $\bf{r}$ denotes the radius vector of the ...
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3answers
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Energy imbalance during conservation of momentum associated with the collision of a molecule with the wall of a container
I've read a couple of answers related to this topic, but none of them answer my specific question.
My question is that, when a molecule collides with the wall of a container, having $X$ component of ...
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1answer
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Resulting slurry characteristics of mixing slurries of different densities in an overflowing reactor [closed]
Given a continuously overflowing reactor of $T \; hr$ residence time, a slurry of known varying flow-rate and varying density is introduced. How do we calculate the resulting density at outlet?
I was ...
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2answers
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Photon hits an electron perpendicular to its velocity, Relativity and Work?
In the phenomenon of the Compton scattering a photon can hit a free electron under any angle.
The photon can be regarded as a 'complex' of two photons one along the velocity v of the electron and ...
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Do conserved quantities tell us more general pattern than what we are taught?
Last year I had a question in m mind that as $mv$ (momentum) and $mv^2/2$ (Kinetic energy) both are conserved then n a closed system and they are dependent on same quantities and look very similar so ...
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In a collision shouldn't objects of different mass have same acceleration?
Suppose two objects of different mass, A and B, collide with each other. Now, during the time of collision, they both apply forces on each other according to Newton's 3rd law. Therefore, their ...
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Problem with the continuity equation for an electron gas
Consider the continuity equation for an electron gas:
$$\tag{1}
\nabla \cdot\left[n(\boldsymbol{r}, t) \frac{\partial}{\partial t} \tilde{\boldsymbol{r}}(\boldsymbol{r}, t)\right]=-\frac{\partial}{\...
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Symmetry principles and analogous Noether's theorem for stochastic systems
In the case of Newtonian mechanics, taking a variational or Lagrangian or Maximum principle (MP) view, one can obtain the conservation laws (energy, linear momentum and angular momentum) by combining ...
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1answer
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Adiabatic Invariant when forcing is at the natural frequency of a classical simple harmonic oscillator
Consider a simple harmonic oscillator of unit mass, natural frequency $\omega_0$, given by the Hamiltonian
\begin{align}
H_0(q,p)=\frac{1}{2} \left[ p^2 + \omega_0^2 q^2 \right] \ .
\end{align}
Now ...
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1answer
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Application of the principle of conservation of angular momentum and the principle of conservation of energy [closed]
I came across this question and was left confused.
A satellite is launched in a direction parallel to the surface of the earth with a velocity of $36900 \; \mathrm{\frac{km}{hr}}$ from an altitude of $...
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Error in Derivation of Tsiolkovsky Rocket Equation?
Can someone point out where the error is in the following derivation of the Tsiolkovsky rocket equation? According to the Newton's second law combined with his third law, we know that the net external ...
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1answer
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Strange conservation of energy in Navier-Stokes Equations
We want to roughly model the fluid flow of a star; consider the following proposition:
In the absence of viscosity, and heat conduction, the Navier-Stokes Equations for a steady, spherically symmetric,...
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2answers
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Can a collision between a large and small mass result in final velocity greater than initial velocity?
If you have some large mass with a velocity $v$, and some small stationary mass, is it possible for a collision to occur that results in the smaller mass having a velocity $v_f> v$, and perhaps the ...
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1answer
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Differences in using Clausius-Duhem inequality vs Principle of Virtual Work/Power in derriving constitutive equations?
I am a novice getting my toes wet in continuum mechanics and nonlinear elasticity. I have seen papers that use both approaches in developing constitutive connections to compliment balance equations of ...
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1answer
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Higher form symmetries and massive gauge fields
I have seen all kinds of questions and answers about how to identify a higher-form symmetries, but they all seem rather abstract. What I would like to do is investigate two very simple examples.
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2answers
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Why is angular momentum conserved in a central field?
I am trying to understand how a gyroscope works, which in the broad strokes is due to conservation of angular momentum. I understand the case when the angular momentum passes through the origin of ...
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State an equation for conservation of mass and use it to show that fluids of constant density are incompressible
I have the following question:
State an equation for conservation of mass and use it to show that fluids of constant density are incompressible
My solution (1):
My solution (2):
I don't know how ...
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1answer
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Intuition for the time/energy connection?
I find the following analogy reasonably intuitive:
translational symmetry : conservation of linear momentum :: rotational symmetry : conservation of angular momentum
In contrast, I find the analogy ...
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3answers
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Momentum conservation when virtual photon decay into lepton pair
I know the fact that one photon can not decay into electron-positron pair.
at the CM frame, the momentum of electron + positron is zero. However, the momentum of a photon can not be zero.
Though, I ...
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Constant expectation values for spin components of Dirac particles
My question is largely related to this one: Spin expectation values in Dirac theory
It regards a free Dirac particle, with spin z+ in its rest frame, and moving with momentum in the x direction as ...
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2answers
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Mass conservation in fluid dynamics
I am trying to derive the mass conservation equation:
In one of the step we are given the equation to find Fluid mass gained through a small element of the surface 𝑑𝑆 in a time 𝑑𝑡 is:
I don't ...
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4answers
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Least Action in General Relativity
For an affinely parameterised geodesic we can form the Lagrangian:
$$
\mathcal L = g_{ab}\dot x^a\dot x^b = \text{constant}
$$
The Lagrangian is constant by the fact that the geodesic parallel ...
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2answers
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Validity of continuity equation $\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \vec{V}\right)=0$
$\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \vec{V}\right)=0$
When is the continuity equation valid? And how can i find it mathematically?
Is it valid only for newtonial fluids?, ...
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1answer
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Kinetic energy produced in an explosion
If there is a train moving at 2 m/s with a cannon attached to it loaded with a ball, and then the ball is launched from the train, how would one find the kinetic energy produced by the explosion if ...
