All Questions
Tagged with inertial-frames conservation-laws
80 questions
4
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1
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Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
- 41
1
vote
0
answers
33
views
Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
0
votes
1
answer
78
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Is momentum conserved relative to all reference frames?
Assuming that there is an observer S in a train that is equipped with a cannon moving to the right relative to another observer S' in a train moving to the left relative to S, which is also equipped ...
9
votes
5
answers
3k
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If energy is relative, then how it can remain conserved?
If energy depends on frame of reference of observer, then how it can remain conserved?
Same question also for linear and angular momentum.
I think energy is conserved when seen from a specific frame ...
- 91
0
votes
1
answer
127
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Invariance of continuity equation for Galilei transformations
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index ...
- 115
0
votes
1
answer
2k
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General Lorentz boost of four-momentum in CM frame, particle physics
In particle physics, we observe a scattering of the type: $$a+b \rightarrow c+d$$
Known quantities in the LAB frame are a, b and c. I want to transform c into the CM frame of the initial state and ...
- 65
3
votes
1
answer
843
views
Proof that conservation of momentum is Lorentz invariant
In classical mechanics, if
$$\frac{\mathrm d}{\mathrm d t}\sum_i m_i\vec{v_i}=0$$is true for one frame of reference, then it is easy to prove that this is true for all frames (since different frames ...
- 1,911
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2
answers
128
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Can kinetic energy be transferred between two objects even if they are not in contact?
This question is better explained with a thought experiment. It is inspired by this answer, stating that the amount of work done depends on the inertial frame.
Consider a one-dimensional space with ...
- 101
0
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2
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834
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If two objects collide and one is initially at rest, is it possible for both to be at rest after the collision?
I know that the straight answer to my question is no. Since the initial momentum is not zero, the final momentum is not zero.
What about when object A impacts object B that is rigidly fixed to earth ...
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9
votes
6
answers
3k
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Apparent kinetic energy paradox
Imagine two cars (A and B) of mass $m$ that want to destroy themselves by colliding. They need a velocity of magnitude $2v$ with respect to each other to achieve the destruction that they want and ...
- 260
0
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2
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232
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How to understand continuity equation intuitively as Lorenz covariant?
As we know, it is natural that we derive the differential form of continuity equation
$${\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =0$$
from the integral form, in the view of ...
- 15
0
votes
4
answers
598
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Centre of mass frame
I was just looking at the equation:
$$v2-v1=-e(u2-u1).$$
This equation is to describe the collision between two masses, where $v$ is the final velocity and $u$ is the initial velocity, $e$ is the ...
- 23
5
votes
1
answer
527
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Charge conservation vs. Lorentz invariance of charge - including non-conserved charges
Conservation of a charge
$$ Q = \int dV \, j^0 $$
follows from current conservation
$$ \partial_\mu j^\mu = 0 $$
and
$$ \dot{Q} = - \oint dS \, j = 0 $$
where the Gauß divergence theorem has been ...
- 947
2
votes
2
answers
200
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Global conservation + Lorentz invariance = local conservation?
On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example:
It seems that global conservation law and local conservation law can be related. ...
- 342
14
votes
4
answers
3k
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Why should momentum be conserved in special relativity?
This is more of a philosophical question than an actual physics question, but I don't see a clear reason why relativistic momentum, or energy for that matter, should be conserved.
The equivalence ...
- 920
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3
answers
638
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Man moving on a frictionless plank
A person of mass $m$ is standing on one end of a frictionless plank of mass $M$ and length $L$ and floating in the water. The person moves from one end to another and stops. The displacement of the ...
- 8,040
4
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6
answers
2k
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If a train hits a ball at $200$mph how fast does it bounce off the train?
So I'm taking some classes on Brilliant and I'm starting with the basic stuff I already know and learned in hs/ms. We come to this question where we're dealing with switching frames of reference.
Now ...
- 41
1
vote
2
answers
4k
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Is it possible to find the final velocities of two objects in a perfectly elastic one dimensional collision where both objects have initial velocity?
I'd like to know how to generally solve for final velocity of both objects after a perfectly elastic collision. Cannot be in a lab reference frame because I'm programming it. Must be able to solve ...
- 27
1
vote
3
answers
209
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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)...
2
votes
2
answers
367
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What exactly happens in a rigid body collision?
Consider a situation in which a body of mass m moving with a velocity v is collided with a similar mass, applying momentum conservation,the initial mass will come to rest and the other mass will move ...
- 538
4
votes
7
answers
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Where does the law of conservation of momentum apply?
Take the scenario of a snowball hitting a tree and stopping. Initially, the snowball had momentum but now neither the snowball nor tree have momentum, so momentum is lost (thus the law of conservation ...
- 87
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votes
4
answers
2k
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Velocities in an elastic collision
My teacher keeps saying that, in a head-on elastic collision of two bodies of equal masses, the velocities get exchanged. But consider two balls of equal mass moving with the same velocity in the ...
- 1,637
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2
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305
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Why is the loss of energy maxed in perfectly inelastic collision?
I was doing a physics problem, and it had asked me to find the maximum $K_e$ loss, but I don’t understand why the loss is maxed when the objects stick together (the collision is inelastic).
user276754
0
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1
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How to understand this relativistic decay question?
The upsilon is an unstable particle that decays into a tau and an
antitau according to the reaction:
The upsilon is at rest relative to the laboratory when it decays. The
momemtum of the tau relative ...
- 876
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votes
1
answer
177
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Inelastic Collision of two balls [closed]
Is it possible that two balls of the same weight collide (in 1 dimension) and then stay at the rest?
How is such a collision called?
What are all the possible situations (velocities of 2 balls of the ...
- 255
1
vote
2
answers
98
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Is absolute motion inconsistent with homogenous space? [closed]
I read that homogenous space implies conservation of momentum (according to Noether's theorem) Conservation of momentum is kinda the statement that bodies continue moving with constant velocity unless ...
- 6,770
2
votes
5
answers
495
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Looking for a proof relativistic momentum is conserved Using first principals
Could someone help show that in special relativity, conservation of momentum is independent of inertial frame by applying Lorentz transform.Or better, can you derive the formula for relativistic ...
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1
answer
518
views
Why doesn't the speed of objects change in the reference frame of center of mass?
We often say that before and after 1-d elastic collision, one objects velocity only changes its direction in the reference frame of their centre of mass.
I can show this algebraically, writing ...
0
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3
answers
2k
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Confusion regarding a case of head-on elastic collision of two bodies of equal mass
If two bodies collide elastically, it's common to hear that the velocities, speeds and momenta are interchanged. I thought this was obvious. But if we consider two bodies moving with equal mass and ...
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1
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783
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Conservation of linear momentum in a non-inertial frame
It is known that total linear momentum of a system is conserved in an inertial frame in which net force is zero. I tried extending it to non inertial frames by taking into account the pseudo forces. ...
- 29
0
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0
answers
74
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ENERGY TRANSFER
Why does an electron carry half the center of mass energy after undergoing RELATIVISTIC elastic scattering at 90 degress with a proton in the center of mass frame. Is there a reference that you may ...
- 21
3
votes
3
answers
956
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Why a ball doesn't stop when it collides with a wall?
If a ball collides with a ball of same mass the first ball stops and the second ball gets the velocity of first ball.The first ball stops due to the reaction force acting on it. But when a ball ...
- 315
0
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1
answer
464
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Using zero-momentum frame to solve a 2D oblique collision
How could I solve this problem using the ZMF concept? I understand how this would be done in a 1D problem, so could I apply the same logic, finding a vector that makes momentum in each direction zero, ...
- 358
0
votes
4
answers
108
views
Momentum is not conserved during inelastic collision?
When considering room as a system, when a ball is made to fall freely and it collides with the floor it loses speed each time it collides. The momentum hence is not conserved in this case?
Can anyone ...
- 1
0
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0
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129
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Fluid dynamics continuity equation in not inertial reference frame
I know that the "canonical" Navier-Stokes equations must be modified when the reference frame is not inertial (e.g. Coriolis force has to be taken into account).
Does the continuity equation (mass ...
- 739
2
votes
5
answers
311
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Where is the momentum going?
When a ball of mass $m$ collides elastically having velocity $v$ with a wall, then it retraces itself with the same velocity. Impulse on the ball due to wall is $2mv$ and since there is no external ...
1
vote
1
answer
97
views
Linear momentum of a system remains conserved, but with respect to which frame of reference?
I have studied that linear momentum of a system remains conserved. But i can't figure out with which reference of frame it is conserved. Is it conserved with respect to system reference frame or in a ...
2
votes
1
answer
84
views
Do the balls keep moving forever?
In a hypothetical world where there is no friction, and all collisions are elastic would an object in lateral motion be perpetually moving and never come to a stop?
Assumptions:
Perfect vacuum: zero ...
- 123
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votes
2
answers
1k
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With respect to what does a Gyroscope maintain its orientation?
Assume ideal conditions, no friction, no energy loss in any form.
Just an ideal gyro, in ideal conditions, spun into rotation and left alone. And placed somewhere on earth.
From what I've read so ...
- 116
1
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0
answers
259
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Colliding elastically in lab and CM frame
Two spherical bodies of mass $m_1$ and $m_2$ are placed in gravity free space as shown. Initially, the body with mass $m_2$ is at rest and the body with mass $m_1$ approaches the other body with a ...
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3
answers
339
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Is it possible writing conservation of relativistic energy in this naive way?
Conservation of charge or rest mass can be written in this way and it is Lorentz invariant
$$
\nabla \cdot (\rho \mathbf{u}) + \frac{\partial \rho}{\partial t} = 0
$$
So we could be tempted to naively ...
- 1,179
1
vote
2
answers
2k
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Conservation of momentum in different reference frames
Does the total momentum of a system in a given inertial reference frame have the same numerical value in other inertial reference frames?
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1
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135
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Centre of mass problem
I came across a problem where there was an ice and tray system. The system was placed in a gravity free hall. After the ice melted the shift in centre of mass was to be found. But the answer is 0. Is ...
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6
answers
754
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Violating Newtons First Law!
Suppose you are inside a very large empty box in deep space , floating ( i.e not touching the box from anywhere initially).The box is at complete rest.
Now you push the box forward from inside.
Now ...
- 69
2
votes
2
answers
1k
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Are these collisions equivalent?
Similar to the question if two cars with a velocity of 50 mph each colliding is the same as one car colliding with wall at 100 mph, I was wondering if the same amount of energy is produced when ...
- 23
1
vote
1
answer
137
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Can an energy-momentum four vector include the quantities of all objects in a closed system?
Say I have a particle moving along the $x$-axis in the Earth's reference frame. It decays into an upsilon and a proton, each of which has an energy of 60 GeV. They are traveling in opposite ...
2
votes
1
answer
18k
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Total kinetic energy of two particle system
Please help me understand this equation :
Total kinetic energy of two particle system = K.E. of system w.r.t. centre of mass + K.E. of centre of mass
Here's the derivation from my book :
The author ...
- 422
0
votes
2
answers
1k
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Lorentz Boost of the Lab Momentums
Lets assume we have a two body scattering like;
$$a + b = c+d$$
In the lab frame particle $a$ is moving with a certain beam energy $E_a$, and hits stationary particle $b$. Before the collision, ...
- 95
1
vote
1
answer
820
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Why is linear momentum not conserved for a particle in a central force? [duplicate]
I am studying a two-body central force system in which the two particles, one of mass $m$ and one of mass $M$, experience a force directed along the line connecting the two particles.
We can reduce ...
- 19
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votes
1
answer
69
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Analysis of collision of a non-pivoted rod with a ball at one end?
Suppose a a unpivoted rod in free space is struck by a ball at one end and we know the initial condition what will be the outcome of the collision?
