All Questions
Tagged with classical-mechanics energy-conservation
32
questions with no upvoted or accepted answers
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Why does the law of conservation of energy not hold true when the work-function $U$ depends explicitly on $t$?
[...] the infinitesimal work $\overline{\mathrm dw}$ comes out as a linear differential form of the variables $q_i$: $$\overline{\mathrm dw}= F_1~\mathrm dq_1 +F_2~\mathrm dq_2+ \ldots + F_n~\mathrm ...
user36790
3
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0
answers
222
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Does the additivity property of Integrals of motion and Lagrangians valid in all situations?
I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
- 345
2
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2
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293
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The so called "Energy Approach" vs "Force Approach", when and how should they be used?
I'm new to physics and I've been trying to solve a few high school olympiad questions. I've figured that I approach the questions by analyzing the forces acting on objects and trying to induce ...
- 657
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A particle constrained to always move on a surface whose equation is $\sigma (\textbf{r},t)=0$. Show that the particle energy is not conserved
In Goldstein's Classical mechanics question 2.22
Suppose a particle moves in space subject to a conservative potential $V(\textbf{r})$ but is constrained to always move on a surface whose equation is ...
- 173
2
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0
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Does $\frac{d}{dt}E=0$ always yield unambiguous equations of motion?
If you have a conservative system, one way you can derive the equations of motion is by using the fact that the total energy $E$ of the system is conserved, i.e.:
$$ \frac{d}{dt}(T+V)=0 $$
For example ...
- 65
1
vote
2
answers
108
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Law of Conservation of Energy ambiguity in Giancoli textbook
In my version of the textbook by Giancoli: Physics for Scientists and Engineers, in chapter 8, there is a formulation of the law of conservation of energy that seems unintuitive and correctable to me. ...
1
vote
1
answer
59
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Statistical Analysis of motion under central force
My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
- 11
1
vote
1
answer
91
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Energy conservation for changes in the Hamiltionian
If the Hamiltonian represents the total energy of the system,
then how does it change?
Does a change in the Hamiltonian violate the conservation of energy?
Of course, we know from the Hamiltonian ...
- 11
1
vote
2
answers
94
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Law of conservation of energy and potential energy
I completely understand how this law goes and how energy is changed from one form to another. But there is something that I thought about, we all know how the potential energy works and when an object ...
- 11
1
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0
answers
73
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What's the meaning of $\Delta E-W_{nc}=0 $?
Suppose a system of particles is subject to internal forces, some of which are conservative and some of which are non-conservative. Let $\Delta E$ be the change in mechanical energy of the system as ...
- 11
1
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0
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What is the physical interpretation of a Lagrangian with $\dot{x}^4$?
Among the exercises in the first chapter of Goldstein's book "Classical Mechanics", it appears the lagrangian
$$
L\left(x,\frac{dx}{dt}\right) = \frac{m^2}{12}\left(\frac{dx}{dt}\right)^4 + m\left(\...
- 1,211
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Question about Helmholtz's paper "ON THE CONSERVATION OF FORCE"
Below follows the exact extract from Helmholtz's paper "On the conservation of force".
Let us now imagine, instead of the system $A$, a single material
point $a$, it follows from what has been just ...
- 155
1
vote
1
answer
41
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When can I go in the reference frame of a moving object?
Two particles separated a distance r, each of mass m, are being launched at opposite directions with the same speed v. If we’re in the reference frame of the center of mass of the particles, what ...
- 131
1
vote
1
answer
108
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Lagrange Equation - Basics
The basic equation of Lagrange is given by,
$$\frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q_j}} - \frac{\partial L}{\partial q_j} = Q_j \tag{1}$$
where $T$ is the kinetic energy, $V$ ...
- 17
1
vote
1
answer
29
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How are the equations for the final velocities of objects derived here?
Assuming linear momentum is conserved in an elastic collision between 2 objects ($\Delta K= 0$) the initial equations one can set up are:
$m_{1}v_{1i} + m_{2}v_{2i} = m_{1}v_{1f} + m_{2}v_{2f} $
$\...
- 123
1
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0
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76
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Conceptual Difficulty About Work
So my issue is best explained with an example.
Let us consider a ring of mass $m$ and radius $R$ sliding down an incline of angle $\theta$ ($I = mR^2$). It starts from a height h, and we wish to ...
- 11
1
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0
answers
514
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Phase plane of simple pendulum
I'm trying to create a phase plane of simple pendulum motion by plotting $\dot\theta$ against $\theta$ in Matlab. I have the equation $\ddot\theta + \sin\theta = 0$, then by integrating I come to the ...
- 11
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1
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38
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Does A Pivot Exert A Force
On a frictionless horizontal table, a uniform stick is pivoted at its middle, and a ball collides elastically with one end, as shown in Fig. 8.10. During the collision, what are all the quantities ...
- 13
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3
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44
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Ways of losing energy of a bouncing objects in vacuum other than Heat and Sound
When we released a bouncing object in a vacuum chamber, the object will fall, contact the ground of the chamber and bounce back up. We know that the object will not return to its original height ...
0
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2
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120
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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 ...
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534
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Deformation of gradually applied load vs impact loads?
When a load P is applied gradually on an object, the work done on it is the average of the initial and final loads, which is generally P/2 multiplied by the deflection Δ1. In the case of impact load, ...
- 11
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1
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90
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Calculating impulse to frame from a flywheel and piston system
My question is related to a previous question, presented in 342655. I am taking the same scenario to ask a different question: In a flywheel and piston inertial system, how do you calculate the ...
0
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1
answer
65
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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 ...
- 141
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1
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48
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Friction or not?
Say I have a differential equation in $\mathbb{R}^n$, Newtons Equation :
\begin{align}
\frac{d\gamma(t)}{dt}=&\dot{\gamma}(t),
\nonumber
\\
\frac{d\dot{\gamma}(t)}{dt}=&-\...
0
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0
answers
38
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To find the angle of slipping of a falling coin
In an attempt to predict the outcome of a toss, I dropped a coin with its edge just touching another sharp edge as shown in figure. (The edge is flat and sharp with very less friction as in case of a ...
- 2,000
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1
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435
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Confusion About Conservation Of Energy When Analyzing This Experiment
The video here shows a clear demonstration of conservation of angular momentum. Given the experiment is performed within an isolated system, these are my thoughts:
The spinning bike wheel continues (...
0
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0
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95
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Angular momentum conservation during motorbike jump - modelling
I have now found 2 ways of describing this phenomenon and I would like to know which way is correct or better:
When the rear wheel rotates, we can take a look at the angular momentum (around the ...
- 448
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1
answer
416
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How to calculate velocity of an object at the bottom of a circular hill if there is an energy loss due to friction?
Object slides down a circular hill and loses some of its initial mechanical energy due to friction. As an object slides down, friction increases and force in direction of motion decreases until the ...
0
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0
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635
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Block Sliding on a Wedge: Conservation of Energy
I have a question regarding a physics problem where a block is sliding down a wedge (which can be seen here). All of the solutions I've seen to this kind of problem involve the conservation of the ...
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How Conservation of energy due to time symmetry appears in lever system?
Consider a lever or a machine which acts as a force multiplier in that case we do the same work or create a greater force by moving a smaller distance how the idea of conservation of energy due to ...
