Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

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Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
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Why is the total energy of an orbiting system negative?

Assume it's an circular orbit. Object A orbits around object B. Take object B as frame of reference. .$E=KE_a + GPE$ .$E=\frac 12m_av_a^2 +(-\frac {GM_bm_A}r)$ .$E=\frac 12m_a(GM_br)+(-\frac ...
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How does potential energy work out for floating things?

Seeing a ship canal lift in TV spawned the following thought: "Oh my, this sure is a heavy ship and it can be lifted by simply adding water. What a marvellous machinery. After all, I could lift that ...
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Lagrange equation and a force derivable from a generalized potential

I was reading the solution of this exercise and I have a doubt: A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = ...
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183 views

Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical? Lets assume that a planet is 'born' when lots of ...
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57 views

What is this equation $f^e = f^a - \nabla U$?

Recently in a mechanics class my prof scribbled down something looked like $$f^e = f^a - \nabla U.$$ Where he claimed $f^e$ is the external force on an object, $f^a$ is the applied force on the ...
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If the great pyramid was built in 20 yrs for Khufu, what forces were used for its building? [on hold]

If the great pyramid was built in 20 yrs as they claim, this means that every 2.3 minutes a stone as heavy as a car was quarried, moved 500 miles up the nile river shaped, hoisted and set. This would ...
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36 views

Hamilton's principle for elastic bodies [on hold]

I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : \begin{equation} E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ ...
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112 views

Potential Energy of Springs and Gravity, and Work of a force

I am currently really stuck on this problem and I am not sure how to actually solve it, I think I can reason it out logically but I do not know how to show it. Here it is and under I will show what I ...
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34 views

Conceptual doubt about mechanic energy and two body problem [closed]

Suppose that two bodies are in plane, let's call the first m and the second M: In the first case m is moving in plane, so it has kinetic energy. M is attached at the origin (i.e not moving), so it ...
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53 views

How this formula for work follows from the definition?

If a particle moves along a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ then the work done by a force $\mathbf{F}$ is defined by $$W = \int_{\gamma} \mathbf{F} = ...
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What was the amount of energy released in the 9/11 terrorist attacks?

I read somewhere on the internet that the amount of energy released by the terrorist attacks on the twin towers on 9/11 should have been of the order of 100 tons of TNT. This number surprised me, ...
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1answer
24 views

Water in a U-tube [closed]

I'm currently working on a problem that states: a U-tube has vertical arms of radii $r$ and $2r$.... The U-tube contains liquid up to a height $h$ in each arm. The liquid is set oscillating and at ...
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16 views

Buckling of a slender column - total energy

I'm following Goldbart's Mathematics for Physics book, and I ran into a problem with exercise 1.4 (page 43). We have a formula for the energy stored in a slightly bent rod aligned on the $z$ axis: $ ...
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Electrostatic Potential Energy Integral

I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
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What kind of potential profile that an electron live in provides bound state energy levels?

Given the electron Hamiltonian $$H=T+V(r)$$ where $T$ is the kinetic energy, $V$ is the potential energy and it is not necessarily isotropic. If $$V \sim -\frac1{|r|},$$ we have hydrogen-like bound ...
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26 views

Which is the right sign convention for the potential difference?

The circulation of the electric field gives the potential difference, but is it : $$V_B-V_A = \int_A^B\vec{E}.\vec{dOM} \hspace{1.5cm} (1)$$ or $$V_B-V_A = - \int_A^B\vec{E}.\vec{dOM} \hspace{1cm} ...
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65 views

How is energy converted when massless spring is attached to a rigid support

Say a massless spring of length l is attached to a rigid support. It is extended to length l + x. Now at this position, the ...
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45 views

Rest masses, binding energy - mechanism for negative mass

Let us have an two objects (in a box) both of mass $m_0$ far from each other. They attract each other and at some moment their distance is close and they have substantial kinetic energy. Something ...
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origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$ \sigma_{ij} = C_{ijkl} \epsilon_{kl} $$ Because $\sigma$ ...
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Why is Energy = Voltage x Charge, and how to prove that?

As you know the equation $\mathbf{E=V\times Q}$. Where: $\mathbf E$ is the energy measured in joules, $\mathbf V$ is potential difference (Voltage), $\mathbf Q$ is the charge. So my qustion is: ...
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Why does negative energy imply that a system is bounded? [duplicate]

I wanted to know why "negative energy" of a two particle system implies that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
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Bounce height of ball on Mars vs Earth

I understand that if a ball is dropped on mars and on earth the ball will bounce back to basically the same height on both planets thanks to the law of conservation of energy. But can anyone prove ...
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Pendulum point in polar coordinates for Lagrangian

So I'm really stumped with this. I have a particle in a cone, like pictured. The particle orbits the z axis on the dotted line for $r$. So knowing that $\alpha$ and $r$ remain constant in this ...
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93 views

Help understanding the solution to a problem regarding kinetic energy of a group of point charges

The problem provided by my professor goes as follows: "Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a ...
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295 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - ...
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Can we define the zero potential at an imaginary point?

Consider a force field defined as $$\vec{F}(x) = \left(\frac{A}{x^2}-B\right)\hat{i}\space$$ where $A, B$ are positive constants. We want to get the potential energy function for this field. We can ...
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107 views

Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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61 views

Understanding the relationship between electric energy and force

I'm trying to do the following problem: One of the three types of radioactive decay is "β decay", during which protons decay into neutrons or vice­versa, emitting either electrons (β­) or positrons ...
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99 views

Violation of conservation of energy… or not? [closed]

The work done by surface tension is double the increase in potential energy. This is a clear violation of conservation of energy. What is the flaw here? Work done by surface tension is \begin{align} ...
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27 views

Why the gravitation potential in a uniform field has negative values?

As we know the gravitational potential is the work done per unit mass in taking a point mass from zero potential (at infinity distance) to the point in a gravitational field. But why the work is ...
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How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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Velocity increase calculated from kinetic energy in different frames

Say we have an aeroplane cruising along at constant height with velocity $v_0$. It dives by height $h$ and levels out, at a new velocity $v_1$, in a gravitational field of strength $g$. If all the ...
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1answer
42 views

Potential Energy of Interaction Between a Sphere and a Particle Formula Derivation [closed]

A sphere of radius R has density described by ρ=ρ(r). Derive equation for pontetial energy of interaction between the sphere and some point particle of mass m which is at distance r from the center of ...
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122 views

What happens to gas molecules after ionization?

I know that gas molecules conduct electricity after they get ionized but what will happen if we keep increasing the voltage even after ionization? Will it explode? If it will then how much energy ...
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72 views

Hooke's Law vs. Elastic Potential Energy

I am currently learning about elastic potential energy and this is a question that was given to us by my teacher: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses ...
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What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any ...
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Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
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What is the meaning of the negative sign in $W = -\Delta U$?

What is the meaning of the negative sign in $W = -\Delta U$ ? As far as I understand, $W = -\Delta U = -(U_f - U_i) = U_i - U_f$. While $U_i$ is the initial potential energy (before applying the ...
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664 views

Mechanical Equivalent of Heat

Recently I have been looking up James Joule's experiment regarding the mechanical equivalent of heat. After viewing some drawings of the apparatus, I assumed that the lines holding the weights would ...
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Kinetic energy on macro and micro situation

I just have this random question in my mind. If you drop something in deep space, and it falls due to a gravitational pull. As it's falling, its kinetic energy increases. I just wonder, is the average ...
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Determine the value of $g$ with rolling ball

At first, I thought the value of $g$ ($9.8m/s^2$) could be determined simply by placing a ball at the top of a ramp at a known height. The ball was released with no initial velocity, and the final ...
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Is work needed to bring a test charge from a higher potential to a lower potential?

I don't understand whether work is needed to bring a test charge from a higher potential to a lower potential. It seems that no work is needed because the positive test charge will be under the ...
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1answer
46 views

Isolation of a Physical System and Energy

I'm trying to grasp basic concepts of energy and i have a little doubt regarding conservation of energy. According to Feynman book and Wikipedia, the Law of Conservation of Energy states that ...
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Conservation and forces/energy

Are there really non-conservative forces in actuality ? Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close ...
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Using Electric Potential to Float an Object

I've been trying to answer the following question but I'm stuck at one step. The question essentially states that a magician is trying to perform a "floating objects" act, for which she has a thin ...
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Energy density in electrostatics

Imagine two hollow spheres with radius $R$ with charges $q$ and $-q$. $L>2R$ is distance between them. Potential energy of the each sphere is \begin{equation*} W_1=\frac 1{8\pi \epsilon_0}\frac ...
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How do I correctly introduce time into this equation?

So, for the past few years it's been my goal to create an equation that would give me the position of an object in a gravitational field at time $t$, given it's initial position and velocity. At first ...
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1answer
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Why is the objective function used in Nudged Elastic Band method reasonable?

In Nudged Elastic Band (NEB) method, which is used to find reaction pathways when both initial and final states are know, an objective function is first constructed and then minimized to find reaction ...
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How much energy does it take to hold a bag? [duplicate]

I'm holding a bag with some mass $m$. The force required for not letting it fall is equal to its weight $m \cdot g_L$ (where $g_L$ is the local gravity, assuming Earth this is $\approx 9.8 \; \text{m} ...