In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.
The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, and does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work.
Homework Statement
I have a particle of mass m. The particle is moving in direction of axis z because of the gravitational force of a homogeneous circular disk of mass M and radius a. There is a formula for gravitational force of the disk on the picture.
Task:
1) Find the formula of...
picture: https://ibb.co/k5P0GG
Two objects slide without friction on a circular ring of radius R, oriented in a vertical plane. The heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. The fixed end of...
Hello guys, came across some Analytical Physics lectures (http://www.physics.rutgers.edu/ugrad/227_f11/classes/lect08.pdf) that got me confused.
It is described in the lecture the problem of determining the force between capacitor plates for a constant voltage (ie. connected to a battery). For...
In class while learning about electromagnetism, I was given the following two equations:
U=-μ⋅B
τ=μ×B
where μ=IA
First of all, what does μ stand for?
How should I interpret the relationship between potential energy (U) and torque? Can someone explain this in terms of μ and B?
I have a discussion going on with some friends. The discussion goes like this:
We have two identical tanks. One is empty. One is full of water. Both placed on the ground.
They are connected with a hose at the bottom. There is a ball valve in line with the hose.
The full tank has a given...
In the case of lifting a box, I know potential energy is negative because negative work is done by gravity. What does the negative part of -PE denote? Does it denote the direction of the energy or does it mean that energy is being lost? But how is energy being lost if the box gains more...
My book says:
"Let us derive an expression for the potential energy associated with an object at a given location above the surface of earth. Consider an external agent lifting an object of mass ##m## from an initial height ##y_{i}##above the ground to a final height ##y_{f}##. We assume the...
2 frictionless tracks have equal length bumps with one going up and the other down. Halfway through the track which one has more energy?
Assuming that they started at the same height, I thought that they had the same amount of energy, but since Ball B ends up having a greater velocity at the...
work done in taking positive charge from A to B in electric field E=
potential energy at B - potential energy at A
OR
potential at A-potential at B
Am i correct in both formula?
How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it?
The string is uniform, so I know its center of mass is at L/2.
My textbook states that an alternative definition of the change in potential energy is the work required of an external force to move an object without acceleration between two points.
I am confused on why it says acceleration. Wouldn't that mean that the acceleration is 0 and therefore the...
Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$
Homework Statement
An electron that accelerates from a point near a collection of negative source charges toward a point near a collection of positive source charges experiences
A) a decrease in electric potential energy as it moves toward a region at a lower electric potential
B) a decrease...
Homework Statement
Homework EquationsThe Attempt at a Solution
In case of uniform E, torque ##\vec N = \vec p \times \vec E
\\ U = \int_0 ^ \theta N d \theta = pE \int_0 ^ \theta \sin \theta d \theta = - pE \cos \theta
\text { Here, I assumed that the direction of } \vec N ~ and ~ \vec d...
Homework Statement
I'm trying to digest the concept of change in potential energy being set equal to a change in kinetic energy. Does this relationship always hold? Please see below for more details.
Homework Equations
PE = mgh
KE = .5mv^2
W = ΔKE = -ΔPE
W = f*d
The Attempt at a Solution...
Homework Statement
Consider the arrangment of charges (fixed in place) shown in the figure. The square has side length d. (Figure 1)
Now suppose the particle with charge q is released. It is "kicked" so that it's initial speed is v. After an unspecified trajectory, it is observed that the...
1. Homework Statement
This is my first question and I'll try to stick to the forum rules as much as possible.
imgur.com/a/2JyZC
Imagine a cylinder filled with air which is uniformly distributed and a piston above it, so the air can expand vertically. Let the system be the air itself, so the...
hey guys! i am very confused about the concept of potential energy and gravity. we know that as an object is continuously lifted above ground, its potential energy increases. but i was wondering if that potential energy is physically affecting the body, like if the potential energy increases...
At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?
The more I think about it the less clear the respective natures of kinetic energy and potential energy (and of their sum, the so-called total energy) become. The thing is I have the impression that once you try to go a bit further than the usual description of "scalar values assigned to systems...
Homework Statement
Which of the following Graphs BEST illustrates the potential energy vs. time for the system in Figure 1, where t=0 is defined as the time at which the incident box 1st contacts the box on the spring?
My question is why can't the Elastic PE be negative?
The answer is A...
Hi All,
Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...
My question is:
If gravitational potential energy is normally negative, and E=m•c^2, doesen't that means that negative mass could exist?
(I don't know much about general relativity so please explain as simple as posible)
Homework Statement
Q7. Some lead shot with a mass of 50 grams is placed into a card board box the distance from one end to the other being 1m. The ends are sealed with rubber bungs in order to prevent the lead shots from falling out, the tube is rotated so the lead shots fall down from one end...
potential energy is the work done by an external force in taking a body from a point to another against a force. on the surface of a conductor the electrostatic charges arrange themselves in such a way that the net electric field is always zero. so if there isn't any force to act against why...
Say, we have two particles of equal and opposite charge in an isolated system in which we neglect gravity.
The energy of particle 1 is: E1 = U1 + T1
Where U1 is electrostatic potential energy and T1 is the kinetic energy of particle 1.
The energy of particle 2 is: E2 = U2 + T2
Where U2 is...
We have two conducting spheres of radius r1 and r2 far away from each other. The first sphere has a charge Q. What is the change in electrostatic potential energy when they are connected together?
Before the connection ,
Ube = ##
\frac{Q^2}{8\pi\epsilon_0 r_1} ##
After the connection ,
Uaf = ##...
From my understand, electric field is the force emitting from a charge. This means that if a charge was placed in the vicinity of the charge that was emitting the field of force, that charge placed would experience a force from it. How does potential energy differ from this? I understand that...
K= ∫mvdv = ∫m dx/dt dv = ∫m dx/dv dv/dt dv = ∫m dv/dt dx = ∫Fdx = U
=> K=U, why isn't this true? If it is, wouldn't that mean that Kinetic Energy is always equal to Potential Energy?
Homework Statement
So I have been building a mouse trap car at my school, and I need to hand in a report on it tomorrow. :biggrin: I don't have all of the measurments at the moment, but the only thing I want to know is how to calculate this. I want to see how much energy is lost to...
I want to prove ##\displaystyle U = {1\over 8\pi}\int \vec E \cdot \vec E dV## and ##\displaystyle U = \frac12 \int \phi \rho dV## are equal.
I started with ##\nabla \cdot (\phi \nabla\phi) =(\nabla \phi)^2 + \phi \nabla^2 \phi##'
Then
##\displaystyle {1\over 8\pi}\int \vec E \cdot \vec E dV...
Homework Statement
Concentric spherical shell of radius ##a## and ##b##, with ##b > a## carry charge ##Q## and ##-Q## respectively, each charge uniformly distributed. Find the energy stored in the E field of this system.
Homework EquationsThe Attempt at a Solution
Field between ##a## and...
Homework Statement
A charge of Q = −1 µC is moved from point A to point B.
Which of the following situations will result in an increase in electrical potential energy?
I've now uploaded the files below
Homework Equations
F = qE
U = qV
a
b
c
d
e
f
g
h
The Attempt at a Solution
I think...
Homework Statement
consider a 3300 lb car whose speed is increased by 35 mph over a distance of 200 ft while traveling up a rectilinear incline with a 15% grade. model the car as a particle, assume the tires do not slip, neglect all sources of frictional losses and drag. find the work done by...
Hi.
Getting straight to the point, what is the difference between electrical potential energy and electric potential?
Please be as specific as you can.
Thank you.
Homework Statement
potential energy function of :
$$
U(x) = 4x^2 + 3
$$
And have to
i) Work out the equation of motion
ii) Prove explicitly that the total energy is conservedHomework Equations$$
F = \frac{dU}{dt}
$$
The Attempt at a Solution
I'm not too sure how to go about this...
Homework Statement
This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b.
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf
Homework Equations
K = 1/2Iω2
U = mgh
The Attempt at a Solution
The potential energy of the bar when...
Homework Statement
I was wondering in what situation would the potential and the electric field of the system both be equal to zero at the same time?
Homework Equations
W=-ΔU=-ΔVq
ΔV=-∫Edr
V=kQ/r (with reference r->∞)
The Attempt at a Solution
I know for the middle of a dipole the potential...
<Mentor's note: moved from a general forum and therefore no template>
This is the equation of potential energy in rubber bands, however, I don't know how to calculate the inertia of the arm of catapults or get the k constant. And what does n mean? Basically, i don't understand the whole...
How do I find the total potential energy at the highest and lowest points of oscillation without velocity or time?? I do not believe there is any air resistance, only gravity. I also already have the elastic potential energy and the gravitational potential energy.
I have two simple examples of potential energy and kinetic energy.
First example: Imagine a book on the ground and I want to lift it.At first I apply a force just a little more than the gravitational force of the Earth so that it has some velocity. After the book gets that velocity, I keep my...
Homework Statement
Imagine a thin tower 4000 miles tall; ı.e. as tall as the earth’s own radius Re, placed at the north pole of the earth. Suppose you start at rest at the base of the tower and climb to the top (wearing a spacesuit and carrying supplies you need, so that your total mass is M)...
Homework Statement
Calculate ##\left< \frac 1 r \right>## and ##\left< \frac 1 {r^2} \right>## and the expectation value and uncertainty of the potential energy of the electron and proton for a hydrogen atom in the given state.
The given state is:
$$ \psi_{2,1,-1} \left( r,\theta,\phi \right)...
Homework Statement
Using the equations, show the bulk modulus is about r^-4.
Homework Equations
The Attempt at a Solution
Tried to plug Uij but it is not same as U. To be honest, I don't know where to start.
Homework Statement
A point charge +Q is placed at the centre of an isolated conducting shell of radius R. Find the electrostatic potential energy stored outside the spherical shell if the shell also contains a charge +Q distributed uniformly over it.
Homework Equations
[/B]
E=kQ/r2...
I have just read chapter 7.4 FORCE AND POTENTIAL ENERGY in Sears and Zemansky's university physics 14th edition. There they show that a conservative force always acts to push the system toward lower potential energy in a one-dimensional motion with the equation Fx(x) = - dU(x)/dx. As I...
Homework Statement
A 4.0 kg block starts at rest and slides a distance d down a frictionless 35.0 incline, where it runs into a spring. The block slides an additional 16.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 429...