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.
So masses on springs store potential energy. Height in a gravational field store potential energy for the mass there.So why isn't there a potential energy stored inside rotating objects? Surely there are ways to translate the rotational energy to kinetic. Its kinda like a spring. If a set down a...
Homework Statement
Picture: https://drive.google.com/open?id=0B39n6QfDU8f3bWY3OWxyaGZBYU0
[Moderator: Image inserted to make problem statement visible]
Homework Equations
F=-dU/dx
The Attempt at a Solution
I have no idea in this question...
The slope is always the same for the graph...
I'm studying relation between conservative force and potential energy,and getting a big question on change in potential energy is always negative.
For gravitational PE ,when an object is lifting up, it's work done is negative(opposite direction). so the change in work done is negative. On the...
Homework Statement
If a ball is dropped from a height (H) its velocity will increase until it hits the ground (assuming that aerodynamic drag due to the air is negligible). During its fall, its initial potential energy is converted into kinetic energy. If the ball is dropped from a height of...
Homework Statement
A particle of mass m moves along the x–axis under the influence of force ##F_x=-ax+bx^3## , where a and b are known positive constants.
(a) Find, and sketch, the particle's potential energy, taking U(0) = 0
(b) Identify and classify all equilibrium points
(c) Find the...
1. A comet that passes by Earth has GPE, which will be all lost if it begins to fall towards Earth. If it's shot back up, it will now start with Ek and finish with a higher GPE.
Now, what exactly is this GPE? if energy cannot be created or destroyed, but transformed, where does it get stored at...
Hi, I'm studying undergrad mechanics, Central force motion, Marion's book in specific,
Here, the Potential Energy is defined weird way (in my opinion though)
(μ is reduced mass)
So potential Energy becomes
Called "Effective Potential Energy"
But, I can't agree with calling it potential just...
Homework Statement
I've been looking at examples of motion derivations for my class, and it's honestly just very confusing. I heard Dynamics should prep you for this but I must have had a very poor course because we never had to understand geometry and physics to this degree...
Homework...
When work done is positive How does potential energy decrease? Work done and energy cannot have different direction can they? Can someone help me out in understanding this properly ?
Homework Statement
Homework Equations
U = 1/2 kx2
The Attempt at a Solution
So, I took dynamics off campus and needless to say, we didn't really do very much deriving so that aspect of physics really bogs me down and I'm trying to learn it now in another class. So if anyone wants to also...
Homework Statement
Prove that the total energy of an electron orbiting a hydrogen nucleus is Etotal = -e^2/ 8ε0 π r where e is the magnitude of charge of an electron and r is the orbital radius. Homework Equations
Knowledge
The Attempt at a Solution
Here is my attempt:
For KE,
mv^2/r =...
Hi,
I wonder which steps of my following deduce are wrong
dU=-dW
dU=mg dh
dW=Fdx
thus, mgdh=-Fdx (dx=dh)
then, F=-mg which is a constant in most of situation
However, F does change in some situation.
I am confused about this.
Does the value of the potential energy of a system of objects depend on the reference point or the nature of force existing between them (attractive or repulsive)?
Hi everyone, first post here.
Today i crushed into a question. I was going to write it down here, then i crushed into another one.
Lets say we want to know the potential energy of a body relative to a center of gravity.
I will refer to gravitys acceleration as "g" and to mass as "m". "k" will...
Homework Statement
When a -2C is moved from point A to B, the potential energy of the system increases by 10J. What is the voltage V(ab)?
Homework Equations
U=qV
The Attempt at a Solution
10=(-2)V, I thought the voltage was -5V but the correct answer is +5V. Could someone explain why this is?
Is there any difference between the meaning of the equation W=-ΔU and the meaning of the statement that potential energy of system is always negative when the reference point(zero point) is taken to be located at infinity or do they both convey the same message?
Hello everyone, currently working on a physics project.
I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can...
Homework Statement
Homework Equations
I know that U = q * V, so my attempted approach will rely on that method
The Attempt at a Solution
I was wondering if people could help me solve the problem and help me figure out why B is the correct answer and what the pitfall in my problem solving...
Dear all,
I was wondering what exactly the correspondence/relation is between Hamilton's principle (extremizing the action gives the allowed configurations) and the fact that a system wants to configurate such as to minimize its potential energy. Is there any? Somehow I can't find a decent...
I know that when an object A a does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy...
I have seen some sites say that it doesn't and other says the opposite. So let's see
Source of the pic: Chemguide
Lets look at the hydrogen (Oxidation) half cell. If we assume that it contributes x volts until the electron reachs the copper, then no matter how big is the distance the voltage...
I am currently reading Gravitational Curvature by Theodore Frankel. In the derivation of Einstein's equations in chapter 3, he states that the gravitational potential energy of a blob of fluid is
∫B½p0U√gVdx
where the integral is a volume integral, p0 is the rest energy density and √gvdx is...
Homework Statement
A body of mass m is taken at a constant speed from the surface of the Earth (radius = Re) to infinity.
(a) What is the work W1 done on the body in the process?
(b) If m is taken from a distance r > Re to infinity, how much work W2 is required?
(c)Which quantity is larger, W1...
The form of the Lagrangian is: L = K - U
When cast in terms of generalized coordinates, the kinetic energy (K) can be a function of the rates of generalized coordinates AND the coordinates themselves (velocity and position); a case would be a double pendulum.
However, the potential energy (U)...
Homework Statement
A particle with a charge of 2e moves between two points which have a potential difference of 75V. What is the change in potential energy of the particle?
Homework Equations
U = (75 V)(2e)
The Attempt at a Solution
[/B]
When a particle with charge e moves through a...
I have found that even though knowing the potential energy is vital for classical mechanics, most of the times what you know is actually the force, so you have to determine the potential energy based on that. So, here's the issue:
The relationship between the force and the potential energy is...
So I know that things in the Universe tend to move toward a state of least potential energy. This is why forces point in the direction of decreasing potential energy, as everything is trying to minimize its potential energy.
So my main question is: does Gibb's free energy basically just...
Hi.
What is the total energy of a particle in a potential? Is it
$$E=\gamma m_0 c^2+E_pot$$
or is it still
$$E=\gamma m_0 c^2$$
where ##m_0## is a bigger mass than the particle would have in absence of the potential?
Homework Statement
Homework Equations
Power = Work Done / Time
Work Done = Force * Displacement
PE = mass * gravity * height
The Attempt at a Solution
I got the first part (i) right, so the mass of the sea water is 1.32 x 10^12 kg.
Part (ii) is the bit I am stuck on. My thoughts were that...
Let's say we have a mass M at the ground of the Earth with speed U going upwards so its energy is E= kinetic. The speed is enough to surpass Earth's gravitational field so now it has a speed U2<U and its energy now is E= kinetic+potential. So my question now is: Is this potential energy lost? I...
My question is:
Does a spring between two differing masses, each with an initial momentum of zero, transfer half of its stored elastic potential energy to each?
My intuition says yes. But it seems to not be the case. If you apply the conservation of energy and momentum, the answer you get is...
Homework Statement
A 15.0 kg stone slides down a snow-covered hill leaving point A (at the top of the hill) with a speed of 10.0 m/s. There is no friction on he hill between point A and point B (at the foot of the hill). There is friction on the level ground at the bottom of the hill between...
Homework Statement
To derive Potential Energy for dipole p in Electric Field E.
2. Homework Equations
Potential Energy is the work done by the external agent in turning the angle of the dipole from the U=0 position to another position against the influence of the electric field applied...
Why does the potential energy of a system of two charged particles decrease as the distance between them increases? It seems that the PE should increase, as in U=mgh; as h increases, the PE increases. Why does this not occur in electrical potential energy, and in the gravitational potential...
Does the rest mass of an object increase when it acquires gravitational potential energy, and if so, is this the reason why Einstein believed that the inertia of a mass increases in the presence of other masses?
Hi Guys,When we are finding the wasted energy when something is dropped a tower, we do this: mgH-0.5mv^2
My question is, does the velocity of the kinetic energy have to be vertical component, or can it be the impact velocity when it hits the ground?
Thanks
I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##.
Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...
Homework Statement
Five identical masses of mass M are suspended by a spring stretched a distance of L. If three of the masses are removed, what is the potential energy stored in the spring?
1) (4 / 25) * M * g * L
2) (2 / 5) M * g * L^2
3) (5 / 2) * M g * L
4) (4 / 25 ) * M * g L^2
5) 5 * M *...
Hello, I do not quite get this. Can anyone provide examples?
" We may feel that it takes a force greater than the weight of the object being raised to lift it upwards, but it is not so. Provided the force is equal to the weight, the object will move upwards at a steady speed. "
Homework Statement
Consider the equations for electric potential energy:
and gravitational potential energy:
GPE=m*g*h
In the case of GPE, the potential energy increases as the distance between the two objects increases. This makes sense (to me), as the greater distance between the Earth...
Homework Statement 1. Homework Statement [/B]
Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}##
Homework Equations...
Hi
I want to calculate the potential energy of the following figure in function of x
Here is my attempt :
mgx + 1/2*k*(sqrt(x^2+L^2)-L)=1/2*m*v^2
Is that correct ?
thanks
For my Quantum II class I am working on a paper about masers. I am using a naive model (a coupled pair of infinite potential wells), and I would like to find out where I can find a graph of the inversion potential energy curve. This would be a simple one dimensional curve of the potential...
Suppose the mass of planet is" M" and there is body in its surface whose mass is "m" and the field strength is "g" . If the body is thrown 1800 m then Gravitational Potential energy = mg(1800). My question is why can't we use formula GPE= GMm/x ? This is also the formula for gpe but why...
Homework Statement
Homework Equations
ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf)
where
G = gravitational constant
M₁ = mass of one object
M₂ = mass of the other object
Ri = initial distance
Rf = final distance
ΔPE = -ΔKE
The Attempt at a Solution
My solution is v = 2√(GM/d). I am making sure it is...
Homework Statement
Problem: Consider a "crystal" consisting of two nuclei and two electrons arranged like this:
q1 q2 q1 q2
with a distance d betweem each. (q1=e, q2=-e)
a) Find the potential energy as a function of d.
b) Assuming the electrons to be restricted to a one-dimensional...
Hello!
The (potential) energy of an electron in a solid structure is always negative; also the E_c and E_v levels (conduction band and valence band limits) are negative, in the band diagram of a pn junction.
When the junction is built and thermal equilibrium is reached, the depletion region...
Homework Statement
Homework Equations
The Attempt at a Solution
Kinetic Energy + Potential energy=0
1/2mv^2 = mgcos(20)
100v^2 = 1.96cos(20)
v^2 = .0184
v = .136 m/s
No idea if this is correct or if I should proceed with energy considerations. Please advise.
Homework Statement
A child starts from rest and slides on a sled first slope
down over a distance of 25 m . Then, the child slides further over a
horizontal plane. The angle of inclination is 35 ° and the kinetic
coefficient of friction between the sled and the snow is 0.100. The mass
of the...
I have read posts about this but still don't have a good handle on it. I am confused about something that I know is simple. If a mass is attached to a spring, the spring will stretch according to Hooke,s law, correct? So won't the weight, (mg) balance out the spring force of -kx? So in other...