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.
I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this...
Homework Statement
Charged sphere with a mass of 15 mg and charge 2 nC moves with a speed of 15 cm/s towards a fixed point charge of 3 nC. How close will sphere approach charge?
Homework Equations
K=(1/2)*mv2
U=k*(Q1Q2/r)
The Attempt at a Solution
So I am not sure I approached correctly but...
Homework Statement
Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...
Homework Statement
As an electron (q2) moves from point A to point B, it moves farther from a positive charge (q1). Does the electric potential energy increase, decrease, or stay the same.
Homework Equations
U=-kq1q2/r
The Attempt at a Solution
The electric potential energy decreases in...
A consequence of Coulomb's law is that oppositely charged particles have a negative potential energy. I'm having trouble undsrstanding how anything can have a negative potential energy and what consequences that has. Does it just mean the change in potential energy is negative or is it a matter...
well, we say that an object on Earth has a potential energy that is dependent on its position, i.e height. In this case we take Earth as reference point, similarly if we take sun as reference point, the Earth should have some sort of potential energy.
Homework Statement
Homework EquationsThe Attempt at a Solution
U = 5x2 - 20x
F = -dU/dx
F = -10x + 20
The expression for force doesn't look like motion is SHM .
How should I deal with this ?
Hi.
In all of my question, I mean degrees celsius when I say degree.
Think we have a 0 degree ice. we give some energy to it (by a heater) and all of it get into a 0 degree water.
How does the kinetic and potential energy of the molecules change?
In the book in which I saw this question, it...
What exactly is this potential energy? I was searching and its looks like electric potential energy (U = K*Q*q/d - K*Q*q /d0), because the two atoms attract each other that means that the product of Q*q = negative, so, a negative energy. Ok, that's make sense, but why when the repulsive forces...
I'm trying to understand what exactly it means in terms of the voltage of a battery. I know that the voltage in a battery is just the potential difference between the two terminals. But, is the negative terminal used as a relative point and seen as 0? If that's the case does 12V mean that the...
So in my physics textbook a problem is stated. We are given an external electric field directed downwards of 150N/C. We are then told that an electron is released in the electric field and it moves upwards 520m. Finally we are asked to calculate the change in electric potential energy of the...
Can someone explain the math of how potential energy travels from higher potential energy to lower potential energy (PE) along a uniform electric field?
I understand that in order for the point charge to move, gaining kinetic energy, it will lose potential energy. But using the equation...
Hi everyone.
I've been doing a lot of reading regarding electric potential and electric potential energy. Unfortunately, I have a lot of confusion regarding this topic, as I keep receiving different information. My main confusion is regarding the signs, positive or negative, of work and it's...
Four identical particles, each having charge q and mass m, are accelerated from rest at the vertices of a square of side L. How fast is each particle moving when their distance from the center of the square doubles?
I used the Conservation of Energy => Kf= -deltaU = Ui-Uf
4(mv^2 /2) = kq^2...
How can one find the potential energy of a particle. The derivation of PE can be done by the fact that change in PE of a particle is equal to negative of work done by a force on the particle. This combined with Kinetic energy work theorem gives us an equation on conservation of mechanical energy.
Homework Statement
A 95-kg mountain climber hikes up a mountain to an elevation of 5000 m. What is the change in the climber's potential energy?
Homework Equations
I might be missing something but here's everything that might be relevant:
w=fx
p=w/t
p=f*v
KE=1/2mv^2
PEg=mgh
PEe=1/2kx^2
Wnet=E...
Homework Statement
14.37 A 75-kg ski jumper starts his run in the position shown on the parabolic
track. The equation of the parabola is ##y = (12/225)x^2##, where x and y are in meters.
Neglecting friction, calculate the contact force between the skis and the track at O.
Homework...
Homework Statement
14.34 The 0.5-kg bob of the pendulum travels a complete circle about the pivot
point O. Determine the smallest possible speed of the bob in position A if it is
suspended from (a) a rigid rod of negligible mass; and (b) a string
Homework EquationsThe Attempt at a Solution...
Homework Statement
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A small cube, with a mass of 2 kg, slides along a frictionless horizontal surface at a constant speed of 20 m/s until it collides with, and sticks to, a large wooden 5 kg block. The large block is attached to the left end of a spring with a spring constant of 75 N/m as...
Homework Statement
I'm trying to figure out the setup of an experiment I have to complete. The experiment calls for a rubber band to be secured by rods on the sides, and for a clothespin to be attached to the rubber band. I have to figure out how far back the clothespin needs to be pulled down...
Homework Statement
14.27 The 2.5-kg weight is released from rest in position A, where the two springs
of stiffness k each are undeformed. Determine the largest k for which the weight
would reach position B
Homework EquationsThe Attempt at a Solution
Hi. Can you check if I am going at...
Homework Statement
I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string).
For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1)
What about gravitational...
Homework Statement
14.28 The spring of stiffness k is undeformed in the position shown. The 30-g ball
is placed on the spring and launched vertically by compressing the spring 150mm and
releasing it. If the ball reaches an elevation of 14.25m above A, determine the value of
k.
Homework...
Homework Statement
Question: what rate does the water lose gravitational potential energy?
Data:
I have a pipe that water is flowing through and the pipe has 2 sections.
In section 1:
- the pipe is 11.9m above section 2 so, h = 11.9m
- the velocity of water is $$v_1 = 0.3240ms^{-1}$$...
Let's assume an electron and an anti-electron are in a gravitational field so they both have potential energy.
What will become of this energy if they annihilate?
Will the momentum of the photons after the annihilation will increase so the total energy will be conserved?
Thanks for answering!
Homework Statement
Homework EquationsThe Attempt at a Solution
I think : the question means that almost all of the potential energy gets used into the explosion.
If this is true then the potential energy gets reduced by ## \frac { GM^2} R ## or if the star just gets transformed into a...
Homework Statement
Calculate the potential energy created by the spring in the mousetrap as a function of the angle the spring is pulled back.
Homework Equations
PE = ∫Fdx = ∫ kxdx = ∫k rΘ rdΘ ??
The Attempt at a Solution
Is this a linear spring? we can use x = rΘ, and dx = rdΘ, so PE =...
Hello. I've been watching Susskind's online Stanford lectures on classical mechanics to review the subject, and I believe he said that adding a constant to the potential energy does not change the action of a system. I see how it doesn't change the Euler-Lagrange equations and therefore...
The force constant of the spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 0.012m?
The formula for spring force is F =kx
When I do 550 x 0.012m I get 6.6 but I am supposed to round my answer four decimal...
1. With an elevation of 5334 m above sea level, the village of Aucanquilca, Chile, is the highest inhabited town in the world.
What would be the gravitational potential energy associated with a 64.0 kg person in Aucanquilca? Assume that the free-fall acceleration at Aucanquilca is equal to that...
Homework Statement
The spring in the figure (Figure 1) is compressed by length Δx. It launches the block across a frictionless surface with speed v0. The two springs in the figure (Figure 2) are identical to the spring of figure 1. They are compressed by the same length Δx and used to launch...
Homework Statement
A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules.
Homework...
Homework Statement
An electron acquires 3.16*10^-16 J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential.
Homework Equations
w =Δv * q
The Attempt at a Solution...
I am confused how a charge could have negative work done.
To clarify, I was doing a problem earlier in which a positive charge and negative charge are moving towards each other. I used the equation
work = Δv * q
And when I was doing this, the change in electric potential, Δv, was negative, and...
Assume a person is at space, and assume there's no friction or gravitational force in that space.
The person has a bow and arrow. He stretches the arrow on the bow, and then shots the arrow out in the space. Since there are no friction and gravitational force in that space, the arrow will have...
Homework Statement
I'm trying to figure out how to do D) and relate time to this potential energy graph.
Homework Equations
All I really know is that F = -dU/dx
The Attempt at a Solution
I tried to do something with F = ma
and a = d2x/ dt2
and then set the - derivative of U(x) equal to the...
Here is problem I quickly made up:
Suppose there is a ramp with a height of 6 meters and length of 12 meters. A block of 5 kg is pushed up to the top of the ramp with a constant velocity. The force of friction is 15 N.
Here's the confusion:
By using the non-conservative force work energy...
The gravitational potential energy of two massic points ##P_1## and ##P_2## with respective masses ##m_1## and ##m_2## is given by
$$U = -G \frac{m_1 m_2}{|| P_2 - P_1 ||}$$
Now I was wondering how this formula could be applied to continuous matter. Let us imagine a very simple case where we...
There is something that has been bothering me for some time about binding energy (and respective mass difference) but I was not sure how to formulate the question. Now it feels like I can ask it meaningfully enough.
In GR energy produces gravity just like mass. But how potential energy is...
Homework Statement
The problem is to take a small ball of mass m on a uniform rod of mass m which is hung on a hinge vertically downward, they're asking to find the velocity to be imparted for it undergo a complete rotation.
I have the kinetic energy bit worked out but I'm getting the wrong...
Homework Statement
In the system below, m1<m2. When the object of mass m2 has descended a distance h, the potential energy of the system has decreased by:
Homework Equations
the answer is (m2-m1)gh
The Attempt at a Solution
I used ΔU= Uf-Ui
m1gh-m2gh=ΔU (I think that the decrease in...
Homework Statement
A 1.00kg mass and 2.00kg mass are set gently on a platform mounted on an ideal spring of force constant 40.0 N/m. The 2.00 kg mass is suddenly removed. How high above its starting position does the 1.00 kg mass reach?
Related to it... An 87 g box is attached to a spring with...
Sorry if something is wrong... this is my first ever post
1. Homework Statement
The Question:
In one dimension, the magnitude of the gravitational force of attraction between a particle of mass M1, and one of mass M2 is given by:
F(r)=GM1M2/r^2
Where G is a constant and x is the distance...
Recent discussions on pressure as a source of gravity and the related Tolman paradox have reminded me that few people seem to be aware that even in Newtonian gravity the pressure is related to the potential energy, which I've mentioned a few times on these forums before.
This is easy to show...
Homework Statement
Four protons (each with mass 1.7 10-27 kg and charge 1.6 10-19 C) are initially held at the corners of a square that is 7.1 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the...
My textbook doesn’t go into it, can someone tell me why Taylor expansion is used to express spring potential energy? A lot of the questions I do I think I can just use F=-Kx and relate it to U(x) being F=-Gradiant U(x) but I see most answers using the Taylor expansion instead to get 1/2 kx^2...
Homework Statement
Homework EquationsThe Attempt at a Solution
## V(r) = \frac 1{r^3} \left( A - Br^2 \right )##
At the bottom of the well, r is verry small.
So, ## V(r) = \frac A{r^3}##
Assuming the validation of Equipartition of energy theorem, since the degrees of freedom is 1,
the...