Potential energy Definition and 1000 Threads

Homework Statement Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement? Homework Equations U = -Gm2 / r The Attempt at a Solution The potential energy is the negative of the work done by gravity in...

Homework Statement Derive equation below. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R. Homework Equations V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2) The Attempt at a Solution So I understand that I need to find the ∫ from infinity...

Sorry, brand new here and this may be in the wrong place or very obvious. When matter and antimatter annihilate is the energy released the sum of all their potential energy? does E=MC2 only work because of the specifics of our universe, and if the universe were to contain more matter (and...

Homework Statement A charge moves towards a positively charged sphere, as it does, it's electric potential (V) increases. Give an instance on when the Electric Potential Energy (Ee) will decrease. Homework Equations V= Ee/q The Attempt at a Solution Alright, This is basically a theory...

How does potential energy fit into mass-energy equivalence in SR? As with all forms of energy, a potential energy of ##E## added to static system ought to increase the system's mass by ##E/c^2##. This is often illustrated by saying that a compressed spring has slightly more mass than an...

Ok, I've been trying to soak up the MIT physics material, but I am stuck on something and it is driving me crazy. They have several questions about graphs of potential energy vs. position, which also includes the total mechanical energy. I just can't fully wrap my mind around these graphs and...

I was reading this article from Wikipedia on resonance structures: http://en.wikipedia.org/wiki/Resonance_(chemistry ) What I do not understand is, what is meant by potential energy in terms of chemistry? In physics, potential energy is defined by location in a force field. What is it that...

Suppose the particle is at distance x from mean position and moving away . The standard formula for calculating potential U is U=-w here wis the work w=kxdx when the particle is moving away .On integration U=1/2Kx^2 . When the particle is moving towards mean position w=-kxdx on integration...

Homework Statement A polymer of ##10^{20}## molecules each 2nm long is hanged from the ceiling. The other end of the polymer is attached to a ##m=4\cdot 10^{-10} g## load. Calculate the average potential energy! Temperature is 300 K. Homework Equations ##<E>=<E_p>=\frac{\mathrm{d} (\beta...

To find the force we will differentiate the function with respect to x (dx) My problem is with the solution If we differentiate: dU/dx = 9x^2 - 7 From where does the negative come from also the j component?

I don't get the difference between these equations: U = \dfrac{-Gm_1m_2}{r} F_g = \dfrac{-Gm_1m_2}{r^2} g = \dfrac{F_g}{m} = \dfrac{GM}{r^2} Also, why are the first two negative? Here's my thinking: The first equation is like U=mgh. Except it's when two masses are very far apart. It...

1) For gravitational potential energy: ##F(r)=-\frac{\gamma M m}{r^2}##. 2) For potential energy of a conservative force-field: ##-\nabla E_p = F##. So the gradient of the potential energy is always equal to the force in that direction, just with the opposite sign. So when you move in the...

What does it mean by 0 V or 0 potential between two charges? If there are two point charges A and B. And if there is a point between them that has 0 V then why is: Va + Vb = 0?

Hello , I was thinking about dams and hydroelectrostations , the turbines can turn because the water before the dam is higher than after it so there is stored potential energy waiting bto be released, Now I wonder if we were to take two places one at the water surface level in the dam reservoir...

Homework Statement What is the gravitational potential energy of a system of 8 masses of 10 kg each placed at the corners of a cube of length 0.25 meter apart. Homework Equations U=-G*m1*m2/r The Attempt at a Solution I have actually taken one particle pair at a time and sum all...

I was having a few problems with Negative gravitational potential energy, I wasn't able to put my finger on why because it worked so well with everything else I had learned. I tried to say it made sense because in space you don't free fall, but that's not actually true, though the...

I am wondering if this method is in use already somewhere, or if its possible to be used. For example, using the equation of gravitational potential energy a 100kg weight that freefalls 100 meters has 98,000 J of energy, which equals 24,000 watts after approx 4 seconds of freefall. Assuming I...

Homework Statement Consider the Earth's radius to be 6.40x103km, its mass to be 6.00x1024kg, the Moon's mass to be 7.36x1022kg, and the Moon's radius to be 1.74x103km. The average value for the Earth-Moon distance is 3.84x105kg. Neglect friction and rotation. a. Sketch the potential...

So today in class we were talking about gravity and my professor said that generally KE = -.5PE And so TME = .5PE I don't understand how that works.

Homework Statement O^^^^^^O^^^^^^O |------------------------------------------→ There are 3 equal masses connected by springs with length a and spring constant k. The system can only move in the x axis. x1,x2,x3 is the position of each massWhat is the...

Homework Statement An outfielder throws a baseball with an initial speed of 79.0 mi/h. Just before an infielder catches the ball at the same level, its speed is 65 ft/s. How much of the ball's mechanical energy is dissipated by air drag? (The weight of a baseball is 9 oz.) Homework Equations...

Homework Statement The problem basically asked me to check if a given force was conservative and if it was conservative, also find the potential energy. F = k(x,2y,3z) Homework Equations (\nabla X F) = Curl of F U = Integral of F 3. attempt So the force is clearly conservative as the curl...

Hi all, I'm having conceptual troubles understanding the significance of the potential energy term in Schrodinger's equation. More specifically, the physical meaning of the potential "wells" is not clicking with me; my textbook is not making this very clear. For clarity, consider an...

Hi, I've managed to get myself confused over the simplest thing. Intuitively I'd think that gravitational potential energy is proportional to distance as described by the near-body equation GPE=-mgh. The alternative for farther bodies (-G*M*m/R) has me confused because it is inversely...

[solved] graph of potential energy Homework Statement A mass of 5 kg follows the potential energy shown by the equation: U(x) = .333(x-4)^3 - \dfrac{x^2}{4} + 5 1. Find the force on the mass at x=2 2. Describe the motion qualitatively if the mass is placed at x=4 m and released 3...

I was writing a script to help me calculate gravitation and various other things when i noticed i don't know how to calculate this I need to calculate the kinetic energy of an object being pulled towards a second object until they meet knowing only the weight of the objects, the distance of the...

This is a question that me and a friend have been wondering. He says that when the ball hits the ground and is at rest for a very brief moment, potential energy will be 0 in the center of the ball, while I thought that it doesn't matter as the entire ball's potential energy is at 0. Which answer...

Hello, I'm studying capacitors in my freshman physics class and I'm not quite following my book here. My book states that we can calculate the potential energy U stored within a capacitor by calculating the work done to charge it. Let q and v be the charge and the potential difference...

Total energy is \frac{1}{2}mv^{2}-mgh=C for a classical non-rotating object right? C can be determined based on an arbitrary initial condition that suits the problem, right? How come it's not \frac{1}{2}mv^{2}+mgh=C? This seems like a more suitable definition of "total" energy. I'm sure there's...

Homework Statement A particle of mass m = 10 kg moves in space under the action of a conservative force. Its potential energy is given by PE = 2xyz + 3z2 + 4yx + 16 where PE is in Joules and x, y, and z are in meters. Calculate the x-, y-, and z-components of the force on the particle...

Homework Statement The potential energy of two atoms separated by a distance r may be written as: U(r) = 4Uatomic * [(r0/r)12 - (r0/r)6] >Given r0 = 4.0 Ao and Uatomic = -0.012795 eV, what is the distance at which there is no net force between the atoms? Express your answer in terms of...

Homework Statement Part 1(complete and correct. I'm including this for context's sake) You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the Earth with enough speed to make it to the moon. You leave the surface of the...

I'm trying to find the avarage enerrgy of an ideal gas when it's under a gravitational potential. I know how to obtain the kinectic avarage energy but the potential energy depends upon the position of each molecule. There is a avarage height lo look for in order to determine this potential term?

Homework Statement Which of the following forces is conservative? (a) F = k(x,2y,3z), (b) F=k(y,x,0), and (c) F=k(-y,x,0). For those which are conservative, find the corresponding potential energy U, and verify by direct substitution that \vec{F} = - \nabla UHomework Equations The Attempt at...

As we all know,Potential energy =mgh.If someone digs a hole and place a ball at 0 height,the potential energy should be zero but it falls somehow.How is this possible?

Greater electric potential but less electric potential energy?? The picture in my book looks like this: 1. The electric potential at pt. B in the parallel-plate capacitor shown here is less than the electric potential at pt. A by 4.50V. The separation between pts. A and B is .120cm, and the...

Homework Statement What happens to the potential energy of a capacitor with length d when said length d is doubled? Use the formula for the potential energy of a capacitor [U = 1/(2C) * Q]. After that, refer to the work done by moving the capacitor the distance d. These two approaches should...

Homework Statement Consider two identical objects released from rest high above the surface of the Earth (neglect air resistance for this question). In Case 1 we release an object from a height above the surface of the Earth equal to 1 Earth radius, and we measure its kinetic energy just...

Homework Statement Here is an illustration to ease understanding: Angle inclined plane: θ = 20.0° spring of force constant k = 525 N/m block: m = 2.71 kg distance of block from spring: d = 0.330 m speed of block: v = 0.750 m/s By what distance is the spring compressed when the block...

is it true that potential energy of a particle always decreases in the direction of conservative force acting on it.

Homework Statement Consider the electric field of two protons b meters apart. The potential energy of the system is equal to: U = \frac{\epsilon_0}{2}\int {\bf E}^2dv = \int({\bf E}_1+ {\bf E}_2)^2dv = \frac{\epsilon_0}{2}\int {\bf E}_1^2dv + \frac{\epsilon_0}{2}\int {\bf E}_2^2dv +...

In my physics class, my teacher has been referring to Potential Energy in a 1D force field as the negative integral of the force with respect to position. AKA: U(x)=-\int{F(x)dx} where U is the potential energy at x and F is the force at x. Can someone please explain this to me in...

Hey all, suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant. I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement. First thing I did was U '(x) = 0 to find the balance points, now...

1. Homework Statement A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass? 2. Homework Equations I know that the potential energy is: Ep = 1/2 kx2 k = mω2

Hello everyone! When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field? If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could...

Homework Statement 3. Water is pumped from one reservoir to another 100m away. The water level in the second reservoir is 20m above the water level of the first reservoir. What is the increase in specific potential energy of the water in J/kg? Homework Equations The relevant equation I've...

Hi, If I have a body which is freely vibrating with kinetic energy given by, say, Ekin=(1-1/10sin(ωt))cos2(ωt) what can be said about the potential energy? Of course the total energy should be constant but how big is it, in other words what is the potential energy? Thanks!

hi, please can anyone analyze the following sentence in terms of the formulas of electrostatic forces or Potential energy (assuming electrostatic force is directly proportional to potential energy) statement: "When the force between two objects is attractive and decreases with distance, the...

I really don't understand this example: A feather or spring or whatever it's called got the stiffness 29.5 N/m. It is lying inside a horizontal tube (feather cannon). The feather /spring is connected in the very end of the tube. The feather / pring is as "long" as the tube if it's not being...

I am wondering how this all works and am hoping to get some guidance. If a 1000 lb weight freefalls vertically from 660 ft the energy is 894,289 joules. If the fall is down a 30 degree slope that is 1300 ft long, then it takes 17 seconds and the potential energy can be said to be 53 KW. If...