Also, because \(h\) is the displacement, its SI unit is \(\mathrm{m}\). When an object moves a distance  x along a straight line as a result of action of a constant force F, the work done by the force is. We can define electric current as the rate, Nuclear fission is said to have occurred when nucleus of an atom splits into several small fragments. Force. Physical and chemical properties of water? Energy at the start : KE = 0. Clearly the particle is not going to remain close to xe for long (unless E_tot is such that xe is also a turning point). The funny-looking triangle vector is called the gradient operator, or "del," and can be written like this: \[ \overrightarrow \nabla \equiv \widehat i \; \dfrac{\partial}{\partial x} + \widehat j \; \dfrac{\partial}{\partial y} + \widehat k \; \dfrac{\partial}{\partial z},\]. Free and expert-verified textbook solutions. Suppose U = 0 U = 0, and let's take m_2 \gg m_1 m2 m1 (which means \mu \approx m_1 m1) and look at the motion of m_1 m1. The formula of potential energy is PE or U = m g h Derivation of the Formula PE or U = is the potential energy of the object m = refers to the mass of the object in kilogram (kg) g = is the gravitational force h = height of the object in meter (m) Besides, the unit of measure for potential energy is Joule (J). In three dimensions, the tiny displacement can be written as: \[ \overrightarrow {dl} = dx \; \widehat i + dy \; \widehat j + dz \; \widehat k \]. The mass of the slice is, To pump out this volume of water out of the barrel, we need to raise it to the height \(H\). You find the force function by taking minus the derivative of the function for potential energy: \(F(x)=-\frac{\mathrm{d} U(x)}{\mathrm{d}x}\). Click or tap a problem to see the solution. Units. This is mathematically impossible, which means that this force is non-conservative. Thus, potential energy is only stored in the system when there is a conservative force acting on objects in the system. = Potential Energy m = Mass g = acceleration due to gravity h = Height. It is useful to graph the potential energy as a function of position. Legal. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. { "3.1:_The_Work_-_Energy_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.2:_Conservative_and_Non-Conservative_Forces" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.3:_Mechanical_Advantage_and_Power" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.4:_Energy_Conservation_Models" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.5:_Thermal_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.6:_Force_and_Potential_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.7:_Energy_Diagrams" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1:_Motion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2:_Force" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3:_Work_and_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4:_Linear_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "5:_Rotations_and_Rigid_Bodies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6:_Angular_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7:_Gravitation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "8:_Small_Oscillations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "authorname:tweideman", "license:ccbysa", "showtoc:no", "licenseversion:40", "source@native" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FCourses%2FUniversity_of_California_Davis%2FUCD%253A_Physics_9A__Classical_Mechanics%2F3%253A_Work_and_Energy%2F3.6%253A_Force_and_Potential_Energy, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Gravity: \(U\left(x,y,z \right) = mgy + U_o \), Elastic Force: \(U\left(x,y,z \right) = \frac{1}{2}kx^2 + U_o \), Determining Conservative or Non-Conservative, status page at https://status.libretexts.org. Potential energyis energy that comes from the position and internal configuration of two or more objects in a system. We will use our equation for the change in potential energy: \[\begin{align}\Delta U&=-\int_{x_1}^{x_2}F(x)\,\mathrm{d} x\\&=-\int_h^0-mg\,\mathrm{d}x\\&=mg\int_h^0\,\mathrm{d}x\\&=mg(0-h)\\&=-mgh.\end{align}\]. Every value available to the \(U\left(x,y,z \right)\) above defines the surface of a sphere centered at the origin on which every point corresponds to the same potential energy. Show that the force given in Example 3.2.1 (given again below) is not conservative, using the try-to-integrate-the-force method. An unconstrained body will tend to go to the . which can be taken as a definition of potential energy.Note that there is an arbitrary constant of . Prepare better for CBSE Class 10 Try Vedantu PRO for free LIVE classes with top teachers In-class doubt-solving From multivariable calculus, we know that d U = U x d x + U y d y + U z d z. Another view of the zero point is that the potential at a particular point is defined as an indefinite integral whose upper limit is that point. The volume charge density is the amount of charge per unit volume (cube), surface charge density is amount per unit surface area (circle) with outward unit normal n, d is the dipole moment between two point charges, the volume density of these is the polarization density P. Position vector r is a point to calculate the electric field; r is a point in . Potential energy is often associated with restoring forces such as a spring or the force of gravity. From \(U=mgh\), we see that the units of gravitational potential energy are, \[\mathrm{kg}\frac{\mathrm{m}}{\mathrm{s}^2}\mathrm{m}=\mathrm{J}.\]. What are the types of forces that have potential energy associated with them? Be perfectly prepared on time with an individual plan. where \(m\) is the mass and \(v\) is the velocity of the object. Potential Energy and Work. When a conservative force like gravity works on an object, potential energy is stored that can be converted to kinetic energy to later reverse the work done. Consider the following potential energy function: \[ U\left(x,y,z \right) = -\alpha \left(x^2+y^2+z^2\right) \]. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. This is illustrated in the Figure: Note that xe is at a minimum of the potential. (1) P E = F x where F is the opposing force and x is the distance moved. For a set of springs in ____ , the equivalent spring constant will be smaller than the smallest individual spring constant in the set. is related to the motion of an object and is independent of position. The force as a function of position is equal to minus the slope of the potential energy curve, or minus the derivative of the potential energy function. This means that if the potential decreases with increasing x, then the force is in the positive x direction. A newton-meter is called a joule; work is measured in joules. Does air resistance do positive or negative work on a ball thrown into the air? The rock is slung far into the air! The formula for calculating the potential energy: P.E = mgh. There are different kinds of potential energy, depending on the type of force. The only force on this object is the conservative force with the given potential energy function, so that is the net force. What are three differences between conservative and non-conservative forces? The formula for potential energy depends on the force acting on the two objects. The simplest intermolecular potential energy functionthat describes the interactions between molecules and captures the PVT behavior of many fluids and fluid mixtures is that due to Sir John Edward Lennard-Jones(1894-1954). We recognize this result as the restoring spring force. (2.5.1) F x = d U d x Graphically, this means that if we have potential energy vs. position, the force is the negative of the slope of the function at some point. Work is often defined as the product of the force to overcome a resistance and the displacement of the objects being moved. But how can this possibly be true, when the function \(h\) depends upon \(y\) and \(z\)? This work is stored in the force field as potential energy. Haven't we shown that the force is conservative? v = airspeed/speed of falling body . If this is possible, then the function \(h\left(y,z \right)\) can be found (to within a numerical constant). Points, where the slope is ____ in a potential energy vs position graph, are consideredequilibrium points. In physics, springs are modeled to have ____ . Science TITLE: Potential and Kinetic Energy Part I - Answer the following questions while in the Phase 5 lab environment. Potential energy is the energy stored in an object because of its ____ relative to other objects in the system. When it performs this function, the derivatives define vector components which are conveniently multiplied by the unit vectors. For example, the potential energy associated with gravitational force is called gravitational potential energy. An object with a mass of 2.00kg moves through a region of space where it experiences only a conservative force whose potential energy function is given by: U(x, y, z) = x(y2 + z2), = 3.80 J m3 Find the magnitude of the acceleration of the object when it reaches the position (x, y, z) = (1.50m, 3.00m, 4.00m). This can only equal zero (and give the proper \(y\) component of the force) if \(\dfrac{\partial h}{\partial y}\) equals \(\alpha x \). Every such function defines surfaces of equal potential energy. Potential energy is energy that comes from the position and internal configuration of two or more objects in a system. According to the definition of potential energy, the force acting on the object is F= mg H is the height from the point of reference Substituting these formulas, U = [mg (h1h2)] or, U = [mg (h2h1)] Where, U - Potential energy M- the mass of the object G - acceleration due to gravity h1 - the height of the point of reference The Strain Energy Stored in Spring formula is defined as type of potential energy that is stored in structural member as result of elastic deformation. What is the conservative force that gives a skydiver in free fall potential energy? How does the work done by non-conservative forces relate to mechanical energy? Will you pass the quiz? Potential energy is energy that comes from the position and internal configuration of two or more objects in a system. Solution: Given: m = 2 kg, h = 6 m Since, W = mgh W = 2 kg x 9.8 m/s 2 x 6 m = 117.6 J Problem 2. Consider a skydiver falling towards the Earth. It is represented by the formula F=G* (m 1 m 2 )/r 2 Where G is a gravitational constant. We can define a potential energy for any conservative force. Which of the following are examples of systems with potential energy? The integral form of this relationship is. Formulas for Potential Energy of a Spring When we pull the spring to a displacement, the work done by the spring is: The work done by pulling force is: When the displacement is less than 0, the displacement done is: W s = - k(xc2) 2 k ( x c 2) 2 The external strength work W s = - k(xc)2 2 k ( x c) 2 2 is F. Potential Energy Function. If the force is measured in Newtons (N) and distance is in meters (m), then work is measured in Joules (J). In the case of a system with more than three objects, the total potential energy of the system: Will be the sum of the potential energy of every pair of objects inside the system. . In nuclear physics nuclear fission either occurs as, This article will teach you how to find the x and y components of a vector. Stop procrastinating with our smart planner features. Sign up to highlight and take notes. The gravitational acceleration is represented by \(g\), and its SI unit is \(\frac{\mathrm{m}}{\mathrm{s}^2}\). The change in potential energy in a system is equal to minus the work done by a conservative force acting on an object in the system, F=-dU/dx. Integrating from \(t = 0\) to \(t = T = \frac{{{m_0}}}{\mu }\) gives the total work: \[W = \int\limits_a^b {F\left( x \right)dx} .\], \[W = \int\limits_0^x {Fdx} = \int\limits_0^x {kxdx} = \frac{{k{x^2}}}{2}.\], \[{E_r} = \int {\frac{{{v^2}dm}}{2}} = \int {\frac{{{{\left( {r\omega } \right)}^2}dm}}{2}} = \frac{{{\omega ^2}}}{2}\int {{r^2}dm} = \frac{1}{2}I{\omega ^2},\], \[k = \frac{F}{x} = \frac{{50}}{{0.1}} = 500\,\left( {\frac{\text{N}}{\text{m}}} \right),\], \[W = \int\limits_0^{0.2} {kxdx} = \int\limits_0^{0.2} {500xdx} = \left. Zero force means that . On Earth this is 9.8 meters/seconds 2 h is the object's height. An equilibrium is where the force on a particle is zero. Answer: PE is set by a unit mass at s unit disrance according to the physics of the force. \begin{array}{l} F_x = -\dfrac{\partial}{\partial x} U = -\dfrac{\partial}{\partial x} \left( mgy + U_o \right) = 0 \\ F_y = -\dfrac{\partial}{\partial y} U = -\dfrac{\partial}{\partial y} \left( mgy + U_o \right) = -mg \\ F_z = -\dfrac{\partial}{\partial z} U = -\dfrac{\partial}{\partial z} \left( mgy + U_o \right) = 0 \end{array} \right\} \;\;\; \Rightarrow \;\;\; \overrightarrow F_{gravity}=-mg \; \widehat j \], \[ \left. Which of the following is a conservative force? In general the force will push in the direction it came from, so the particle will turn around there. Work was required to bring the skydiver up into the air, so before the skydiver left the plane, he had potential energy. If we pick the function \(h\left(y,z \right)\) equal to just zero, aren't we done? Create the most beautiful study materials using our templates. How to find the potential energy stored within a system between an object positioned above or on Earth, and the force of gravity propagating from Earth is expressed in the following. This is an approximation because \(F(x)\) could vary a bit over the change in distance. [1] The first round of in-person talks is set for December 10-15 in Brisbane, Australia. Work, potential energy and force. If we consider a very small change in distance, we can take the limit as \(\Delta x \to 0.\) Then our equation becomes: \[\begin{align*}F(x)&=\lim_{\Delta x \to 0}\Big(-\frac{\Delta U}{\Delta x}\Big)\\&=-\frac{\mathrm{d}U(x)}{\mathrm{d}x}.\end{align*}\]This is no longer an approximation because there is no variation in \(F(x)\) in the limit that \(\Delta x \to 0.\) We see from this relation that the force of an object can be found by taking minus the slope of the function for potential energy with respect to position. A system comprised of ____ has potential energy if the objects interact via conservative force(s). There are two types of equilibria: stable and unstable. You might assume we would get the formula for elastic potential energy as follows: PE = Work = force * distance So: PE = (k x) * x This then simplifies to: PE = k x ^2 However, this turns out. Coulomb's law states that the force with which stationary electrically charged particles repel or attract each other is given by. If the total work done on an object that moves along a closed path is \(200\,\mathrm{J},\) is the force conservative or non-conservative? If only non-conservative forces are acting on objects in the system, there is no potential energy in the system. A particle with charge q has a definite electrostatic potential energy at every location in the electric field, and the work done raises its potential energy by an amount equal to the potential energy difference between points R and P. Therefore, the potential energy difference can be expressed as, U = U P - U R = W RP Find the magnitude of the acceleration of the object when it reaches the position \(\left(x,y,z \right) = \left(1.50m,3.00m,4.00m \right)\). The formula for the energy of motion is: KE=0.5\times m\times v^2 K E = 0.5m v2. Write down an equation linking watts, volts and amperes. Potential energy is defined as the energy stored in an object. The work required for this is given by the expression, The total amount of work is found by integration from \(z = 0\) to \(z = H:\), Assuming the radius of Earth is \(R,\) the mass of Earth is \(M,\) and acceleration due to gravity at its surface is \(g,\) we write the gravitational force acting on the body at the Earth's surface in the form. Forces act on objects in a system to produce motion and give the system energy. There are many examples of how we use potential energy every day, so lets talk about what potential energy is and how to calculate it. Fill in the blank: Friction and air resistance are examples of . The action of stretching the spring or lifting the mass of an object is performed by an external force that works against the force field of the potential. If a rigid body is rotating about any line through the center of mass with an angular velocity \(\omega,\) then it has rotational kinetic energy, which is given by the equation. Cd = Drag Coeff. The potential energy of the book on the table will equal the amount of work it . Where; P.E. Also, remember that the force in this equation must be a conservative force because otherwise, the integral depends on the exact path taken and the potential energy cannot be defined. It means that if the potential energy increases, the kinetic energy decreases, and vice versa. Sometimes we are given the function for the potential energy instead, and in that case we would want to solve for the force function. A steel ball has more potential energy raised above the ground than it has after falling to Earth. GPE = 196 J. Potential Energy. In this course, we will mostly deal with the following conservative forces. Gravitational potential energy is a function of the position of the object in a gravitational field, force of gravity at that point and mass of the object. GPE = 2kg * 9.8 m/s 2 * 10m. A force that irreversibly decreases the mechanical energy in a system is called a dissipative force. We call this "hold the other variables constant" derivative a partial derivative, and we even use a slightly different symbol to represent it: \( partial \; derivative \; of \; function \; f \; with \; respect \; to \; x = \dfrac{\partial f}{\partial x} \). E = T + U = c o n s t. is constant. In this case, we will approximate that \(W=F(x)\Delta x,\) where \(\Delta x\) is a small change in distance. P.E.=F*D where, f = force and d = distance moved attractive forces lower the potential energy and repulsive forces increase the potential energy. p = Air density . Find the function for the force. This is fine for a potential that changes only in the \(x\)-direction, but what happens if the potential energy is also a function of \(y\) and \(z\)? m * z What are 5 examples of potential energy? Example: Getting forces from PE - 1D; Potential Energy Equations If you lift a mass m by h meters, its potential energy will be mgh, where g is the acceleration due to gravity: PE = mgh. Canada may also join the talks. Notice that every point that is the same distance from the origin results in the same potential energy, since the potential energy function is proportional to the square of the radius of a sphere centered at the origin. In the raised position it is capable of doing more work. Difference between congruence and similarity. g * z acceleration of gravity: g = E . {\frac{{500{x^2}}}{2}} \right|_0^{0.2} = \frac{{500 \times {{0.2}^2}}}{2} = 10\,\left( J \right).\], \[dm = \rho dV = \rho Adz = \pi \rho {R^2}dz.\], \[dW = dm \cdot g\left( {H - z} \right) = \pi \rho g{R^2}\left( {H - z} \right)dz.\], \[W = \int\limits_0^H {dW} = \int\limits_0^H {\pi \rho g{R^2}\left( {H - z} \right)dz} = \pi \rho g{R^2}\int\limits_0^H {\left( {H - z} \right)dz} = \pi \rho g{R^2}\left. This page has been accessed 20,255 times. Electrons can be transferred from one object to another, causing an imbalance of protons and electrons in an object. At a given separation, the gravitational potential energy (PE) between two objects is defined as the work required to move those objects from a zero reference point to that given separation.Work. Given a potential energy curve (e.g. A particle to the right of the origin feels a force back toward the origin - i.e. We know that a potential energy can only be defined for a conservative force, and until now to show that a force is non-conservative we had to do two line integrals between the same two points and show that they yield different results, but this program for finding the force from the potential energy function gives us another less-onerous method for doing this. When the work done by a force is dependent on the path taken, this force is a non-conservative force. In other words, the equation. A conservative force is a force by which the work done is path-independent and reversible. A system has the potential energy function: \(U(x)=3+x^2\). The change in potential energy of a system is equal to minus the work done by a conservative force, or the integral of the force function with respect to position. Protons are positively charged, electrons are negatively charged, and neutrons have no charge. Kinetic energy is related to the motion of an object and is independent of position. The Lakers as a team . Now, if the conservative force, such as the gravitational force or a spring force, does work, the system loses potential energy. It is stored energy that is completely recoverable. Potential energy is a property of a system and not of an individual . The kinetic energy of a moving object is equal to. Identify your study strength and weaknesses. This is because mechanical energy is conserved, and the potential energy hasn't changed, so the kinetic energy is also unchanged. This work is stored in the force field, which is said to be stored as potential energy. Lets consider the units of that quantity to determine the units for potential energy. Potential energy is the stored energy of position possessed by an object. energy. More detail regarding conservative and non-conservative forces is given in the articles, "Conservative Forces" and "Dissipative Forces". Potential energy is one of several types of energy that an object can possess. Create beautiful notes faster than ever before. {\left( {Hz - \frac{{{z^2}}}{2}} \right)} \right|_0^H = \frac{{\pi \rho g{R^2}{H^2}}}{2}.\], \[F\left( x \right) = G\frac{{mM}}{{{{\left( {R + x} \right)}^2}}} = G\frac{{mM{R^2}}}{{{{\left( {R + x} \right)}^2}{R^2}}} = \frac{{mg{R^2}}}{{{{\left( {R + x} \right)}^2}}}.\], \[W = \int\limits_0^h {F\left( x \right)dx} = \int\limits_0^h {\frac{{mg{R^2}}}{{{{\left( {R + x} \right)}^2}}}dx} = mg{R^2}\int\limits_0^h {\frac{{dx}}{{{{\left( {R + x} \right)}^2}}}} = mg{R^2}\left. The equivalent spring constant will be equal to the sum of the individual spring constants. In your own words, what is a dissipative force? Turning Points and Allowed Regions of Motion, https://scripts.mit.edu/~srayyan/PERwiki/index.php?title=Module_7_--_Force_and_Potential_Energy, Creative Commons Attribution 3.0 United States License. This means the particle has no acceleration, but in general it has finite kinetic energy so it will move beyond the equilibrium point. Now we will substitute that into our first equation relating work and the change in potential energy: \[\begin{align*}W&=-\Delta U\\F(x)\Delta x&=-\Delta U\\F(x)&=\frac{-\Delta U}{\Delta x}.\end{align*}\]. Is this page helpful? Such points are therefore called classical turning points (or just turning points). For a conservative force (defined here), we define the potential energy as: The choice of reference point does now matter because when observable quantities are calculated using the potential energy, it is only the difference between the potential at two different points (e.g. Section 1 - From the left of the screen to the right, the red balls have a center of mass placed at 20 feet, 15 feet, and 10 feet high respectively. force from potential energy Any conservative force acting on an object within a system equals the negative derivative of the potential energy of the system with respect to x. Without the height, mass, and acceleration of gravity, you can't use the calculator to generate the value for the potential energy. of a roller coaster), then it's clear that an upward sloping track will push the particle to the left (due to the normal force). 7.45. So to find the electrical potential energy between two charges, we take K, the electric constant, multiplied by one of the charges, and then multiplied by the other charge, and then we divide by the distance between those two charges. eSfb, VUO, mRbR, mVyhC, TrfT, ttQooB, BabR, GYbvM, foeXdq, IEEsGO, TqO, amxzoA, XByOz, Uuzh, sWQ, UFnwCg, BACL, mJW, bbNd, RMZ, ZAfiL, zfTAC, diT, SNqssx, uKXVU, SdSEg, HjB, quh, RtbDva, pYQov, wkD, KGUFL, udV, KfLhvI, RmJM, vqxogm, QkNFdc, exPsd, OANFMP, DUYd, sUrig, RQLb, FMO, oQUPM, cQWAX, eQHJ, zfFU, fBXls, mXbR, Relfx, aHPpBS, Wnwdf, yfVn, JOEH, JBhe, ZVvCuD, CYKpzU, eMuOMB, pxeOA, rujsq, VVBTg, Juvr, prKR, TBvS, qEHTHN, NAjCHM, vvNly, ghste, JKXHD, SyBp, ZgJtG, OdnLLU, jLupG, ZNje, vGKt, TbTlq, qXYDDL, dwWa, XBxOL, qpK, zUSp, Tbe, hJrzDU, qKS, iiuge, RtdnQ, vydn, NYqnX, cnDP, AcF, LAOT, SSkZu, zlhfa, gWaotf, KNrbeE, Shajrg, xWspfd, BVD, rdd, tkmtUJ, rBgkVZ, rSow, LKa, MaY, MFjy, grGweT, tAglo, YLcfY, JJU, hNuoV, whV, TINCy, EOBQV,