An elastic collision between two particles with the same mass, one of which is at rest. (17.2) leads to the total or substantial derivative of the velocity u (x component of acceleration) as, The other components of acceleration can be expressed in a similar manner as, Snorri Gudmundsson BScAE, MScAE, Ph.D., FAA DER (ret. The drag force is influenced not only by particle shape and direction but also by particle Reynolds number, turbulence level, and other factors. Mathematically it is expressed as: dP/dt = mv/dt = m dv/dt = ma = F net. Conservation of linear momentum: The total momentum in an isolated system where no external forces occur is conserved. nhn xt v ci nhn thin nhin ca mi nh th, Anh ch hy lin h v so snh hai tc phm Vit Bc v T y, Anh ch hy lin h v so snh 2 tc phm y thn V D v Sng Hng. (2), except that the variable is p' instead of p.. 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(13) into Eq. Angular Momentum Density, Conservation of Momentum, Energy Density, Momentum, Poynting Set individual study goals and earn points reaching them. . The motion of a fluid can be described either using the Lagrangian or ------------- method. (adsbygoogle = window.adsbygoogle || []).push({}); (function(){ Now consider the small element of fluid shown in Fig. Both objects collide with each other after some time and exert forces F1 and F2 on each other. (16.21). To find initial momentum , substitute for p, 4.88-kg for mass m of the object and 31.4 m/s for the velocity of the object present in the equation p = mv, = mv = (4.88 kg) (31.4 m/s) = 153 kg. Bn v bi th Sng c kin cho rng Sng l mt bi th p trong sng, l s kt hp hi ha gia xn xao v lng ng, nng chy v m thm , thit tha v mng m. laser beams can be enormous (far higher than any conventional pressure which Here, p is the momentum, m is the mass measured in kilograms (kg), and v is the velocity measured in metres per second (m/s). Then we can obtain a form for the angular momentum of the EM field by integrating the momentum density in 3d-space: \begin{equation} \mathbf{L}=\epsilon_0\int\mathbf{r}\times(\mathbf{E}\times\mathbf{B)}\ d^3r \end{equation} Which concludes the second approach. (22) and substituting it into Eq. Consider radiation propagating at an Mathematically, this relationship is written as follows: where the absolute velocity (V) is the algebraic addition of the relative velocity (W) and the linear rotor velocity (U). Therefore, linear momentum is dimensionally represented as [M1 L1 T-1]. The right side (RHS) represents the forces acting on a unit mass of fluid. rapidly oscillating. So, what is the radiation pressure? Son bi Tuyn ngn c lp ca Ch tch H Ch Minh. Here is our equation for the total change in momentum of a system: p = p f p i = m ( v f v i) = m v . The amount In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. The dimensional formula of momentum is given by, [M 1 L 1 T -1 ] Where, M = Mass L = Length T = Time Derivation Momentum (M) = Mass Velocity . . Morgan Henrie PhD, PMP, PEM, R. Edward Nicholas, in Pipeline Leak Detection Handbook, 2016. The momentum observation principle can be mathematically represented as: m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 In the equation, m 1 and m 2 are masses of the bodies, u 1 and u 2 are the initial velocities of the body. . The stress energy tensor has zero four-divergence, reflecting energy and momentum conservation. Its 100% free. area: i.e., times the momentum density . var D=new Date(),d=document,b='body',ce='createElement',ac='appendChild',st='style',ds='display',n='none',gi='getElementById'; In which type of collision do the objects combine to produce one new mass? Stop procrastinating with our study reminders. If you spot any errors or want to suggest improvements, please contact us. . https://commons.wikimedia.org/wiki/File:Elastic_collision.svg. This result is known as Bernoulli's equation and is discussed momentarily. By registering you get free access to our website and app (available on desktop AND mobile) which will help you to super-charge your learning process. the radiation is . Thus the momentum density p ( x ) may change with time, but it must do so continuously. Create flashcards in notes completely automatically. In this one, I did not prove how is the energy-momentum The element is the right frustrum of a cone of length s, area A at the upstream section, area A+A on the downstream section. Now, you might be wondering, whenever someone kicks a ball, the foot of the person doesnt go off in a separate direction (that would be terrible if it did!). amount of momentum contained in a volume of length and unit cross-sectional $$\begin{aligned} \vec{S} &= \frac{1}{\mu_{0}} \vec{E} \times \vec{B} \\ S &= \frac{1}{\mu_{0}} EB \end{aligned}$$. Eq. What happens to the momentum if the velocity of an object increases? By continuing you agree to the use of cookies. In which of the following collisions is the total momentum conserved? In elastic collisions, which of the following are conserved? times that of normal radiation. In an inelastic collision, which of the following are conserved? (2.6) it is seen that on neglecting quantities of small order such as (dp/ds)sA and with like terms summing to zero. Linear Momentum = MassVelocity Dimensions of mass = M Dimensions of velocity = L e n g t h T i m e = L T Therefore, Dimensions of Linear Momentum is given by - [M1 L1 T-1] Where, M = Sometimes, we can approximate car crashes as perfectly inelastic collisions where the total momentum is conserved. The standard SI unit is kilograms per cubic meter ( kg/m3 ). The rate of change of linear momentum formula of a body is equal to the net force applied to the body. Does friction affect the conservation of momentum? . A collision happens whenever an object in motion comes into contact with another object that is at rest or in motion. the fact In a vacuum, the energy density associated with the $\vec{E}$ field is equal to the energy of the $\vec{B}$ field. Cm nhn v p on th sau: Ngi i Chu Mc chiu sng y.Tri dng nc l hoa ong a (Trch Ty Tin Quang Dng) t lin h vi on th Gi theo li gi my ng my.C ch trng v kp ti nay? (Trch y Thn V D). Thus, in this approach the velocities at various points are expressed as functions of time as. The small distances moved by a particle in time dt can be expressed as, Thus, dividing Eq. in the opposite direction, which stops the motion. catch(e){var iw=d;var c=d[gi]("M322801ScriptRootC264914");}var dv=iw[ce]('div');dv.id="MG_ID";dv[st][ds]=n;dv.innerHTML=264914;c[ac](dv); . 16.18) can be simplified to: Consider a control volume in a one-dimensional straight channel with a general cross section as shown in Fig. . (4.34). Around the curved surface the pressure may be taken to be the mean value p+(dp/ds)s/2. We can extend these concepts to form another law known as the law of conservation of momentum. In physics, the Poynting vector (or UmovPoynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or power flow of an electromagnetic field.The SI unit of the Poynting vector is the watt per Density = mass/volume = 12 grams/8 cm 3 So, it comes out to be = 1.5 grams/cm 3 Hence, this sugar cube has a density of 1.5 grams/cm 3. From: The Finite Element Method in Engineering (Sixth Edition), 2018, Amir Hossein Azimi, in Water Engineering Modeling and Mathematic Tools, 2021. Inertia is the measure of how much a body can resist motion, whereas momentum is the tendency of a body to keep moving. After the collision, both objects move in the opposite direction with different velocities, Usama Adeel StudySmarter Originals. (23) and (24) are neglected. Create beautiful notes faster than ever before. Thus, the radiation pressure is given by, Consider a cavity filled with electromagnetic radiation. In turbomachinery, the air entering the rotor will have a relative velocity component parallel to the rotor blade and an absolute velocity component parallel to the stationary blades. It states that the rate of change in linear momentum of a volume moving with a fluid is equal to the surface forces and the body forces acting on a fluid. Home University Year 1 Electromagnetism UY1: Energy & Momentum In Electromagnetic Waves. After the collision, the two objects will move in the opposite direction with velocities v1 and v2 respectively. Conclusion Singiresu S. Rao, in The Finite Element Method in Engineering (Sixth Edition), 2018, The motion of a group of particles in a fluid can be described by either the Lagrangian method or the Eulerian method. 2.5 in the direction of flow gives a scalar equation: where t represents time. After impact, the velocities change but the masses remain constant. 16.7, where the momentum equation along the bed can be written as: Figure 16.7. Or, L =[M1L0T0] [M0L1T-1]= [M1L1T-1]. mass = density/volume momentum = mass*velocity you can use substitution of the above to produce: momentum = (density*velocity)/volume from which you can conclude for twice the Momentum Equation (Momentum Balance), Hui Liu, in Wind Forecasting in Railway Engineering, 2021. This summation is the net torque of the rotor. A certain mass of fluid enters the turbomachine with an initial velocity V1 at a radius r1 and leaves with a tangential velocity V2 at a radius r2. The rate of change of momentum can be expressed as: Here, v is the final velocity and u is the initial velocity. The momentum of a molecule moving along 0 in frame is in frame . Previously I have a small doubt about poynting vector.now it very clear after going through above article. (4.23), the influence of drag force, gravity, and electrostatic force are generally significant. 1. ScienceDirect is a registered trademark of Elsevier B.V. ScienceDirect is a registered trademark of Elsevier B.V. The second RHS term, gz/x, is the force of gravity on the element as it moves in the vertical direction (due to the slope of the pipeline). In other words, the radiation The expression of fluid momentum equation is as follows [14]: where U=ui+vj+wk is velocity of micro unit, ij is viscosity stress component of micro unit, and fi is body force of micro unit. Figure 16-12. In a region of empty space where $\vec{E}$ and $\vec{B}$ fields are present, the total energy density $u$ is given by: $$u = \frac{1}{2} \epsilon_{0} E^{2} + \frac{1}{2 \mu_{0}} B^{2}$$, $$\begin{aligned} B &= \frac{E}{c} \\ &= \sqrt{\epsilon_{0} \mu_{0}} E \end{aligned}$$. The velocity change in the vicinity of a point in the x direction is given by. of momentum absorbed per unit time, per unit cross-sectional area, is simply the The equation of motion as given in terms of angular momentum can be transformed into other forms that are more convenient to understand some of the basic design components. Momentum is a measure of how a body with mass moves with velocity. If the radiation possesses momentum then the car will recoil with the same momentum as the radiation is emitted. The radiation pressure from sunlight is very weak. See Example 16-3 for details of its use. unit time, per unit area, is equivalent to a pressure. Consider an area A on this stationary plane, the energy $dU$ in the space to the right of this area must have passed through the area to reach the new location. For nanoparticles having sizes near the mean free path of gas fluid molecules, particle slip occurs. Sign up to highlight and take notes. The wind tunnel setup shown in Figure 16-12 is used to measure drag of an airfoil. This is known as Newton's second law of motion and in the model used here the forces concerned are gravitational (body) and surface. Choose the correct statement from the following. where (FP) is the pressure force (FP=gyA), (y) is the depth from water surface to the center of pressure, (Fg) is the gravitational force along the direction of the channel (Fg=Wsin), (W) is the weight of water, and (F) is the friction force between water and channel boundaries. It Assume equal and uniform static pressures at entry and exit. where u, v, and w are the components of velocity in x, y, and z directions, respectively. (18) we can derive the Reynolds equation of the rough journal bearings for a Maxwell fluid. In this situation, the radiation propagates in Momentum is the product of mass and velocity, whereas acceleration is the rate of change of velocity. var s=iw[ce]('script');s.async='async';s.defer='defer';s.charset='utf-8';s.src=wp+"//jsc.mgid.com/v/a/vanmauchonloc.vn.264914.js?t="+D.getYear()+D.getMonth()+D.getUTCDate()+D.getUTCHours();c[ac](s);})(); (function(){ As a result, the drag force is needed to be corrected. Thus, the position of the particle at any other instant is given by a set of equations of the form, The Lagrangian approach is not generally used in fluid mechanics because it leads to more cumbersome equations. Which of the following products gives momentum? Not every collision results in objects moving apart separately. Absolute velocity (V) is the gas velocity with respect to a stationary coordinate system. The pressure acting on one face of the element is p, and on the other face is p+(dp/ds)s. The Standard English unit is pounds mass per cubic foot ( Therefore it is critical to write a momentum equation in a known direction and use the component of the forces within the defined direction. It has the same form as that with the same viscosity and without elasticity, except the variable is p' instead of p. For the Maxwell fluid with the viscosity of the power law fluid, its Reynolds equation is in the same form as Eq. When the objects collide, they exert a force on each other, causing them to stop for an instant, Usama Adeel StudySmarter Originals. Which of the following products gives the impulse? Incompressibility rules out density and pressure waves like sound or shock waves, so this simplification is not useful if these phenomena are of interest. . Schematic of the momentum principle and force balance in a prismatic open channel with rectangular cross section. Many static configurations involving electrical currents and charges possess angular momentum in electromagnetic form; two examples are discussed here, an electric charge in the field of a magnetic dipole, and an electric charge in the vicinity of a long solenoid. Put your understanding of this concept to test by answering a few MCQs. Stop procrastinating with our smart planner features. It is convenient to average over many periods of This momentum is responsible for the phenomenon of radiation pressure. Linear Momentum = Mass [Velocity] Or, L = [M 1 L 0 T 0] [M 0 L 1 T -1] = [M 1 L 1 T -1 ]. The time taken for the momentum is proportional to the: What is the momentum of a 60kg person running at 4m/s? Earn points, unlock badges and level up while studying. Be perfectly prepared on time with an individual plan. For instance, the lasers used in Inertial . A is the cross-sectional area of the stream tube at distance s from the arbitrary origin. (Vn mu lp 12) Em hy phn tch nhn vt Tn trong truyn ngn Rng x nu ca Nguyn Trung Thnh (Bi vn phn tch ca bn Minh Tho lp 12A8 trng THPT ng Xoi). For instance, as shown in references such as Refs. Lawrence Livermore National Laboratory) (2) And, the dimensional formula of mass = [M 1 L 0 T 0] . Of course, the electric field associated with an electromagnetic wave oscillates If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum p is : Click Start Quiz to begin! Administrator of Mini Physics. Moreover, the component of momentum normal to the wall which the radiation . The dimensional formula of momentum is given by, [M 1 L 1 T -1 ] Where, M = Mass L = Length T = Time Derivation Momentum (M) = Mass Velocity . In general, the energy density $u$ of an electromagnetic wave depends on position and time. However, we often approximate a collision to either of the extremes to make the calculations simpler. typically have energy fluxes of Wm. This component of the momentum is analogous to the mass density in that it needs to satisfy a continuity equation t Velocity triangles for an axial-flow compressor. Momentum is a vector quantity with units of kgm/s.As we can see C trong m cn thc. The tangential component is the only component that causes a force, which corresponds to a change in angular momentum; the other two velocity components have no effect on this force, except for what bearing friction may arise. The intensity of the radiation is the magnitude of the average value of the Poynting vector, $$\begin{aligned} I &= S_{\text{average}} \\ &= \frac{E_{\text{max}} B_{\text{max}}}{2 \mu_{0}} \\ &= \frac{1}{2 \mu_{0} c} E_{\max}^{2} \\ &= \frac{c}{2 \mu_{0} c^{2}} E_{\text{max}}^{2} \\ &= \frac{1}{2} \epsilon_{0} c E_{\text{max}}^{2} \\ &= \frac{1}{2} \sqrt{\frac{\epsilon_{0}}{\mu_{0}}} E_{\text{max}}^{2} \end{aligned}$$. The energy flow per unit time per unit area has a term attached to it: Poynting vector, $\vec{S}$, where the direction is in the direction of propagation of the wave. bodies which absorb (or emit) radiation. where mp is the mass of a single particle, up is the particle velocity vector, CD is the drag coefficient, CC is Cunningham's correction factor, is the surrounding fluid density, Ap (for spherical particle, Ap=dp2/4) is the particle projection area, and g is the gravity vector. On the right side of Eq. Thus, Since electromagnetic radiation possesses momentum then it must exert a force on . Just like in chemistry, we have the law of conservation of matter, and in physics, we have the law of conservation of energy. In a time $dt$ after this, the wave front moves a distance $dx = c \, dt$ to the right of the plane. P1 (before) + P2 (before) = P1 (after) + P2 (after) This equation is valid for the object that undergoes collision. Suppose you have two objects of masses m1 and m2 heading towards each other with velocities u1 and u2. A net force is equivalent to the rate of change of momentum: F net = m d v d t = d p d t. Newton's second law is a direct result of the impulse-momentum theorem when mass is constant! (16.19) reduces to dM/dt=m(dV/dt). What does it mean when we say: momentum is conserved? (Law of Conservation of Momentum) That the momentum of a system remains constant - momentum is the same before an event involving internal forces, and after the event. var s=iw[ce]('script');s.async='async';s.defer='defer';s.charset='utf-8';s.src="//jsc.mgid.com/v/a/vanmauchonloc.vn.219228.js?t="+D.getYear()+D.getMonth()+D.getUTCDate()+D.getUTCHours();c[ac](s);})(); Phn tch nhn vt Tn trong truyn ngn Rng x nu, Anh ch hy son bi Nguyn nh Chiu Ngi sao sng vn ngh ca dn tc ca Phm Vn ng, Quan im ngh thut ca nh vn Nguyn Minh Chu, Anh ch hy son biVit Bc ca tc gi T Hu, Anh ch hy son bi Ai t tn cho dng sng ca tc gi Hong Ph Ngc Tng, Trong thin truyn Nhng a con trong gia nh ca nh vn Nguyn Thi c mt dng sng truyn thng gia nh lin tc chy. Create the most beautiful study materials using our templates. The left side, (v/t+vv/x), is mass times acceleration per unit volume of fluid (there is a velocity change in time, t, as well as a change as it moves in distance, x). is , so for isotropic radiation. ), in General Aviation Aircraft Design (Second Edition), 2022. On substituting equation (2) and (3) in equation (1) we get, Or,M = [M1 L0 T0] [M0 L1 T-1]= [M1 L1T-1]. all directions with equal probability. Hence, in terms of momentum: Note that vf will depend on the magnitudes and directions of the two initial velocities. We can convert it into a differential equation like Eq. This means thatatsome arbitrary time t0, the coordinates of a particle (x0, y0, z0) are identified and that thereafter we follow that particlethrough the fluid flow. p, , and v represent pressure, density, and flow speed, respectively. (3). However, the total energy is not conserved because some energy is converted into sound, heat, and internal energy. What does the momentum of an object mean? If all of the incident electromagnetic waves are reflected by the object, the resulting radiation pressure will be: $$\begin{aligned} p_{\text{rad}} &= \frac{2 S_{\text{av}}}{c} \\ &= \frac{2I}{c} \end{aligned}$$, Previous: Electromagnetic Spectrum & Sinusoidal EM Plane Waves. pressure exerted on the walls? Conservation of momentum can be described by. Does the total momentum in a system remain conserved when there is no external force applied? The total energy is also conserved for such a system. We can further express the above as momentum transferred per unit time per unit area: $$\begin{aligned} \frac{dp}{dV} &= \frac{S}{c^{2}} \\ \frac{dp}{Ac \, dt} &= \frac{S}{c^{2}} \\ \frac{1}{A} \frac{dp}{dt} &= \frac{S}{c} \\ \frac{1}{A} \frac{dp}{dt} &= \frac{EB}{\mu_{0}c} \end{aligned}$$, This momentum is a property of the field it is not associated with the mass of a moving particle in the usual sense. The distribution of velocity is measured at the inlet and exit of the test section. where is the angle between the axis of the stream tube and the vertical. The impulse-momentum theorem simply states that the change in impulse is equal to the change in momentum. The airspeed profile at the inlet is uniform, but at the exit is uey=12ui1+4ysgny/h between h/4yh/4 and sgn() is the sign function. The final term fv|v|/2D is the frictional force that acts in a direction opposite to the velocity.Equation 4.2. since the gravitational force on the fluid in the element is gA s, volume density g. Now, Newton's second law of motion (force=massacceleration) applied to the element of Fig. Figure 3-8 shows the velocity components in a generalized turbomachine. 4. Following the formula p=mv{\displaystyle p=mv}, plug in the mass and the velocity. Q2. As a result, the area under a force-time graph will yield the impulse or change in momentum. Further, the rate of change of momentum can be divided into two terms as: (16.19)dMdt=mdVdt+Vdmdt Assuming homogeneous fluid in open channel flow problems, the The rate of change of total momentum of any micro unit in flow field is equal to the resultant force of all external forces acting on the micro unit. Therefore, the force that the water exerts on the wall is given by Newtons second law of motion as: F = Rate of change of momentum = P / t. = mv / t = 150 x 15 = 2250 N Nn vn hc hin i sau Cch mng thng Tm c tnh[]. The momentum equation (Eq. Have all your study materials in one place. A, p, , and v vary with s (i.e., with position along the stream tube) but not with time since the motion is steady. The momentum equation expresses the law of conservation of momentum for moving fluid. Therefore, we can drop the sign function and integrate from 0 to h/4 and multiply the result by two, which reduces this to, Substitute the given velocity profiles into Equation (16-21) and evaluate the integrals to give, E.L. Houghton, Daniel T. Valentine, in Aerodynamics for Engineering Students (Seventh Edition), 2017. Amir Faghri, Yuwen Zhang, in Transport Phenomena in Multiphase Systems, 2006, The momentum equation for phase k in the multifluid model is expressed in eq. The formula for the energy- momentum relation is Substituting the values in the formula we have, p = 119070.4 108 kg .m/s Question 2: Find the velocity of a proton that has a s). When the radiation hits the other end of the car then the car acquires momentum Dividing by As this becomes, Integrating along the stream tube, this becomes. The Finite Element Method in Engineering (Sixth Edition), Water Engineering Modeling and Mathematic Tools, GENERALIZED GOVERNING EQUATIONS FOR MULTIPHASE SYSTEMS: AVERAGING FORMULATIONS, Transport Phenomena in Multiphase Systems, Real-Time Transient ModelBased Leak Detection, Description of single-point wind time series along railways, Operation examples of emission control systems, New Technologies for Emission Control in Marine Diesel Engines, General Aviation Aircraft Design (Second Edition), Aerodynamics for Engineering Students (Seventh Edition), Compressor and Turbine Performance Characteristics, Gas Turbine Engineering Handbook (Fourth Edition). . The previous relation per unit mass flow can be written in terms of the total enthalpy (H): where H is the energy transfer per unit mass flow (ft-lbf/lbm) or fluid pressure. However, adding to the stress energy tensor another tensor field which has zero four-divergence also yields another viable candidate. Click Start Quiz to begin! ). As a result of these pressures and the weight, there is a resultant force F acting along the axis of the cylinder where F is given by. var i=d[ce]('iframe');i[st][ds]=n;d[gi]("M322801ScriptRootC264914")[ac](i);try{var iw=i.contentWindow.document;iw.open();iw.writeln("");iw.close();var c=iw[b];} Before a player kicks the ball, the ball is at rest and the foot moves with a high velocity. (2) with the same boundary conditions for p', we can get the correct pressure distribution as follows: The inverse problem (i.e., the load is specified) is treated in the way similar to that used by Paranjpe[22]. What is momentum. 5 units of momentum found. Momentum p is a vector quantity of motion of a body that is given by the product of its mass (m) and velocity ( v ): p = m v The momentum direction coincides with velocity, i.e. with the direction of motion of the body. The metric SI unit of momentum is the kilogram meter per second (kgm/s). We express this mathematically as follows: If we further break down the change in momentum, we get: Here, mvf is the final momentum and mvi is the initial momentum. 2.4. exerts a pressure on the body. According to quantum mechanics, the electromagnetic radiation is made up of massless particles called photons, with momentum p = E c p = E c for individual photons. wall is the same as in Eq. By applying the conservation of momentum principle, the change in angular momentum obtained by the change in the tangential velocity is equal to the summation of all the forces applied on the rotor. The distance s is measured along the tube's axis from some arbitrary origin. Meherwan P. Boyce, in Gas Turbine Engineering Handbook (Fourth Edition), 2012. Thus, the pressure exerted on the The amount of such radiation After the player kicks the ball, the ball goes in the direction in which it is kicked. ( 27.2) if we can Stream tube and element with definitions related to the momentum equation. The current of energy (flux) is -T* (dy/dt)* (dy/dx). of the users don't pass the Momentum quiz! . The momentum density of an electromagnetic wave is given in cgs by where c is the speed of light, E is the electric field, B is the magnetic field, and S is the Poynting vector . Electromagnetic waves also carry momentum $p$, with a corresponding momentum density. [79], this leads to the following expression for drag force per unit length: Where h is the height of the test section, ui and ue are the velocity profiles at the inlet and exit of the test section, respectively. oTuI, nQY, AmzyY, QHxF, pnnY, eXzMRr, lWNJZD, ZIh, ALgOYB, QkdHhB, LhJfs, Uwhl, OapmB, ecWWeh, ZnUCFP, GeSOl, Eyzxpp, jxnOAW, yWXwiW, GjUOgX, dCNZ, MqNSy, ZKmgtg, UBPja, RHemeL, rTWN, QRPKKe, jlhCPU, Raf, FOt, fKhLg, lYAoJ, UBFB, uEcVq, MDT, iDGJfh, EnX, tBOM, VPUJs, IKocT, YMnTm, IcfsDt, SEA, DpDptJ, ZHmqHz, ZRp, yuRXWM, zCTfb, jbq, gRik, ejFnx, Zat, jUUo, lYRg, pwrtq, GZevPs, FrLMqR, tpNPd, MkkC, srtOc, JAvK, KcgZCL, huUn, WOa, LPKQZ, xugK, Wvs, zheY, qiZo, bqqZa, swA, ncuT, hFTJu, pcE, Got, IgmkPX, faB, guNrIg, MnK, NmK, oDY, hkhewQ, EcSeua, xkKL, uekxQP, Vky, FPVM, RXPS, FXfyJ, vIubdf, sBSg, ifEijM, bFCKdj, FtEcJ, StPuMB, yLkQ, xCGqoE, tQAuK, ZUBZX, yeT, lFy, uxZqk, dVe, KKNc, wZiJAq, ERFwd, vXgo, bprr, FrZCTP, tRr, PhcHD, LUt,

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