Electric Dipole Moment, Force, Torque, Potential Energy, Work, Electric Field, Physics 197,522 views Jan 8, 2017 This physics video tutorial explains how to calculate the magnitude of the. To the vast replacement business, Torque is the preferred original equipment supplier to many of the companies in the existing battery field. . [1] It is also referred to as the moment, moment of force, rotational force or turning effect,[citation needed] depending on the field of study. {\displaystyle \mathbf {F} } If the angular acceleration of a wheel is 1.00 radians/s 2, what is the torque? He applied the force which is perpendicular to the arm of the wrench. The magnitude of that rotation is torque (), expressed in newton-meters (Nm). The above equation represents the universal torque equation of relay. Note that although force and acceleration are always parallel and directly proportional, the torque need not be parallel or directly proportional to the angular acceleration . s In brief, it is a moment of force. Differences between electromagnetic power and electromagnetic torque. This equation is normally used to derive the horsepower output for a given shaft speed and torque value. Ques.1: Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. , the lowercase Greek letter tau. The handle of the door is located at 20 cm. t (Normally, : approximately 0.05 to 0.1) * The friction coefficient value varies depending on the machine processing accuracy, lubrication condition, and other factors. And let's say you were given these distances here and we want to figure out how much torque does this force of 20 newtons apply if it's at this angle of 60 degrees. For an induction motor; we can write; Put this value in torque equation; Now, consider = constant = K. E1 is nearly equal to V1; At starting condition, slip s = 1; Tst V12. This article follows the definition used in US physics in its usage of the word torque. is the angular velocity. Mathematically, for rotation about a fixed axis through the center of mass, the work W can be expressed as, where is torque, and 1 and 2 represent (respectively) the initial and final angular positions of the body. Torque has the dimension of force times distance, symbolically T2L2M. So, to avoid confusion, we will use the units \(N.m\), and not \(J\). Angular momentum. Rotational inertia. Note! = 22.3 kW approximately 22kW. Torque and Angular Acceleration Fields in Physics Alternating Currents Capacitance Capacitor Charge Capacitor Discharge Coulomb's Law Electric Field Strength Electric Fields Electric Potential Electromagnetic Induction Energy Stored by a Capacitor Escape Velocity Gravitational Field Strength Gravitational Fields Gravitational Potential Whereis the angle between the force applied and the axis of rotation. Energy can be defined as the ability to perform work in physics. Torque (also called moment mostly by engineers) is calculated by multiplying force and distance. Learn More: RLC Circuit Formula, Calculator, Calculation of . The law of Conservation of energy can also be used to understand Torque. A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm) is its torque. * The transmission efficiency between the motor and load varies depending on the . Calculate the torque produced which causes the door to open? These . Force exerted = 2N Take a driveshaft sitting on a fulcrum-like seesaw for examplea 1,000-pound force acting at a perpendicular distance of -feet from the rotation point, A, causes a 500 lb-ft moment about the rotation point, A. Torque and moment in the US mechanical engineering terminology, Definition and relation to angular momentum, Relationship between torque, power, and energy. The SI unit of power is watt, while the SI unit of . . The product has been added to your shopping cart. The unit of work/energy is also Newton-meter or Joule. By contrast, a lateral force on a beam produces a moment (called a bending moment), but since the angular momentum of the beam is not changing, this bending moment is not called a torque. What is the Difference between Interactive and Script Mode in Python Programming? Your Mobile number and Email id will not be published. Force Force is pushing or pulling interaction with an object that can alter its movement, shape, or size. It's unit is Newton-meter. For example, the torque on a current-carrying loop in a uniform magnetic field is the same regardless of the point of reference. = The law of conservation of energy can also be used to understand torque. Torque Energy PMs are well trained and experienced with a vast number of industrial settings. is not zero, and {\displaystyle 5252.113122\approx {\frac {33,000}{2\pi }}.\,}. In vector form, torque is the cross product of the radius vector (from the axis of rotation to the point of application of force) and the force vector. Pay enough attention when calculating the load torque. Answer: The torque can be found using the torque formula, and the moment of inertia of a solid disc. Note that the power injected by the torque depends only on the instantaneous angular speed not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed not on the resulting acceleration, if any). 3. Kane, T.R. A single newton-meter is equal to the energy transferred by a one-newton force acting on an object over a one-meter distance. | When a force F is applied to the particle, only the perpendicular component F produces a torque. Ball hits rod angular momentum . Substituting equations of T 1, T 2, T 3, and T 4 in the above equation, we get, T = K1 I2 + K2 V2 + K3 V I cos ( - ) + K4. By using our site, you This controller operates in the partial load (Region 2), and should maximize the energy production while minimizing mechanical stress and actuator usage; Controller operating in full load condition. d Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. A force of 3N is applied at its edge (which is away from the hinge). Linear velocity v, in metres per second, is related to the angular velocity by the radius of curvature R: w = v / R. This allows us to rewrite the force equation as: F = m R w^2. power) does not change. By the definition of torque: torque = radius force. . [7] If you need to know the output torque of the gear . Torque forms part of the basic specification of an engine: the power output of an engine is expressed as its torque multiplied by the angular speed of the drive shaft. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. In the case of torque, the unit is assigned to a vector, whereas for energy, it is assigned to a scalar. A force of 3N is applied at its edge (which is away from the hinge). The equation for torque can be represented with the following equation: = F * rsin (). Unit. , then the torque measured from To achieve this, we need to do the following three things to the torque equation: 1. If the movable part is kept fixed, the entire electrical energy input will be _____ a) stored in the magnetic field b) stored in the electric field c) divided equally between the magnetic and electric . One can measure the varying torque output over that range with a dynamometer, and show it as a torque curve. r 2. Just as a force is a push or a pull, a torque can be thought of as a twist. F By definition, torque = r F. Therefore, torque on a particle is equal to the The calculator will work out what value you should set into the wrench to achieve the required fastener torque. = When the net force on the system is zero, the torque measured from any point in space is the same. F Question 4: A body is in rotation motion, is it necessary that a torque be acting on it? 5252.113122 000 The torque is: = I. The individual torques add to produce a net torque about the axis. It is easier to open or shut the doors provided with handles near the outer edge far away from the hinges. So, for a given speed and time period, energy delivered by a rotating machine (say engine, turbine or motor) will increase with torque. Did you get all that? The input power provided by the cyclist is equal to the product of angular speed (i.e. In the US, torque is most commonly referred to as the foot-pound (denoted as either lb-ft or ft-lb) and the inch-pound (denoted as in-lb). Apply our torque to kilowatt conversion formula, Motor power in kW = 0.105 x 144 x 1480 / 1000. The distance between bolt to the hand is 60cm. Our products are optimized to generate power for all kinds of electrical loads right from light, fans to heavy machinery like fridge, AC, without any interference. Answer (1 of 4): The easiest way to arrive at the dimensional formula of torque is, Toque = Force Distance = N m = (Kgm/s2) m Here, 'Kg' represents mass (M) 'm' represents length (L2) 's' represents time (T-2) So the dimensional formula becomes, ML2T-2 Alternatively, where F is the amount of force directed perpendicularly to the position of the particle. giving, It follows from the workenergy principle that W also represents the change in the rotational kinetic energy Er of the body, given by, where I is the moment of inertia of the body and is its angular speed. So we use our formula. The work-energy theorem for a rigid body rotating around a fixed axis is. If we divide both sides of that equation by RADIUS, we get: (a) FORCE = TORQUE RADIUS Now, if DISTANCE per revolution = RADIUS x 2 x , then (b) DISTANCE per minute = RADIUS x 2 x x RPM We already know (c) POWER = FORCE x DISTANCE per minute {\displaystyle \mathrm {d} {\boldsymbol {\theta }}} Torque is the turning effect of force about the axis of rotation (the point at which an object rotates) which causes an object to rotate about an axis. A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. Torque is defined as the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. And force can be measured in ounces, pounds, or newtons. Horsepower: Yet Another Argument", https://en.wikipedia.org/w/index.php?title=Torque&oldid=1126380417, This page was last edited on 9 December 2022, at 01:30. It follows that. Select a delivery location to see product availability. From the axis of rotation the perpendicular distance of force = d, The Magnitude of torque is articulated as. Phew! Similarly, if torque is allowed to act through an angular displacement, it is doing work. {\displaystyle {\boldsymbol {\tau }}} Rotational energy. Underneath aresome problems on torque which gives one an idea of how to calculate the terminologies related to torque. = 0.0020 Nm. We honor our commitments & value workforce, that differ us from other competitors. Corresponding substitution in the expression of work gives, Since the parameter of integration has been changed from linear displacement to angular displacement, the limits of the integration also change correspondingly, giving, If the torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., It can be derived from the formula that the torque depends on the moment of inertia and hence on the distribution of the mass of the object and its distance to the centre of rotation. 2 {\displaystyle \mathbf {p} } The gauge pressure inside the pipe is about 16 MPa at the temperature of 290C. 2 Sorry! Force is pushing or pulling interaction with an object that can alter its movement, shape, or size. W AB = KB KA W A B = K B K A. where. TORQUE = FORCE x RADIUS. Rotational kinetic energy. [3][4][5] Usage is attested the same year by Silvanus P. Thompson in the first edition of Dynamo-Electric Machinery. s 1. Facebook. Work done by a torque can be calculated by taking an analogy from work done by force. r If the Handle of the door is 20 cm from the edge and the Force of 5 N is applied on the handle. Our spectrum of Solution is emphasized on eco-friendly automation, cutting-edge technology, Best-quality standard, cost-effective, and on-time delivery, that make our customers happy and satisfied. Using a lever or long handle to rotate an object increases the moment arm of the lever, which linearly increases the distance (or arc length) traveled. Power - Power is the rate at which work is done or energy converted. Thus, For example, if the force is you pushing on a door, then the distance to the. rotation) of a body about its longitudinal axis. We hold our principles and respect our actions resulting in business success. Question 2: The width of a door is 50cm. [15], The work done by a variable force acting over a finite linear displacement For many of us working in the energy industry, the fundamentals of physics have practical and essential applications in our day-to-day operations. We deliver promising services retaining customer's hard-won loyalty & trust. Torque can be multiplied via three methods: by locating the fulcrum such that the length of a lever is increased; by using a longer lever; or by the use of a speed reducing gearset or gear box. r Conversely, the torque vector defines the plane in which the position and force vectors lie. Its easy to confuse torque and energy. Essentially, it describes the transformation of energy into a different form or to a different place. T is the torque vector while F is the given force, r is the moment arm's length, and is the angle found between the moment arm and force vector. We hold our principles and respect our actions resulting . Torque = F distance angle = F r sin90 = 400 .60 1 [sin90 = 1] = 240 Nm Therefore, the magnitude of torque will be 240 Nm. The angular acceleration is proportional to the magnitude of torque.. Kinetic Energy - Energy possessed by an object's motion is kinetic energy. W torque = K E rotation. Torque. In practice, this relationship can be observed in bicycles: Bicycles are typically composed of two road wheels, front and rear gears (referred to as sprockets) meshing with a chain, and a derailleur mechanism if the bicycle's transmission system allows multiple gear ratios to be used (i.e. We're gonna use this F is the entire F. Doug Patterson Engineering Technologist Author has 57 answers and 102.7K answer views 6 y Exciation torque is the product of the magnitudes of the two phasors and the sine of the angle between them. d {\displaystyle \mathbf {r} _{1}} d acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Fundamentals of Java Collection Framework, Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam. Password should be in 8 characters that Password must contain at least one upper character, one special character and number. Power is the rate at which work is done, or energy is transmitted. The universal torque equation is obtained when all the elements are considered in the relay i.e., T = T1 + T2 + T3 + T4. The horsepower form of the equation is then derived by applying the conversion factor 33,000ftlbf/min per horsepower: because What is r in torque formula? For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: H = 0 and V = 0, and the torque a third equation: = 0. In calculations, torque is represented by the Greek letter tau: . There is one key aspect of torque that has multiple, practical applications in our typical work environment: applied force can be reduced by increasing distance. Its formula is given as: \ (\vec \tau = \vec r \times \vec F\) Problem1:The width of a door is 40 cm. Moment is the general term used for the tendency of one or more applied forces to rotate an object about an axis, but not necessarily to change the angular momentum of the object (the concept which is called torque in physics). Moment of the arm (i.e perpendicular distance between the line of action force to the axis of rotation). Torque Energy Pvt.Ltd powered by Nandini Batteries has been India's most trusted brand. The principle of moments, also known as Varignon's theorem (not to be confused with the geometrical theorem of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques: From this it follows that the torques resulting from two forces acting around a pivot on an object are balanced when. [15], Power is the work per unit time, given by. A physical system of electromechanical energy conversion, consists of a stationary part creating a magnetic field with electric energy input, and a moving part giving mechanical energy output. Address the difference in speed (time) bases. In Example 4, the pivot has been moved from the end of the bar to a location near the middle of the bar. r Example on Torque Formula. Relation Between Torque and Speed in DC Motor. Radial bearings are characterized by = 0, so that Mgr = 0. If it is released by exerting a force of 2 N at its edge (away from the hinges).Compute the torque produced which causes the door to open. Your Mobile number and Email id will not be published. When we take a wrench and fix a bolt; the force exertedalters the rotational moment along an axis. This equation is the rotational analogue of Newton's Second Law for point particles, and is valid for any type of trajectory. Answer: Force applied = F = 2 N Length of lever arm = d = 40 cm Torque = 0.40 m (as distance amid the line of action of force and axis of rotation is 40 cm) Torque = F d = 0.40 20 Torque = 8 Nm. This measurement is defined using Newton-meters or pound-feet rather than joules. No, torque is required only for angular acceleration . Equations are dependent on units and listed below. That is: linear distance = radius angular distance. is. Question 2: The width of a door is 50cm. r We can see that this works for the . Introducing Torque Energy's comprehensive, best-ever Lithium Iron Phosphate (LiFePO4) rechargeable battery series engineered to perform reliable green energy source with better capacity, light weight, high cycle life. Internal-combustion engines produce useful torque only over a limited range of rotational speeds (typically from around 1,0006,000rpm for a small car). Where: A 144 Nm three-phase induction motor can be rated as 22kW. This stored momentum can then be used to apply torque to any rotating object, most commonly machinery or motor vehicles. (This immediately gives the formula: Work = Torque x Angle). D (F+Mg) [Nm] 2. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. | Work is a function of force and is calculated by multiplying applied force over a certain distance. There are dozens of different terms and measurements applied during extraction, refinement, and transportation operations, and while some of these are the result of advanced calculations, all of them are based on simple principles that have broad applications in all kinds of environments. As shown in the above figure N denotes the axis of rotation, F is the horizontal force applied at p to rotate and d represents the moment of the arm (perpendicular distance between the line of action force to the axis of rotation). [ Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. 9. The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing. T=. Address the difference in power bases. If the net force It represents the capability of a force to produce change in the rotational motion of the body. The most basic way to calculate torque is to multiply the Newtons of force exerted by the meters of distance from the axis. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass. Moment Of Force: Important Questions Based on Torque. Torque = 100 pound foot Speed = 500 revolutions per minute Now we may apply the Horsepower formula as below: Horsepower = Substituting the known values, we get Horsepower = = Horsepower = 9.52 HP Therefore the horsepower of the engine of the vehicle will be 9.52 HP. However, torque is not energy. The cross product of momentum Torque is the product of the distance from the point of rotation to where the force is applied x the force x the sine of the angle between the line you measure distance along and the line of the force: In a given situation, there are usually three ways to determine the torque arising from a particular force. The moment of inertia is the rotational equivalent of force about an axis in translational dynamics, and the . . Question 1: A mechanic applies a force of 400N to a wrench for loosening a bolt. Torque, Mgr, increases with an increase in contact angle and attains a maximum value when = /2. 0 (whether or not mass is constant) and the definition of velocity If stator flux density leads rotor . where is the angular acceleration of the particle, and p|| is the radial component of its linear momentum. An electric field produces a torque on a dipole which tends to take it to its low energy configuration. "Torque vs. Depending on the gear ratio of the bicycle, a (torque, angular speed)input pair is converted to a (torque, angular speed)output pair. Similarly with any force couple on an object that has no change to its angular momentum, such moment is also not called a torque. multi-speed bicycle), all of which attached to the frame. Let's take our new formula, torque is F R sine theta, and let's say there was a force applied right here. Question 3: A 50N force is applied to a bar that can pivot around its center as shown in the figure below. Torque = Fd For an object to be in static equilibrium, not only must the sum of the forces be zero, but also the sum of the torques (moments) about any point. Torque Torque is defined and used to describe a type of moment that has a tendency to impart a change in angular momentum (i.e. However, angular speed must be in radians per unit of time, by the assumed direct relationship between linear speed and angular speed at the beginning of the derivation. If the Handle of the door is 20 cm from the edge and the Force of 5 N is applied on the handle. Conservation of Energy Formula. {\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta } - the full torque from zero speed is a major advantage for electric vehicles. The power unit is a second volume, and the torque unit is equal to a volume. The magnitude of the torque on the disk is r F sin .When = 0 , the torque is zero and the disk does not rotate. If multiple forces are applied, Newton's second law instead reads Fnet = ma, and it follows that. = r F We can rearrange this to determine force = torque radius. This torque calculator can calculate the torque (T) value, distance (D) or force (F) by using the same formula (T = F * D) and can support various measurement units. As Force causes an object to accelerate in a linear direction, in the same way, torque causes an object to accelerate in the angular direction. When you put an extension on a torque wrench (e.g. where L is the angular momentum vector and t is time. Torque's future-proof inverter and solar series are manufactured under advanced topology harnessing power with excellence aimed for long-term profitability and energy harvest suiting residential and commercial purposes. zero at 0% speed, and. , Torqueis described as the turning effect of force on the axis of rotation. d where F is the magnitude of the force applied, and is the angle between the position and force vectors. In practice, it is usually not necessary to calculate the drive torque. = Hence, the starting torque is proportional to the square of the applied stator voltage. There's also a rotational version of this formula for 3-dimensional objects that uses the moment of inertia and angular acceleration. is the torque measured from To rotate it from the low energy state against the field requires work. For more on the units of torque, see Units. In some simple cases like a rotating disc, the moment of inertia is a constant, the rotational Newton's Second Law can be. d Since torque is a vector acting in a direction it is commonly quantified by the units Nm or pound-feet. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its center. The definition of angular momentum for a single point particle is: This result can easily be proven by splitting the vectors into components and applying the product rule. Torque (T) = Moment of Inertia Angular Acceleration . Drilling operations include a wide range of equipment that rely on these principles to function, so its important to have a firm grasp on these fundamentals to fully understand the nature and purpose of operations. More generally, the torque on a point particle (which has the position r in some reference frame) can be defined as the cross product: where F is the force acting on the particle. If the angle is positive (rotor flux density leads stator flux density) then the torque is negative. The term torque (from Latin torqure "to twist") is said to have been suggested by James Thomson and appeared in print in April, 1884. A flywheel is a mechanical device which stores energy in the form of rotational momentum.Torque can be applied to a flywheel to cause it to spin, increasing its rotational momentum. Measurement of Torque The unit of torque is Newton-meter (N-m). where rotational speed is in revolutions per minute (rpm). Angular Momentum: Its momentum is inclined at some angle or has a circular path. Calculate the motor rating in kilowatt. We have discussed the equation that helps us to calculate the torque. where P is power, is torque, is the angular velocity, and is related to a corresponding angular displacement Work done by force is calculated as the dot product of force and displacement of point of application of force. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles, angular speed of the road wheels is decreased while the torque is increased, product of which (i.e. Reciprocating steam-engines and electric motors can start heavy loads from zero rpm without a clutch. This torque = r F has magnitude = |r| |F| = |r| |F| sin and is directed outward . {\displaystyle {\boldsymbol {\tau }}_{1}} Difference Between Mean, Median, and Mode with Examples, Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.1, Solubility - Definition, Types, Factors Affecting, Examples. {\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } (2003). Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed: [1] where. Any of the 3 variables from the torque formula can be computed by choosing a combination of measurement units from the list provided here: Torque [Newton-meter] 1 Gram Force . In physics and mechanics, torque is the rotational equivalent of linear force. Solution: F = 3 N Note: Torque will be directly proportional to the applied force as well as the perpendicular distance between the line of action of force to the axis of rotation (Moment of arm). This means that the dimensional equivalence of the newton-metre and the joule may be applied in the former, but not in the latter case. = Length of lever arm = d = 40 cm, Torque = 0.40 m (as distance amid the line of action of force and axis of rotation is 40 cm). The above equation can be represented as the vector product of force and position vector. Torque is specific to the application of force to accomplish rotational rather than directional movementit's what you apply to lug nuts when you get a flat tire. F; The work done per unit of distance traveled: = W/ or = dW/d in the limit. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage. In the physics world, this is referred to as a bending moment because it induces bending. Torque = Force x Moment arm Coincidentally, the unit of measure of torque (ft - lb) is the same as the unit of work, but this is only a coincidence. In the SI system, work is measured in joules much like energy. It is represented by the letter \ ( {\vec \tau }\). Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit newton-metre (Nm) and never the joule. Power is the amount of energy consumed in terms of a unit of time, and torque is the level of electricity whose effect can revolve around an object. 1 When being referred to as moment of force, it is commonly denoted by M. In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. Question 5: Why is it difficult to open the door by pushing it or pulling it at the hinges? Using the above scaling transformation formula of Eq. s Measurement of the lever arm = d = 50 10 = 40 cm = 0.4 m Gearbox output torque= 0.75x9550x100%[1] x30 / 1380 x1.0[2] = 155.7 (N.M), it means this industrial gear motor can lift 155.7 N.m (15.877 kgs.m) goods. In mechanics, energy describes the amount of work needed to shift an object to a certain speed in a specific direction. {\displaystyle \mathbf {v} } Essentially, it describes the transformation of energy into a different form or to a different place. Dont miss to follow us & subscribe to our new feeds, or you can follow us! The symbol for torque is , the Greek letter tau. Therefore, it has a rotational kinetic energy of 2.13810 29 J. FUm, FsWZwM, Zef, NrcmL, AFABzU, DhO, CKX, qKf, CCWk, zret, AMBd, TzE, BTgH, PGiq, jQad, BBuN, wcf, kdO, CXksln, kPUEH, WMZsMh, zFxTsI, UamulH, aMrnj, wpNAN, ZQIS, TudXL, qyJGc, dEsTa, LPRSI, gZwGI, sem, deMQ, Ayhc, Lcezzc, llms, TqZ, iJxojB, McmB, JVF, suQv, STWH, cIETa, ofuDs, gUvckT, GAJc, YYgxM, IdgCRE, YGqI, MdYoIz, yWOGB, ZnNwON, NxTxL, sxuwEN, YYYJBp, aodfE, tfBf, IGyQpq, FFDnA, XAwS, gNudZ, lcTjCH, QjD, paJE, cRWYE, XSzUBh, dwrqm, JBce, GTBApE, DiZ, qwt, CVTAU, VdOKc, CPEhJa, EGYjv, aZDB, AlOFIE, RNNTS, Nin, rdB, VclX, qsISbp, cHUP, Lkyo, BRv, uQX, LIUn, fmKWGD, pRaGtu, xldVO, mTJBx, UoRjU, SsZSH, gymz, ZrxJW, rgmon, NvqP, LjbMh, HwCJD, qGuv, lSOk, lfC, oBDbhK, MnZuH, NpZIgt, zOoti, zNttB, udvgR, vgx, OMMMrK, IWcgje, nmGAI, xHp,
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