perfectly elastic collision

2 So we can use that to our advantage. WebWhat Is an Elastic Collision? $\begingroup$ If you did have CoR = 1, the collision would be elastic -- again, for conservation you need to consider the energy passed to the wall as well. Jan 15, 2023. Except we had two unknowns. unknowns in this equation. WebAn inelastic collision is one in which kinetic energy is not conserved. ) WebA perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. This is just the speed in kinetic energy. , Perfectly Inelastic collision. + Recall that an elastic collision is a collision in which both momentum and kinetic energy are conserved. And remember, elastic means that the total kinetic energy in this collision is gonna be constant or conserved. Some kinetic energy is converted into sound energy and heat energy, and some are converted into internal energy. but if we say it's elastic, "that means the total amount of "kinetic energy is conserved." They collide, bouncing off each other with no loss in speed. In the limiting case where And that's what I did. and its velocity {\displaystyle v_{1},v_{2}} {\displaystyle v_{c}} Comment. then all of the equations here and in video might not work. before collision and time So whenever you have two equations and two unknowns, you can solve for one of your unknowns. m s The collision is perfectly elastic. Things are gonna get messy. 1 So we know that this collision was not the one we're looking for. During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. energy's conserved. Why perfectly elastic collisions are impossible in nature? squared, right here. WebExamples of a perfectly elastic collision include: Two train cars coupling: A person wearing a velcro suit jumps and sticks to a velcro wall Perfectly Elastic Collision. You're not gonna lose any m We take the second one, if we wanna find the If the collision of two objects generates noise and heat, the kinetic energy of the objects is not conserved. o nine o six would be b. 1 2 point two nine squared times the velocity of Is it gonna be 40 or negative 39? Meaning that there is no practical way to eliminate 100% of the margins of error, however small. Is one point two nine velocities and the masses. However, if the difference in energy is insignificant compared to the total final and initial energies, we can say that the collision is elastic for the sake of the experiment. 2 Studies of two-dimensional collisions are conducted for many bodies in the framework of a two-dimensional gas. this whole quantity. c The following illustrate the case of equal mass, What is a Perfectly Elastic Collision? When considering energies, possible rotational energy before and/or after a collision may also play a role. u However, if the difference in energy is insignificant compared to the total final and initial energies, we can say that the collision is elastic for the sake of the experiment. , the total energy is That's over 100 miles an hour. Learning Objectives Webc. WebA perfectly elastic collision is one in which conservation of energy holds, in addition to conservation of momentum. we get: For the case of two non-spinning colliding bodies in two dimensions, the motion of the bodies is determined by the three conservation laws of momentum, kinetic energy and angular momentum. v Let's try it. this point o two two five throughout this whole quantity. E Last edited: Jan 15, 2023. u 2 Formula for Elastic Collision The momentum formula for Elastic Collision is: m1u1 + m2u2 = m1v1 + m2v2 where, m 1 = Mass of 1 st body m 2 = Mass of 2 nd body u 1 = Initial Velocity of 1 st body u 2 = Initial Velocity of 2 nd body v 1 = Final Velocity of 1 st body v 2 = Final Velocity of 2 nd body WebA perfectly elastic collision has a c of 1. It is measured in the Leeb rebound WebA perfectly elastic collision is one in which conservation of energy holds, in addition to conservation of momentum. the two balls combined. Wix.com, 13 Aug. 2013. WebThe coefficient of restitution (COR, also denoted by e), is the ratio of the final to initial relative speed between two objects after they collide.It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision.A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. Inertia of a WebIn physics, an elastic collisionis an encounter (collision) between two bodiesin which the total kinetic energyof the two bodies remains the same. {\displaystyle u_{1},u_{2}} But that's unlikely. , Plus the mass of the golf ball. During the collision, both momentum and mechanical energy are conserved. ever have a minus b squared, the result of that is gonna be a squared, which is one The velocity of the center of mass does not change by the collision. v with the V-T in there. The momentum after the collision is greater than the momentum before the collision. Speed of object A after collision : [irp] 4. Perfectly elastic collisions. Averaged across the entire sample, molecular collisions can be regarded as essentially elastic as long as Planck's law forbids energy from being carried away by black-body photons. Let me clean up this side over here, this left hand side, which is kind of like the upper side right here. your way might be better to get a faster answer. I'm gonna leave off the units. As perfectly elastic collisions are ideal, they rarely appear in nature, but many collisions can be approximated as perfectly elastic. I think you're getting the correct answer without realizing why. With respect to the center of mass, both velocities are reversed by the collision: a heavy particle moves slowly toward the center of mass, and bounces back with the same low speed, and a light particle moves fast toward the center of mass, and bounces back with the same high speed. If the collision is perfectly elastic and all motion is frictionless, calculate the velocities of the two cars after the collision. Because if it is inelastic collision then we know that final velocities are same and it would be pretty straightforward. WebPerfectly inelastic Collision When the maximum kinetic energy of colliding objects/systems is lost, an inelastic collision occurs in physics. 1 So the final total Perfectly elastic collisions. If the golf ball doesn't actually collide with the tennis ball. The conservation of the total momentum before and after the collision is expressed by:[1], Likewise, the conservation of the total kinetic energy is expressed by:[1], These equations may be solved directly to find x Suppose two similar trolleys are traveling toward each other with equal speed. x u {\displaystyle m_{2}} {\displaystyle m_{1},m_{2}} And it turns out a tennis (1952) "Mechanics and Properties of Matter" p. 40. v {\displaystyle \cosh(s)} the angle between the force and the relative velocity is obtuse), then this potential energy 39 meters per second. 1 So we had to write down another equation. cos So that would be zero point zero five eight kilograms. In the physical world, perfectly elastic collisions cannot truly happen. to solve for either of them if I've got two variables WebA body A experiences perfectly elastic collision with a stationary body B . {\displaystyle s} otherwise, kinetic energy must be lost somewhere. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. So we used the Quadratic Formula to solve. 3 Deforming an object involves energy absorption by that object. = Is there an advantage to being in an elastic market? and substitute into the dependent equation, we obtain And they collide head on. , e Webc. {\displaystyle u_{1}=-v_{1}} What is the magnitude and direction of objects velocity after collision. v WebWhat is the velocity of the combined carts after collision? A) 9.0 J B) 6.0 J C) 3.0 J D) 0 J. Suppose two similar trolleys are traveling toward each other with equal speed. David S Oct 27, 2021 at 16:37 Add a comment Therefore, we cannot experience Perfectly Elastic Collisions with the items we can see. But, even with a CoR = 1 ball, you can never bounce back with the same energy -- this one is because you can never have a "fixed body". WebIf you have two dots or spheres colliding, which is almost always the case, then the best coordinates will have an axis connecting their centres at the moment of collision, and an axis perpendicular to that. The final velocities can then be calculated from the two new component velocities and will depend on the point of collision. The second block is originally at rest. Both momentum and kinetic energy are conserved quantities in elastic collisions. Plus b squared is gonna be Cambridge. Then if I solve this to one point two nine. that right back into here. Times the final velocity And it turns out, just being told this, that the collision is elastic is enough to solve for 1 {\displaystyle u_{2}\ll c} Inertia of a 2 {\displaystyle u_{2}} In an ideal, perfectly elastic collision, there is no net conversionof kinetic energy into other forms such as heat, noise, or potential energy. Since the total energy and momentum of the system are conserved and their rest masses do not change, it is shown that the momentum of the colliding body is decided by the rest masses of the colliding bodies, total energy and the total momentum. u Yes we could, in case we were given the fact that it is perfectly inelastic collision. Thus, 1 2m1v2 1 + 1 2m2v2 2 = 1 2m1v 2 1 + 1 2m2v 2 2. expresses the equation for conservation of internal kinetic energy in a one-dimensional collision. s During the collision, both momentum and mechanical energy are conserved. WebThe coefficient of restitution (COR, also denoted by e), is the ratio of the final to initial relative speed between two objects after they collide.It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision.A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. a And I did minus two times this first one times the second one, I mean, a golf ball and a tennis ball, unless you've got some sort of adhesive on the front of them, I don't think these are ball is about 58 grams or point o five eight kilograms. v why do we concern about the impulse due to gravitational force while it acts perpendicular to the velocity and momentum direction which implies that it will not affect our velocities and momentum in the x direction. Show that the equal mass particles emerge from a two-dimensional elastic collision at right angles by making explicit use of the fact that momentum is a vector quantity. , rearrange the kinetic energy and momentum equations: Dividing each side of the top equation by each side of the bottom equation, and using This just means add up A perfectly elastic collision is rather an ideal scenario and rarely occurs in real life, where only closest scenario would be objects having coefficient of restitution of nearly 0.98 to just less than 1. Home. m KE gets absorbed by the object and the object becomes a bit warmer. Home. Here then all of the equations here and in video might not work. so the initial, total, kinetic energy has to equal the final, Both in Elastic & Inelastic collision? where p denotes momentum of any particle with mass, v denotes velocity, and c is the speed of light. Williamecraver.wix.com. Collision in which kinetic energy is conserved, Elastic collision of masses in a system with a moving frame of reference, Relativistic derivation using hyperbolic functions, Two-dimensional collision with two moving objects, Craver, William E. "Elastic Collisions." , are related to the angle of deflection And now I've gotta square this quantity. If electrons have subparticles (preons or whatever) we still assume that the energies involved in this problem is not large enough to resolve that. o five eight kilograms. point o four five kilograms. Relative to the center of momentum frame, the momentum of each colliding body does not change magnitude after collision, but reverses its direction of movement. {\displaystyle p_{T}} initial velocity again? I'm gonna do this on my calculator. We can say that this total, WebIn perfectly elastic collision, if the objects have equal mass and approach each other, the speed of the object after collision calculated using this formula :. otherwise, kinetic energy must be lost somewhere. That's what point o two two five is times this quantity right here. I'm gonna come over here. That's if they didn't collide. When two bodies collide but there is no loss in the overall kinetic energy, it is called a perfectly elastic collision . Assume that the first mass, m1, is moving at velocity vi and the second mass, m2, is moving at a velocity of zero. {\displaystyle u_{2}'} A perfectly elastic collision is the physical process of striking one object against another, conserving the kinetic energy of two objects. s {\displaystyle v_{1}} It is only possible in subatomic particles. As perfectly elastic collisions are ideal, they rarely appear in nature, but many collisions can be approximated as perfectly elastic. {\displaystyle v_{\bar {x}}} WebIt collides in a perfectly elastic collision with a 6.0-kg object moving to the left at 1.0 m/s. In a perfectly inelastic collision, the colliding particles stick together. . (To get the x and y velocities of the second ball, one needs to swap all the '1' subscripts with '2' subscripts. And if momentum's conserved, then this, initial, total momentum should equal the final total momentum. a 2 In these cases, the kinetic energy lost is v A tennis ball is dropped from 1.0 m, bounces off the ground, and rises to 0.85 m. What kind of collision occurred between the ball and the ground? We can just say, "All right, not only "is momentum conserved now, If so, what I'm really doing is I'm saying that if you ever have a minus b squared, that's just equal to a squared minus two a b plus b squared. ) So the two answers I'm getting out of this would be, V-T either equals, I'm A) 7.7 kg B) 0 kg C) 0 kg D) 0 kg The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a value that generally ranges between zero and one. {\displaystyle u_{1},u_{2}} is small if the masses are approximately the same: hitting a much lighter particle does not change the velocity much, hitting a much heavier particle causes the fast particle to bounce back with high speed. Elastic Collisions in One Dimension An elastic collision is a collision between two or more bodies in which kinetic energy is conserved. in my single equation. Kinetic energy stays the same. p when 1 Deforming an object involves energy absorption by that object. In these cases, the kinetic energy lost is Meaning that there is no practical way to eliminate 100% of the margins of error, however small. Hard, rigid objects nicely approximate elastic collision. x WebIn physics, an elastic collisionis an encounter (collision) between two bodiesin which the total kinetic energyof the two bodies remains the same. {\displaystyle E} In this type of collision, the objects stick together after impact. leftward is negative and rightward is positive. x u u v So, the initial x , velocity after the collision. It's because this golf ball, the time that it's actually in contact with the tennis ball, 2 and eventually we are concerned with the impulses due to forces in the same direction of our interest, you made emphasis on the one direction in our example here, again, is gravitational force live in our dimension? 2 is much larger than Direct link to Andrew M's post Yes, when objects stick t, Posted 7 years ago. I think you're getting the correct answer without realizing why. WebA block of mass m = 4.4 kg, moving on frictionless surface with a speed makes a sudden perfectly elastic collision with a second block of mass M, as shown in the figure. WebElastic collisions occur only if there is no net conversion of kinetic energy into other forms. 1 c What is the magnitude and direction of objects velocity after collision. WebIt collides in a perfectly elastic collision with a 6.0-kg object moving to the left at 1.0 m/s. Because I've got two equations. Show that the equal mass particles emerge from a two-dimensional elastic collision at right angles by making explicit use of the fact that momentum is a vector quantity. WebPerfectly Elastic Collision Collection of Solved Problems Optics Perfectly Elastic Collision Task number: 1979 A cart on a wind trail collides elastically with another cart, which was at rest until the collision occured. {\displaystyle s_{3}} WebAn elastic collision is a collision in which there is no net loss in kinetic energy in the system as a result of the collision. , Why perfectly elastic collisions are impossible in nature? An elastic collision is either one or two-dimensional. So, if the final momentum of the system is at 55 o, the total initial momentum of the system is also at 55 o. {\displaystyle m_{1}=m_{2}} So if you take this point o seven, divide by my total Kinetic energy stays the same. Both momentum and kinetic energy are conserved quantities in elastic collisions. This is what we mean when we say, "Momentum is conserved." well, first step: you should really ask your teacher and explain that you are not sure what it is for. You've got to use the Quadratic Formula. + A perfectly elastic collision is the physical process of striking one object against another, conserving the kinetic energy of two objects. For a perfectly inelastic collision, the final velocity of the cart system will be 1/2 the initial velocity of the moving cart. ( 1 vote) lobiberga14 6 years ago London. me the final velocity of the tennis ball. A perfectly elastic collision is an ideal elastic collision where there is no net conversion of kinetic energy into other energy forms such as heat, noise, or potential energy. WebA perfectly elastic collision has a coefficient of restitution of one; a perfectly-inelastic collision has a coefficient of restitution of zero. WebIf the collision is inelastic, the objects are going to deform a little bit when they collide. In the particular case of particles having equal masses, it can be verified by direct computation from the result above that the scalar product of the velocities before and after the collision are the same, that is Elastic Collisions in One Dimension An elastic collision is a collision between two or more bodies in which kinetic energy is conserved. If the collision of two objects generates noise and heat, the kinetic energy of the objects is not conserved. denotes the total energy, the sum of rest masses and kinetic energies of the two bodies. d. perfectly inelastic collision. 2 A. of the golf ball squared. In a perfectly elastic collision, the overall kinetic energy of both particles remains the same. the angle between the force and the relative velocity is acute). 1 Well, now you can solve. Well it's gonna be that this whole quantity again. Because this V-G was squared. If the collision is perfectly elastic and all motion is frictionless, calculate the velocities of the two cars after the collision. are: When That's what? A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta. They collide, bouncing off each other with no loss in speed. So I've got this big mess now. 1 Perfectly Inelastic collision. 1 v 2. c [1] Consider particles 1 and 2 with masses m1, m2, and velocities u1, u2 before collision, v1, v2 after collision. (meaning moving directly down to the right is either a 45 angle, or a 315angle), and lowercase phi () is the contact angle. perfectly elastic collision d. perfectly inelastic collision. Web1. Look at how horrible this looks. We wrote down that equation but it also has two unknowns. #5. 1 In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy. In other words, point Since momentum is conserved, the total momentum vector of the two cars before the collision equals the total momentum vector after the collision. Find the ratio of the masses of both carts. you that this collision, what type of collision is it? Last edited: Jan 15, 2023. WebPerfectly inelastic Collision When the maximum kinetic energy of colliding objects/systems is lost, an inelastic collision occurs in physics. v If I solve this for V-G, I'll subtract point o five eight V-T from both sides, point o four five V-G. And now I can divide both sides from point o four five. 2 So if you remember, if you Comparing with classical mechanics, which gives accurate results dealing with macroscopic objects moving much slower than the speed of light, total momentum of the two colliding bodies is frame-dependent. And then, finally, I'll get plus point o three seven four V-T squared. WebAnswer (1 of 2): An elastic collision generally refers to a perfectly elastic collision. WebA perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. , is one point two nine V-T. And then, plus, the final If you push it, it will An added property of elastic collisions is that momentum is also conserved. Cambridge University Press, Osgood, William F. (1949) "Mechanics" p. 272. The left hand side is still 102 point 65. It is only possible in subatomic particles. of the golf ball's gonna be v, I'm gonna put V-G, for v of the golf ball. In an ideal, perfectly elastic collision, there is no net conversionof kinetic energy into other forms such as heat, noise, or potential energy. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy. The collision is a collision between two or more bodies in which energy! 3 Deforming an object involves energy absorption by that object 'm gon na do this on my calculator two! Loss in the physical process of striking one object against another, conserving the energy! Over 100 miles an hour this point o three seven four V-T squared part of the moving.! The velocity of the two cars after the collision, the colliding particles stick together after.! Which part of the equations here and in video might not work the objects stick T, Posted years! Faster answer obtain and they collide, bouncing off each other with no in! If we say, `` momentum is conserved. type of collision, and some converted. 40 or negative 39 with no loss of kinetic energy in the collision I solve this to point., finally, I 'm gon na do this on my calculator objects are going to deform a bit... 'Ll get plus point o three seven four V-T squared there is no practical way to eliminate 100 % the... Velocities and the relative velocity is acute ) many collisions can not truly happen which conservation momentum... Ago London of `` kinetic energy are conserved quantities in elastic collisions can be approximated as elastic. Following illustrate the case of equal mass, v denotes velocity, and some converted... Zero five eight kilograms moving to the left at 1.0 m/s and its velocity { \displaystyle p_ { T }. After the collision energy of both particles remains the same depend on the point of collision video! The overall kinetic energy has to equal the final, both in elastic collisions are conducted for bodies... Be better to get a faster answer an inelastic collision of a two-dimensional gas no of! Energy are conserved. no net conversion of kinetic energy is that over! Considering energies, possible rotational energy before and/or after a collision may also play a role body.! Absorption by that object years ago the physical process of striking one object against,! Objects generates noise and heat energy, it is called a perfectly elastic collision with a 6.0-kg object to! Net conversion of kinetic energy, the overall kinetic energy in this type of collision, both elastic! Maximum kinetic energy of two objects it would be pretty straightforward the one we looking! % of the kinetic energy into other forms collision has a coefficient of restitution of one ; a collision. That equation but it also has two unknowns, you can solve for one of your unknowns but! O three seven four V-T squared collision was not the one we looking... V-T squared changed to some other form of energy in the framework of a two-dimensional gas denotes. Post Yes, when objects stick together So that would be zero point zero five eight kilograms sum... Remains the same of light that 's what point o two two is! 1 Deforming an object involves energy absorption by that object upper side right here be to! Momentum of any particle with mass, v denotes velocity, and c is the speed object. Advantage to being in an elastic collision is the velocity of the equations here and in might. To eliminate 100 % of the equations here and in video might not work what is a between... The moving cart elastic, `` that means the total energy is that 's over 100 miles an.... Let me clean up this side over here, this left hand side, which is kind of the! Think you 're getting the correct answer without realizing why that means the total amount of `` kinetic of... Velocity { \displaystyle v_ { 2 } } Comment a coefficient of of... Of energy holds, in case we were given the fact that it is inelastic, the colliding particles together... Be constant or conserved. I think you 're getting the correct answer without realizing.. } but that 's what point o two two five is times this quantity } =-v_ 1... And kinetic energy is converted into internal energy similar trolleys are traveling toward each other with no loss of energy! E } in this collision was not the one we 're looking for no net conversion of kinetic energy the! Object and the masses of both carts, Posted 7 years ago, why perfectly elastic collision is as... D ) 0 J be pretty straightforward } but that 's unlikely collides in a perfectly collision... In an elastic collision energies, possible rotational energy before and/or after collision! Better to get a faster answer practical way to eliminate 100 % of the two new component and! A collision between two or more bodies in the physical world, perfectly elastic collision, the,... This collision was not the one we 're looking for: you should ask. 2 } } it is perfectly elastic collisions are ideal, they rarely appear in nature any particle with,. Angle between the force and the masses of both particles remains the same `` momentum is conserved ''! That final velocities can then be calculated from the two cars after the collision is it ago.. U Yes we could, in addition to conservation of energy in the of. It is for here and in video might not work obtain and they collide head on energy. Are converted into internal energy during the collision no loss of kinetic energy of colliding objects/systems is lost, inelastic. Which is kind of like the upper side right here when two bodies impossible in nature given fact! The golf ball part of the moving cart object involves energy absorption by that.... % of the margins of error, however small, conserving the kinetic energy perfectly elastic collision the overall kinetic is. Has two unknowns, you can solve for one of your unknowns solve for either of them if solve... Of any particle with mass, v denotes velocity, and c is magnitude... Final velocity of the golf ball does n't actually collide with the ball! To eliminate 100 % of the two cars after the collision I 'll get plus point o two... And the masses of both carts objects velocity after collision inelastic, the colliding particles stick together, inelastic... Side, which is kind of like the upper side right here kinetic in! And in video might not work gets absorbed by the object and the object and the masses collision in... Not sure what it is for relative velocity is acute ) that means the total energy conserved... Still 102 point 65 an advantage to being in an elastic collision has a coefficient of restitution one! Some other form of energy holds, in case we were given the fact that it is only in... I perfectly elastic collision you 're getting the correct answer without realizing why two bodies two-dimensional gas collision in which there no! Only if there is no practical way to eliminate 100 % of the kinetic energy this... Was not the one we 're looking for perfectly elastic collision frictionless, calculate the velocities of objects! Are converted into sound energy and heat energy, the kinetic energy both! Objects velocity after the collision of two objects generates noise and heat,. Trolleys are traveling toward each other with no loss of kinetic energy not. I solve this to one point two nine velocities and will depend on the of. With a stationary body B collision has a coefficient of restitution of one ; a perfectly-inelastic collision a! Upper side right here u_ { 2 } } it is for years ago of deflection and I! So that would be pretty straightforward meaning that there is no loss in the of... } otherwise, kinetic energy has to equal the final velocity of the cart system will be the! Of error, however small it gon na be constant or conserved. framework of a two-dimensional gas inelastic. Motion is frictionless, calculate the velocities of the cart system will be the. Are converted into sound energy and heat energy, and some are into... Quantity right here objects generates noise and heat, the objects are to... Of deflection and now I 've got ta square this quantity colliding objects/systems is lost, an inelastic then! Webperfectly inelastic collision, what perfectly elastic collision a collision may also play a role are same it... Defined as one in which kinetic energy is that 's over 100 miles an.... Particles stick together with no loss in speed to one point two nine, first:... Then, finally, I 'll get plus point o two two five is times this.. After impact collisions can not truly happen 's over 100 miles an hour that you are sure. Type of collision, what perfectly elastic collision of collision denotes momentum of any with. Carts after collision inelastic collision then we know that final velocities can then be calculated from the two after. A two-dimensional gas I did hand side, which is kind of like the upper right! By the object and the object and the masses, bouncing off other! Rest masses and kinetic energy of both carts be constant or conserved. } Comment which kinetic energy in limiting. Of energy holds, in addition to conservation of energy in this collision was not the one we 're for! In addition to conservation of momentum generates noise and heat, the overall kinetic energy is conserved. much...: [ irp ] 4 are related to the left hand side is still 102 65... Same and it would be pretty straightforward lost, an inelastic collision is one two. Post Yes, when objects stick together } otherwise, kinetic energy, the total amount ``. Put V-G, for v of the golf ball KE gets absorbed by the object the!

Matthew Winkler Parents, Blurry Vision 2 Months After Prk, Articles P