Phys 201 1nd Edition Lecture 18 Outline of Last Lecture I. Inelastic Collisions from rest and with initial velocity.Outline of Current Lecture II. Elastic CollisionsA. Light and Heavy Object CollisionsIII. Gravitational Potential EnergyIV. Black Holes Current LectureElastic Collisions:Remember that an inelastic collision conserves momentum, but not kinetic energy. An elastic collision, on the other hand, is one in which both momentum and kinetic energy are conserved throughout the collision. There are very few real life situations that result in a perfectly elastic collision. A swinging steel ball apparatus provides a pretty good visual example of an elastic collision. If you watch a steel ball apparatus, you’ll notice that if you pull back one ball on the end and allow it to strike the other balls, only the ball on the opposite end of the group will fly away from the group at roughly the same speed as the ball that was dropped. However, if you lift two balls and drop them together, then two balls on the other end of the apparatus will fly off, again at roughly the same speed.Light and Heavy Object Elastic Collisions:If you have a collision involving a light object with a heavy object, the final velocity of the light object is greater when the initial velocity of the heavier object is greater. Consider when you hit a tennis ball with a racket. When the ball rebounds from the tennis racket, the velocity of the tennis ball after its collision with the racket is equal to the initial velocity of the racket plus the final velocity of the racket. Similarly, ifyou drop a tennis ball onto a basketball, it won’t go nearly as high as if you hit the same tennis ball from underneath with a basketball.Gravitational potential energy:Gravity can be described as being related to the height you’re at. Remember the equation we have been using for measuring potential energy;PE=mghThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.For this equation, gravitational potential energy depends on h, which is based on a reference point that we choose. We also assume that a constant force is used to lift something to any given height. This is nottrue. Force does change with distance. Therefore, we need a new equation to give us a more accurate measurement for the force of gravity. For this we use Newton’s universal law of gravitation;F=(mMeG)/R2 Launching a satellite in space should take less energy than the amount calculated by the simple version of gravitational force. For an object on earth though, it really doesn’t make too big of a difference. However, if we’re going to consider a change in potential energy as an object moves, we need to consider a change in position. This means that the radius(R) is not constant. This would make the equation;ΔPE=-GmM(1/rf - 1/ri)This gives us an initial and final radius. The initial and final radius refers to the position an object is in relation to the center of the earth. Applying to Our Know Equations:The total energy(E) on the surface of the Earth can now be described as such;E= KE+PE= .5mV2 - mMG/ReFor this equation to work properly, we need for .5mV2 > mMG/ReThe value for the velocity that makes this condition true is referred to as the escape speed or escape velocity. Because both sides of the equation include the mass of the object(m), this value becomes obsolete. This means that, to find the escape velocity, we can use the equation;Vesc=√(2MG/Re)For any object on earth, the escape velocity is 1.1X104m/sBlack Holes:A black hole refers to a point in space where gravity is so strong that not even the speed of light is fast enough to escape it. No object can generate an escape velocity large enough to escape a black hole. A black hole is formed when the force of gravity of a star is greater than the outward pressure caused by its temperature. When this happens, the force of gravity makes the star collapse and pulls its mass inwards towards a central point. As the mass is pulled more and more inwards, the point gets continuously smaller and denser. Essentially, this central point shrinks to a size of nearly nothing, but with an almost infinite