Conservation of Energy Free Fall Springs and Pendulums

Professor Dave again, let's learn about conservation of energy. We now know about kinetic and potential energy and we know that these quantities can be altered as an object moves, like the way potential energy is converted into kinetic energy when an object experiences free fall towards the ground. But energy can be transformed in variety of other ways as well, so we must learn about all the kinds of energy and how they can transform from one to another. We also must understand that while energy can change forms, the total energy of closed system will always be conserved, that is to say, there will always be conservation of energy. As an object falls, potential energy is converted into kinetic energy, but the sum of the potential and kinetic energies of the object will be the same at every instant during the free fall. We can call this sum the mechanical energy of the system. This is more easily visualized using the simple harmonic motion of mass-spring system which utilizes elastic potential energy, but we can also use the pendulum of grandfather clock, which will use gravitational potential energy. At the top of the swing, the pendulum possesses its maximum potential energy and zero kinetic energy. At the very bottom of the swing it possesses its minimum potential energy and its maximum kinetic energy. As these two forms interchange again and again and again, there is conservation of energy, and the total mechanical energy which again is the sum of the two, is constant. This concept can be described mathematically by the following equation. If mechanical energy is the sum of kinetic energy and potential energy which are in turn represented by these expressions, and this value is conserved then one-half mv squared initial plus mgh initial will be equal to one-half mv squared final plus mgh final. It shows that the sum of the kinetic and potential energy of system like the pendulum will be the same at every point in its motion. This equation will be used frequently in physics when we want to assess the kinetic or potential energy of an object at particular moment, and if we have enough information about system we will be able to algebraically solve for some unknown. This only works when there is no friction present, but for systems like swinging pendulum we can use it anyway as the force of friction will be negligible. Once again, the label of mechanical energy is just way of categorizing energy. It distinguishes kinetic energy of motion and gravitational or elastic potential energy from other forms of energy, which we call non mechanical energy. This includes things like chemical energy, thermal energy, nuclear energy, electrical energy, acoustic energy, and more. These are also some kind of kinetic or potential energy as they involve the motion of tiny vibrating particles, the energy stored in an atomic nucleus, or some other form of energy associated with either motion or storage. But they differ in nature from mechanical energy. As we said, energy can be transformed from one form to another but it is always conserved. car engine converts chemical energy stored in gasoline through series of steps to eventually produce the kinetic energy that is the movement of the car. When we metabolize food we are converting chemical energy within the food into the chemical energy in ATP which can then be used as kinetic energy to move our bodies around. If while moving around you decide to slap your hand down on the table, all that kinetic energy is transformed into thermal energy by heating up the table slightly, as well as acoustic energy which is the sound we will hear. As we progress through the 21st century we will continue to try to find more efficient ways to convert energy from natural sources like solar and wind energy into the energy that our civilization needs to operate all of our technology, but for now there's much more physics to discuss, so let's check comprehension. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so can keep making content, and as always feel free to email me: