Defining energy Relationships
We know that potential energy is defined by the stored energy of position and object has, and kinetic energy is defined by the energy an object has while in motion. They’re both connected because potential energy can be turned into kinetic energy when an object falls. For example, if a box is sitting on the counter at rest, it has potential energy. If it gets knocked down, the potential energy transforms into kinetic energy because the book has now gone into motion. Energy can not be created or destroyed, therefore potential energy transforms into kinetic energy. Kinetic energy can be in transformed into potential energy if the object ceases motion.
The formula PEi+KEi=PEf+KEf can best be explained by the following example; Let's say you're in a car waiting at a red light. Your initial potential energy (PEi) is say 50 for the purpose of this explanation. Your initial kinetic energy (KEi) is 0 because you are at rest, when the light turns green you drive and your kinetic energy increases. However as you come to a stop sign you stop your car and your final kinetic energy (KEf) decreases to 0 and your final potential energy (PEf) is once again at 50. Therefore, once we plug our values into the formula we get 50 + 0 = 50 + 0 which is simplified to 50 = 50.