Up to this point, we have seen that we can use Newton\u2019s laws and kinematic equations to solve numerous problems detailing the motion of an object or a system of objects.\u00a0 However, Newton\u2019s framework is a vector framework and requires that we do the things we need to in order to solve vector problems:\u00a0draw vector diagrams, choose coordinate systems, and set up component equations.\u00a0 In addition, given the calculus required to determine the equations of motion for an object, we have limited ourselves to the set of relatively simple problems where an object\u2019s motion is either uniform or its velocity is changing in a very particular way.\u00a0 For all the problems we have been able to solve so far, is there another framework that we can use, particularly one that either requires less infrastructure or can allow us to get around some of the limitations that we have currently built into our approach with Newton\u2019s second law?<\/p>\n
The answer, of course, is yes.\u00a0 We can use energy as an alternative way to describe an object\u2019s motion.\u00a0 In fact, one of the critical lessons physicists have learned over the years is that energy is such a fundamental quantity, keeping track of the energy of a system and how it is transformed with a system or transferred into or out of it by the work done by forces is an incredibly powerful problem solving approach.\u00a0Initially, we will use the work-energy theorem to keep track of energy and how the energy of a system changes through work.\u00a0 With the work-energy theorem, we will calculate the work done by each force acting on an object or set of objects to see how those forces are causing the object to speed up or slow down.<\/p>\n
From a practical point of view, there are a couple of real advantages to using energy to solve problems that focus on how objects move.\u00a0 First, because energy is a scalar quantity rather than a vector quantity, much of the work that went into setting up equations using a vector approach can be avoided.\u00a0 As a general rule, if you can use the work-energy theorem to solve a problem, it\u2019s just easier.\u00a0 In addition, because of the scalar nature of energy problems, we can relax some of the constraints we have so far placed on how an object moves. \u00a0The work-energy theorem focuses on the initial and final conditions of a system. \u00a0The details of how the system got from its initial state to its final state tend to be much less important when we are keeping track of energy.\u00a0 This will allow us a relatively simple way to deal with objects whose motion may be quite complicated without the math becoming intractable.\u00a0 Though we won\u2019t be able to use an energy framework to solve every problem we come across, what we will learn pretty quickly is that, if you can solve a problem using energy, then do it using energy.<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t