Up to this point, we have seen that we can use Newton’s laws and kinematic equations to solve numerous problems detailing the motion of an object or a system of objects.  However, Newton’s framework is a vector framework and requires that we do the things we need to in order to solve vector problems: draw vector diagrams, choose coordinate systems, and set up component equations.  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’s motion is either uniform or its velocity is changing in a very particular way.  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’s second law?

The answer, of course, is yes.  We can use energy as an alternative way to describe an object’s motion.  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. Initially, we will use the work-energy theorem to keep track of energy and how the energy of a system changes through work.  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.

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.  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.  As a general rule, if you can use the work-energy theorem to solve a problem, it’s just easier.  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.  The work-energy theorem focuses on the initial and final conditions of a system.  The 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.  This will allow us a relatively simple way to deal with objects whose motion may be quite complicated without the math becoming intractable.  Though we won’t 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.