Our Conservation of Energy equation gives us a powerful new tool for solving physics problems. It allows us to determine the amount of energy the system has initially ( `E_i` ), the final amount of energy of the system ( `E_f` ), and the amount of energy transferred into or out of the system ( `W_{nc}` ). At this point in the course, we will focus on the mechanical energy of a system, `E = K + U`. But later in the course, we will add new forms of energy to keep track of using energy conservation.

Even though we haven’t yet worked physics problems using energy, many of the problems we have previously worked can be solved using conservation of energy. However, because energy is a scalar quantity rather than a vector one, using an energy approach to solve a problem is often mathematically much simpler than the vector problems we have worked up to now. As a result, using an energy approach will quickly become your preferred method for attacking physics problems. Energy isn’t always helpful for solving a particular problem, but when it is, it is almost certainly the easiest way to find a solution.