Given how useful the work-energy theorem is, why don’t we use it all the time?  The short answer is that there are some questions that are either difficult or impossible to answer using an energy framework.  The most important example is time.  Both Newton’s second law and the kinematic definitions relating position, velocity, and acceleration are what are known as time-dependent equations. This means that they can be expressed as function of time, which allows you to solve for how long it takes for an object to move a certain distance or reach a certain speed given the force that are acting on it.  The work-energy theorem, on the other hand, usually does not include time as a variable when we calculate out the work done by each force acting on the object.

A second example of a question that can difficult to solve for using the work-energy theorem is the direction an object is traveling in at a certain point.  Because energy is a scalar, the work-energy theorem tends to blur out information about the direction an object is traveling in if it isn’t constrained by the problem.  If you throw a ball off the roof of a building, the angle the ball is traveling in when it hits the ground depends on how you threw the ball.  But the work-energy theorem only captures the speed at which the ball was released, not it direction.

So what does this mean going forward?  Mostly it means that we see our forces framework and our energy framework as two different approaches and we need to make sure we are equally comfortable using either approach.  It also means that one of the additional skills we need to develop is recognizing when a vector approach or a scalar approach is preferable to solve a particular problem.  For many of the problems we have already solved using Newton’s second law, we could go back and also solve them using the work-energy theorem.  (And in fact, since we have to get the same answer regardless of the approach we take to solve the problem, solving a problem both ways when you can is a great way to check your work.). But there will also be problems where, depending on what information we are given and what we are being asked to solve for, there will be a clear preference for using one approach over the other.  Identifying whether you want to work a mechanics problem using a vector process or an energy one is a skill you will want to practice as we move through the remainder of the course.