Chapter 2
Conservation of Mechanical Energy I: Kinetic Energy & Gravitational Potential Energy
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2
Conservation of Mechanical Energy I: Kinetic Energy &
Gravitational Potential Energy
Physics professors often assign conservation of energy problems that, in terms of
mathematical complexity, are very easy, to make sure that students can
demonstrate that they know what is going on and can reason through the problem
in a correct manner, without having to spend much time on the mathematics.
A
good before-and-after-picture correctly depicting the configuration and state of
motion at each of two well-chosen instants in time is crucial in showing the
appropriate understanding.
A presentation of the remainder of the conceptual-
plus-mathematical solution of the problem starting with a statement in equation
form that the energy in the before picture is equal to the energy in the after picture,
continuing through to an analytical solution and, if numerical values are provided,
only after the analytical solution has been arrived at, substituting values with units,
evaluating, and recording the result is almost as important as the picture.
The
problem is that, at this stage of the course, students often think that it is the final
answer that matters rather than the communication of the reasoning that leads to
the answer.
Furthermore, the chosen problems are often so easy that students can
arrive at the correct final answer without fully understanding or communicating the
reasoning that leads to it.
Students are unpleasantly surprised to find that correct
final answers earn little to no credit in the absence of a good correct before-and-
after picture and a well-written remainder of the solution that starts from first
principles, is consistent with the before and after picture, and leads logically, with
no steps omitted, to the correct answer.
Note that students who focus on correctly
communicating the entire solution, on their own, on every homework problem they
do, stand a much better chance of successfully doing so on a test than those that
“just try to get the right numerical answer” on homework problems.
Mechanical Energy
Energy is a transferable physical quantity that an object can be said to have.
If one transfers
energy to a material particle that is initially at rest, the speed of that particle changes to a value
which is an indicator of how much energy was transferred.
Energy has units of joules,
abbreviated J.
Energy can’t be measured directly but when energy is transferred to or from an
object, some measurable characteristic (or characteristics) of that object changes (change) such
that, measured values of that characteristic or those characteristics (in combination with one or
more characteristics such as mass that do not change by any measurable amount) can be used to
determine how much energy was transferred.
Energy is often categorized according to which
measurable characteristic changes when energy is transferred.
In other words, we categorize