Energy! (The review.)

Work, W – defined as the product of force and displacement

W = F d

The units are new:  newton-meter = joule (J)

Work is part of the energy concept – a book-keeping technique for keeping track of real changes in a system.  For example, you “do work” on something and that work shows up as (or “transforms into”) a type of energy.

Energy – the ability to do work

There are several types of energy:  kinetic, potential, chemical, electrical, nuclear, geothermal, hydroelectric…… all of these can be quantified.  In essence, energy is a way of mathematically encapsulating some other manifest changes.  For example, kinetic energy (KE) is a way of describing an objects mass and velocity; potential energy (PE) describes an objects weight and location.

KE = ½ mv²

PE = mgh

The units of energy are the same as work:  joules.

Conservation of Energy

Energy is never created or destroyed – it only changes forms.   Consider this:  if you lift up a weight (mg) to a certain height (h), you were able to do this because you’d eaten food recently.  The food had some “energy content” and that energy was transferred to the weight.  Now, the weight has some potential energy – the potential to fall, actually.  If the weight were to fall, it would gain speed (and thus, kinetic energy).  The exact amount of potential energy it loses is how much kinetic energy it gains:

PE = KE

mgh = ½ mv²

v = sqrt (2gh).

This is an easier way to do freefall problems, for instance. 

Energy is conserved:

Initial energy = Final energy

E_i = E_f