Notes-Energy

Energy is a concept that can be difficult for students, but it can also be easy if you can relate it to their everyday experience. I like to begin with an analogy between their feeling of having energy to the definition of energy in physics, which is the ability to do work. So, if they have energy when they wake up in the morning, they can do a lot of work either at school or at their job. With no energy, they have difficulty getting motivated for work and accomplish less. Thus their feeling of having energy determines how much work they can do.

Energy takes many forms and is transferred from one form to another continually in our experience. I start this unit by having students brainstorm energy terms and types, while I write them on the board. I will then try to define each term that was stated, and explain the relationships between each. I make sure that terms like potential energy, kinetic energy, electromagnetic radiation, chemical energy, and nuclear energy are on the board. This gives me a good chance to discuss EM radiation and the difference between that and what we call mechanical energy, the sum of potential and kinetic energy. Once students have listened, I check understanding by having them organize their terms into a concept map (or web) of energy terms. The web should start with a bubble for energy in the middle, with KE, PE, and EM radiation coming off that. If you have access to computers and the program Inspiration, this is an ideal use of that technology. If not, I have them sketch it first, then I check each sketch before I have them make a final product on construction paper.

The first section of this unit will focus on Kinetic and Potential energy. and in particular gravitational PE which we will refer to as PE, event though PE can take many more forms than that stored by your relative position to the Earth.

I start by writing definitions of PE and KE, then of work. I do a simple example of work by pushing a chair across a room. If I push with 1N of force for 3m, I do 1N∙3m = 3 N∙m of work. Thus the units for work are N∙m. By definition, one N∙m equals one Joule. I then will look at the work done in lifting a mass m a height h in the room. If I lift a 2.2kg mass 1.3m, I am clearly working against gravity or the weight of the mass as I lift it. Thus the work I do is equal to the weight times the distance vertically that I lift the mass, or:

W = m∙g∙h

So I do m∙g∙h of work in lifting the mass a height h. Where does this work go? If I am careful not to accelerate the mass and just lift it at a constant speed, then it should be easy to see that the work done in lifting the mass goes into its potential energy. Thus we have our first equation for energy:

PE = m∙g∙h

Now, consider what happens when we drop the same mass from rest, for the same height drop h. As the mass falls, what happens to its PE? It loses its P, but we know it must turn into something. That something is its kinetic energy, or energy of motion. we know that kinetic energy should be proportional to an object’s speed and its mass, so we are looking for an equation with m and v in it. To find out what our equation is, consider:

As the mass falls from rest, its kinetic energy goes from zero to some value we are looking for. We also know that the potential energy it loses turns into kinetic energy. Thus:

KEgained = PElost = m∙g∙h

Now, let’s try to eliminate the h and g from this equation. To do this , we will do a motion problem for the falling mass. As the mass falls,

v0 = 0 a = -g d = -h v = ?

So, the equation we need is:

v2 = v02 + 2ad. Plugging in, we get

v2 = 02 + 2(-g)(-h), or v2 = 2gh, and solving for h, we get

h = v2/2g. Now we can substitute into our equation KE=m∙g∙h to get:

KE = m∙g∙( v2/2g) = 1/2m∙ v2, which is our other equation for energy.