What to Remember from Lesson

8.9. What to Remember from Lesson#

8.9.1. Energy Conservation#

The big idea of this lesson is that energy is conserved in all physical interactions. In any process, the energy of the initial state must equal the energy of the final state—even, if in everyday life, that final state energy might be a mixture of motions of the final state objects themselves, but all of the losses that become heat. “Might”? No, “Is.” Everyday interactions create losses and hence heat. These are called “inelastic” collisions and when object stick together, that’s called a “totally inelastic” collision and the most heat is made as waste energy in those kinds.

But ideal interactions are a tool for approximating everyday interactions. In ideal interactions, the objects have no parts and are perfectly stiff, rigid to vibration and compression. Therefore, there is no heat lost and…they’re silent. These are called “elastic” collisions. In everyday life, there are no elastic collisions.

But in elementary particle interactions? Well, they’re ideal! We’ll deal with elastic collisions when we talk about elementary particles.

And that’s good, because an important feature of elastic collisions is that not only is total energy conserved, but kinetic energy is conserved also.

And…of course, momentum is always conserved. See Emmy above.

8.9.2. Energy Units#

Here I introduced the primary unit of energy in the MKS system, appropriately named “Joules.” The scale is an everyday one:

\[1 \text{ J} = 1 \text{ kg-}{\text{(m/s)}^2}\]

and it’s about the potential energy of holding an apple one meter above the floor, or equivalently, the kinetic energy that that apple acquires just before it hits the floor after it’s dropped.

Energy units will become huge in cosmology and very tiny in electricity and magnetism, quantum mechanics, and particle physics. Factors of \(10^{-19}\) will start to float around and so we’ll evolved into a new kind of unit when we get there. For now, Joules works just fine.

8.9.3. Energy Relations#

The Kinetic energy of an object (ideal or everyday) of mass, \(m\) moving at velocity, \(v\) is:

(8.1)#\[ K=1/2 mv^2 \]

If an object is oriented and constrained in such a way that if the constraint were released, it would move, then we say that object has Potential energy. If an object has a mass, \(m\) and if that orientation is the act of being lifted above some surface by a distance \(h\), then the Potential energy of that object is:

(8.2)#\[ U=mgh \]

Two caveats to these simple relations:

  • The kinetic energy in the form of Equation (8.1) is for speeds which are low. See Einstein, below.

  • The potential energy in the form of Equation (8.2) is…well, going be weird. See Einstein, below.

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