Re: [Phys-L] [**External**] Re: escape speed

[Matthew Heaney <matthewjheaney@gmail.com>]

On Tue, Aug 6, 2024 at 8:36 AM Philip Keller via Phys-l <
phys-l@mail.phys-l.org> wrote:

> I really enjoy teaching this topic!  It's fun to show that it is an
> extension of earlier work but with a new formula for potential energy.

The escape velocity problem is interesting because you learn about what a
potential well is, and knowing this helps you understand how quantum
mechanical problems are framed, or why molecule formation releases energy.
Once you understand the idea that a spaceship needs just enough kinetic
energy to overcome the negative potential energy of the gravitational well,
that leads naturally to the work function for the photoelectric effect, or
what it means for an electron to be bound to an atom.


> The scaffolded notes I give my students are here:
>
>
> https://docs.google.com/document/d/1iaqnQFsu0K-_di_O-i9bCadi4SMgRt4qn9PMBJnrKeA/edit?usp=sharing
>
> And I use a collection of Interactive Physics models as we work our way
> through these notes.  If you happen to be one of the few dinosaurs left who
> use Interactive Physics (I think we number in the tens!)  and would like me
> to send you the simulations, let me know.
>
>
>
> On Mon, Aug 5, 2024 at 5:16 AM Matthew Heaney via Phys-l <
> phys-l@mail.phys-l.org> wrote:
>
> > On Sun, Aug 4, 2024 at 6:57 PM Matthew Heaney <matthewjheaney@gmail.com>
> > wrote:
> >
> > > On Thu, Aug 1, 2024, 18:20 Anthony Lapinski via Phys-l <
> > > phys-l@mail.phys-l.org> wrote:
> > >
> > > > I teach about gravity early on in my high school astronomy course. I
> > > > discuss/derive surface gravity, orbital speed, and escape speed. And
> > then
> > > > we do comparative fractions. I want to add some ideas about
> > > > their importance. I know that gravity affects atmospheres of planets
> and
> > > > stars, and is used to calculate physical properties of stars. What
> about
> > > > escape speed? Is it mostly important for space travel? But isn't
> gravity
> > > > the main factor here?
> > >
> > > The issue is how much work you do against gravity - it's about energy,
> in
> > > other words.  The existence of gravity is why you're sitting in a
> > potential
> > > well (you're bound, so it's negative), and you need enough kinetic
> energy
> > > to get back to zero.
> > >
> > > Force and energy should always be discussed together.  Force is simply
> > the
> > > mechanism by which your change your energy.
> >
> > The force is equal to the (negative of the) derivative of the potential
> > energy.  The sign is telling you that the force points in the direction
> > that lowers the potential energy.  From there you can have a nice segue
> > into entropy and the 2nd law.  Systems tend towards a state of lowest
> > energy.
> >
> >
> > > But to derive the escape velocity, you need to be thinking about
> energy.
> > > The only thing that matters is your speed (that is, your kinetic
> energy).
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