11:00 PM
Like look at the conservation of energy
E_t = \frac{1}{2}mv^2 + E_p
If you assume that to be true then we can derive that equation from that

@WilliamOliver Exactly. Potential energy is (simply said) a form of energy which is defined as the position in a force-field. So it is clear that the force which acts on the particle must be equal to its potential energy.
Or did I misunderstand the situation now ?

@PhysicsGuy No you understood what I said. I shouldn't have worded that last part like that
I realized that as soon as I typed it haha.
My point was that the conservation of energy doesn't give an explicit form of E_p like it does for kinetic energy

Did you find more members ?

@WilliamOliver why do you actually start speaking about conservation of energy? How does that relate (I know what it is)
?

No not yet haha

11:05 PM
@WilliamOliver If you want $\frac{1}{2}mv^2+U$ to be constant, then you get $F=-U'$.

@0celo7 that ^

Namely, the time derivative of that is $m\dot x\ddot x+\dot xU'$.
Dividing out $\dot x$ gives $m\ddot x+U'=F+U'$

Thats the point.

@privetDruzia By the way, I am starting a study group for a book that describes all of this in great detail :D

unfortunately still didn't get it...
I am a beginner in physics
@WilliamOliver
:((

11:09 PM
@privetDruzia Do you know calculus?

yes
up to linear differential equantions
ie laplace and eigenvectors etc...

Then thats all you need! I didn't understand this stuff up until a month or two ago.
Its because of the first few pages of this book.

@WilliamOliver which page(s) do u recommend?

the first few :D
Hahaha

:((

11:13 PM
@privetDruzia Up to page 15

Sorry.

just to be clear, I am not going for a PhD in physics

@PhysicsGuy haha no worries I thought it was funny

@privetDruzia Noone here does, i think

those crazy people hide somewhere else I guess...

11:14 PM
@privetDruzia Ah well then I would just suffice it to say that the potential energy is defined that way

@privetDruzia Read a bit in that book, its interesting.

I hoped that maybe there would be some easy example that would help me understand that
the opposite rate of change of the potential energy with respect to the x-position of the particle = force
@PhysicsGuy I am reading that one for the moment: amazon.com/…
that s more my kind of stuff
although what you posted seems interesting as well

Aaaaah, Spacecraft.
;)
So are you interested in astrophysics or in technology (like spaceships, satelites, and stuff..) ?

both actually
love it
love physics, but it s difficult

Who doesnt ? ;)

11:21 PM
IMO there are a few things that are much more complicated than engineering and one of those are physics

Well you can think about it like this
Lets say you have a ball
and someone is tugging on it
But you are holding it, so you "feel" the force

mhm

What you feel is sort of like the potential energy in a way
By changing the position of the ball in the opposite direction of the force

develop plz

Whereas before the force was 0

11:23 PM
if the guy tuggs the ball the ball is moving in the direction of the force

The potential energy changes with respect to the position (your mgh)

so why/where "opposite" direction?

You are pulling against his force
Thats why there is the opposite direction

you just have to adjust g

oh when holding the ball I am trying to not let him tugg?

11:24 PM
@PhysicsGuy good point

kinda...

Basically gravity is like the tugging guy
if you lift a heavy weight

mhm

its like you are playing tug of war with gravity

11:25 PM
with respect to the earth, the potential energy increases
(as you lift it)
But if you aren't moving it at all
the total force is 0

about the ball tugging: when would be the potential energy the greatest?

your force up is equal to the force down.
It could be infinite
in this scenario
But my point is that once you start lifting up there is a non 0 force. But only when the potential energy changes with your position
Since you are moving opposite the direction of the earth's gravitational force, thats why the negative sign is there

ok
@WilliamOliver so according to this example: the quicker I would lift the object upwards, the stronger the gravitational field (F) would react downwards?

No, the stronger the force would be upwards.

but due to the negative sign there must be an opposition somewhere
which is the direction of the force of the gravitational field
here

11:33 PM
Hm maybe I am still explaining it poorly.
Okay, think about mgh as mgx.
Height is x

don t worry, I need some time to understand things

then you take the derivate of that with respect to x, you get -mg. Your force when you aren't moving at all.
When you aren't accelerating at all.

@privetDruzia I guess your problem lies there, that you dont know what - and + signs stand for in this context, could that be ?

could be
I don't understand why you have a derivative and why it s negative
This
is how potential energy and force were introduced to me
it has to do with intermolecular forces

Well are you looking for an intuitive explanation or a formal one?

11:40 PM
I think intuitive is the best

Ok guys, i have to leave now.
See you.

@PhysicsGuy See you

@privetDruzia Its really hard to explain intuitively I guess..

ok do whatever you think is the best

11:42 PM
Potential Energy in itself really doesn't have much of an intuitive counterpart in real life, other than the "potential" to do "work".

Getting rained on when it wasn't raining when you left the building is an insult from god
like wtf

@0celo7 nuclear engineering wow that sounds cool!
why didn t u go for renewable energy? Isn t that the future?

Essentially Force and potential energy are related by definition, you could say that what you feel when you hold a heavy object in one place is force, and the "pain" that you feel when you hold the weight is the potential energy. Its the thing in your arm that says "please drop this thing now".

@privetDruzia Fusion energy
renewable won't allow us to colonize the universe

11:47 PM
Neither will nuclear

@Slereah fusion
go back to your negative energy BS

Even antimatter isn't all that good for conquering the universe

There's no reasonable spaceship design that would bring us to the nearest star in under 200 years

@0celo7 why wouldn t it? Solar energy is available in big parts of the universe (sorry for the poor wording here)

@WilliamOliver ok I see

11:49 PM
@privetDruzia solar really doesn't work well at all

and 200 is a pretty optimistic estimate

@Slereah I plan to become immortal.

that would help

@Slereah not yet. If guys like werner von Braun were more active nowadays we d have better technologies. That dude spoke about conquering Mars in the eighties...

I need PDE help, @Slereah

11:50 PM
To be fair I'm pretty sure we'll live a thousand years way before we develop FTL technology, if ever

@0celo7 why do you think solar energy doesn t work well in space?

1 hour ago, by 0celo7
@yuggib Let $F:\Omega\times [0,\tau]\to\Bbb R$ be smooth, where $\Omega\subset\Bbb R^n$ is open. Suppose $\partial_t F\le\Delta F+C\tau^{-2}$ on $(0,\tau]$, where $C>0$ is a constant. Why does the maximum principle imply $\sup_\Omega F(\cdot, t)\le C\tau^{-2}t$?
1 hour ago, by 0celo7
Oh, also $F(x,0)=0$ for all $x$.
@privetDruzia The mars rovers are barely functional
they have plutonium cores to supplement the solar

Also solar energy is nothing when you go to interstellar space

but to actually sustain life using solar is not going to happen
Putting a fission reactor into space is also not going to happen
I attended a talk on power in space
Nuclear powered rockets were big in the 60s

@0celo7 didn t know they weren t working well. Source?
@Slereah we have berely sent ppl beyond mars. Let s first make sure this works well before going interstellar and so on. Most of the satellites use solar panels in combination with batteries

11:53 PM
I attended a talk, if you want to email the dude, I can give you his name
He's a researcher at Oak Ridge

@0celo7 naah s okay I ll trust u and google a bit :)

They have to very carefully manage how much power the rovers use
They are definitely not getting an abundance of power from the solar panels
and Mars is further away from the sun
thinner atmosphere might mitigate that somewhat
@privetDruzia the biggest challenge for satellites is making power without having moving parts
moving parts always break
solid state nuclear power is what's used right now + solar

well we r making babysteps, ppl now use solar panels and batteries. We re now waiting on either Elon Musk to find an incredible alternative or some random dude at a university writing a paper about some hypotetical solution that can eventually work.

solid state is in jeopardy because you need weapons-grade plutonium and no one wants to make that

@0celo7 not sure about that. Depends on what you use. If you use reaction wheels or magnetorquers (which are inside the spacecraft) I think chances that those break are much smaller

11:58 PM
the "always" is not meant literally
@Slereah so what do you think about that PDE above