non-Euclidean mathematics was explored prior to applying the ideas to quantum mechanics.
If math is the language of the universe, something interesting should fall out of all of it.
The above 3 are the building blocks if it all, and it just seems like all combinations of...
No aether, what was it- splitting light and bouncing back no matter how the thing is rotated with respect to the rotating earth that is flying around the sun.
I'm on vacation, just looking for book suggestions.
So the pattern goes:
You can keep taking slopes of lines, and slopes of slopes - my questions is, what happens in the other direction- areas under curves and more areas under curves.
What is the area under the x(t) curve?
x*t, what is position multiplied by time?
F= V dm/dt = V (dm/dx)(dx/dt) = V^2 (dm/dx)
Fdx = V^2 dm
E = m v^2. ,mass flowing with constant velocity
If velocity is changing rather than mass, then E = 1/2 m V^2
Ok, joking aside, what is the best derivation of E= mc^2 ?
Can't wait to see what no one has seen before with LSST Vera Rubin Telescope and James Webb Space Telescope.
The LHC should be added to the list, will be interesting what the new system will produce.
"The discovery of the Higgs boson was only the first chapter of the LHC story. Indeed, the...
A couple things just a little off in your written work, need w^2 for constant acceleration equations, and moment balance needs to add to both rXma and I*alpha:
Here are two different ways to walk around it, using an energy balance, and also using constant acceleration equ's with moment balance...
The same starting potential energy turns into the same kinetic energy at the bottom: Ksphere = Ksolid cylinder = Khoop; K = K = K, they all have equal energies. same mgh → same kinetic energy
they do have different translational and rotational velocities due to their different I's...
Land Yacht racing has been around for awhile -
a few people still trying it out
The question, is has anyone seen ideas of sail-boating applied to semi-trucks, trains, even cars to improve energy efficiency?
Another application - has anyone seen...
Thanks for the replies, I guess I need to study tidal locking more. I can visualize the oceans on the Earth with high and low tide getting tugged around by the moon. It is much harder to visualize solid rock as a viscus fluid. Are there any good computer models of this? I am now googling...
I always thought of planets forming like whirlpools, or almost like hurricanes - perhaps something Coriolis like about them? Mercury does not have surface fluids, so how does tidal locking work there? Is it lopsided?
What forces make the stream curved instead of straight? An object in motion wants to stay in motion - wants to travel in a straight line. What stops it from traveling in a straight line? Seems like a good place to start?
Looks like an old thread, but if you are still out there - think of cars piling up in a traffic jam, or sticks flowing down a river. As soon as two particles bump into one another, they lose energy - so then those two particles slow down, and others catch up, and traffic jam! On highways, it...
Ok, I know there are a lot of strange things in our solar system. Can anyone explain why the small planets spin so slowly? and why does Jupiter spin so quickly? It seems like a ball of debris, getting smaller and smaller, would increase its speed like an ice-skater pulling their arms in...
So, let's say you have a donut - shaped planet, so a second object can move right on top of the center of mass of the first object. Does force go to infinity? How about potential energy?
Or, just take one object, divide it into elements, what happens to the central element of mass within the...
You feel gravity though - an accelerometer in a complete void, just one object surrounded by nothing, and the spring is not stretched out. If there are two objects, those masses attract one another, you can feel it - could detect the other object with an accelerometer, right? Th moon tugs at...
Forces can be felt - accelerometer, we can detect a mass tugging on a spring. Moment of inertia - we can detect resistance to change in rotational as well as translational velocities
Seems like there should be a way to create something that could distinguish between acceleration created by...
Yes, just a thought experiment - so pretend you don't have bodily fluids sloshing around, just a homogeneous point mass with each point undergoing the same constant acceleration.
Can you model the top point as rotational motion? Perhaps consider r→0,
a = (change in magnitude of velocity) +...
Calculate the potential energy created by the spring in the mousetrap as a function of the angle the spring is pulled back.
PE = ∫Fdx = ∫ kxdx = ∫k rΘ rdΘ ??
The Attempt at a Solution
Is this a linear spring? we can use x = rΘ, and dx = rdΘ, so PE =...
mva + mvb +Fabdt+Fbadt = mva'+mvb'
Fab = Fba → internal equal and opposite forces, so in the absence of external forces momentum is conserved.
0.5mava^2 + 0.5mavb^2 + Fabdx+Fbadx = 0.5mava'^2 + 0.5mavb'^2
Same scenario, Fab = Fba, only energy is not conserved if the collision is plastic (e <...
A rock in air then - given the choice of the energy staying in the form mgh, or the energy changing into 0.5mv^2 the system naturally wants to change mgh into 0.5mv^2 → it likes KE better. If it did not like KE better than it would just remain floating in mid air - it would just keep the...
vs. this: https://en.wikipedia.org/wiki/Inelastic_collision#Perfectly_inelastic_collision
Elastic has conserved energy, while plastic does not. Fdt vs. Fdx. Fdt goes to zero (equal and opposite pairs), Fdx does not go to zero even though...
Between kinetic energy, potential energy, thermal energy - it seems like some forms of energy are preferred over others.
A rock on a hill wants to change its energy from PE → KE
and anything with KE wants to change KE into heat.
Is there are reason that some forms of energy are preferred over...
Sorry, I should have put a summation sign on the forces:
mVa + mVb + Fab dt + Fba dt = mVa' + mVb' → forces are equal and opposite, cancel out, and you get conservation of linear momentum
0.5 mVa^2 + 0.5mVb^2 + Fab dx + Fba dx = 0.5 m Va'^2 + 0.5 m Vb'^2
I think it is because part of dx does...
For collisions between particles, Fdt goes to zero while Fdx does not
F = mdv/dt
mv + Fdt = mv
if you have two particles colliding
mva + mvb +Fdt = mva'+mvb'
in the above case, Fdt goes away as there are equal and opposite forces between the two particles during the collision, linear momentum is...
This is probably a stupid question - but let's say you have a hollow Sun (M is hollow), with another mass in the center, so M and m share the same center of mass, the distance between the centers is zero.
Would GMm/r^2 be infinite in this case?
The force at the center of any object - if you...
Cause / effect = why. The trouble is there is some infinite cause/effect loop with no ultimate beginning to trace it all back to. You can always ask "but why did that happen?" one more time.
It feels like being in one of those movies with a twist ending - going through calculations with all...
Haha - didn't mean to take this into a philosophical route, just trying to better understand what a force is. ... Force is something you cannot really see, cannot measure with a ruler, is not always mdv/dt - I guess you have to just "feel" it - so we can all close our eyes, hold hands, and...
pressure involves a bunch of dv's, I can visualize that one...
but gravity, GmM/r^2, no dv's in that one... it exists without anything changing velocity? What is the physical sig of G? 6.67 × 10-11 m3kg-1s-2 ... what do those units even mean?
let's say we are breaking the net force up, and just looking at each individual component. we call each component a force, it could be mg, or uN or kx or F=kq1q2/r^2, or whatever the case may be. If you let go of the system each of those individual forces can turn into a change in velocity for...
There are different types of waves - we usually visualize waves as what we see happen in water, but waves in air or emf waves are fluctuations in pressure, or in magnetic fields. Any non-static system that has something alternating in it = waves. You can get all kinds of different patterns...
example; F=kx=ma is not zero, a = kx/m, a positive value even though dv/dt = 0 if the system is in equilibrium. It just seems like there is some other acceleration going on, or some other way to think of it - were a is not dv/dt in all cases?