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• Users: JLT
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1. ### I What is the best derivation of E= mc^2?

Sorry, on my phone without equation editor. Instead of E=m c^2, could be E=mv^2 where v is any constant velocity of any fluid. See original post, a chain rule, its a mass flow rate equation.
2. ### I x*t, what is position multiplied by time?

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. time position mass The above 3 are the building blocks if it all, and it just seems like all combinations of...
3. ### I What is the best derivation of E= mc^2?

Is there any relationship between: E = m v^2 and E = Pressure*Volume? PV = (density *Volume) * velocity^2 Pressure=density*velocity^2 almost starts looking like Bernoilli's equation.
4. ### I x*t, what is position multiplied by time?

Why are some physical quantities multiplied or divided by other quantities interesting, and other combinations not explored?
5. ### I What is the best derivation of E= mc^2?

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.
6. ### I x*t, what is position multiplied by time?

So the pattern goes: x(t) v(t) a(t) jerk(t) 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?
7. ### I What is the best derivation of E= mc^2?

Darn, I'm on my phone, cannot see posted equations. Best? Occam's razor kind of best.
8. ### I What is the best derivation of E= mc^2?

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 ?
9. ### Bold, Monster, Engineering Successes

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...
10. ### Comparing the kinetic energies among a solid sphere, a cylinder and a hoop

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...
11. ### Comparing the kinetic energies among a solid sphere, a cylinder and a hoop

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...
12. ### Land Yachts -- Why don't cars and trucks also use sails?

I was thinking more highway miles / use on semi's and trains than in the city. Googling for sailboats, did not find anything more recent than:
13. ### Land Yachts -- Why don't cars and trucks also use sails?

Really neat to get a reply from someone who has experimented with it! How difficult would it be to automate it? Self-driving / self-adjusting sail?
14. ### Land Yachts -- Why don't cars and trucks also use sails?

Ok - so how about using wind to help with brakes?
15. ### Land Yachts -- Why don't cars and trucks also use sails?

Haha - it could be retractable. Just seems like there is something that could be done with all that free energy:
16. ### Land Yachts -- Why don't cars and trucks also use sails?

Land Yacht racing has been around for awhile - https://en.wikipedia.org/wiki/Land_sailing 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...
17. ### I Rotation rates of planets seem odd?

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...
18. ### I Rotation rates of planets seem odd?

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?
19. ### A What are the forces acting on an air particle along a fluid streamline curve?

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?
20. ### A Diffussion-limited aggregation and the mobility of particles

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...
21. ### I Rotation rates of planets seem odd?

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...
22. ### B Exploring Force & Potential Energy of a Donut-Shaped Planet

Interesting, thank you for the replies!
23. ### B Exploring Force & Potential Energy of a Donut-Shaped Planet

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...
24. ### Feeling Forces (like feeling gravity while in free-fall)

Thanks, I'll go study those.
25. ### Feeling Forces (like feeling gravity while in free-fall)

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...
26. ### Feeling Forces (like feeling gravity while in free-fall)

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...
27. ### Feeling Forces (like feeling gravity while in free-fall)

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) +...
28. ### Feeling Forces (like feeling gravity while in free-fall)

a = (change in magnitude of velocity) + (change in direction of velocity) → Can you feel when you change direction? Even if force and acceleration are constant? ↑ ↓ ↑ ↓ ↑ ↓ o
29. ### Mousetrap potential energy

Homework Statement Calculate the potential energy created by the spring in the mousetrap as a function of the angle the spring is pulled back. Homework Equations 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 =...
30. ### B Why does Fdt go away during collisions while Fdx does not?

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 <...
31. ### B Uncovering the Preference for Certain Types of Energy

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...
32. ### B Why does Fdt go away during collisions while Fdx does not?

This: https://en.wikipedia.org/wiki/Elastic_collision 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...
33. ### B Uncovering the Preference for Certain Types of Energy

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...
34. ### B Why does Fdt go away during collisions while Fdx does not?

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...
35. ### B Why does Fdt go away during collisions while Fdx does not?

forces between two colliding objects. you can set it up so that momentum is conserved, while energy is not conserved.
36. ### B Why does Fdt go away during collisions while Fdx does not?

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...
37. ### B GMm/r^2 for r = 0?

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...
38. ### Flywheel Inertia: Calculating Mass & Radius

What CAD software are you using? that really is the easiest way to find I.
39. ### I Acceleration w/o Velocity Change: Gravity Ques

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...
40. ### I Acceleration w/o Velocity Change: Gravity Ques

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...
41. ### I Acceleration w/o Velocity Change: Gravity Ques

Knowing "how/what" is different than knowing "why"... without knowing the why's it doesn't feel like knowing much. Thanks again.
42. ### I Acceleration w/o Velocity Change: Gravity Ques

So science only describes interactions, but never actually explains the thing itself? We'll always be standing on the outside looking at the surface of things? That's disappointing...
43. ### I Acceleration w/o Velocity Change: Gravity Ques

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?
44. ### I Acceleration w/o Velocity Change: Gravity Ques

I guess I'm having a hard time understanding what a force really is if it does not have to involve dv. Thanks for all the replies!
45. ### I Acceleration w/o Velocity Change: Gravity Ques

kg m/s^2... if the individual component is not mdv/dt, then what is it?
46. ### I Acceleration w/o Velocity Change: Gravity Ques

So the "net" force is always ma, but the individual components of the forces are not equal to ma?
47. ### I Acceleration w/o Velocity Change: Gravity Ques

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...
48. ### What is a wave actually?

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...
49. ### How does water escape the pot?

interesting - so a syphon without a tube? where the surface tension is the tube? I wonder if you could calculate the surface tension based on the final water level?
50. ### I Acceleration w/o Velocity Change: Gravity Ques

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?