[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 567

 
Reshetov:

1) a polygon cannot be inscribed into another polygon of the same area

2) There are 100 polygons and 50 needles, so the solution does not work

 

A trick question along the way. If there are polygons on one side that do not intersect with any polygon on the other side, then the sheet can be folded, and the needle can be poked in 2 times, thus compensating for the lack of needles. If there is an intersection, however, you should select those piercing points where exactly 2 polygons overlap.

The considerations are not strict, but you can get there.

 
alsu:

A trick question along the way. If there are polygons on one side that do not intersect with any polygon on the other side, then the sheet can be folded, and the needle can be poked in 2 times, thus compensating for the lack of needles. If there is an intersection, however, you should select those piercing points where exactly 2 polygons overlap.

The considerations are not strict, but you can get there.


Don't.
 
alsu:

A tricky problem along the way. If there are polygons on one side that do not intersect with any polygon on the other side, then the sheet can be folded, and the needle can be poked in 2 times, thus compensating for the lack of needles. If there is an intersection, however, you should select those piercing points where exactly 2 polygons overlap.

The considerations are not strict, but you can get there.

One thing I forgot, I thought it would be taken as obvious

The sum of the areas of the polygons (on each side) equals the area of the sheet

So there will be polygons on the other side for everyone. The challenge is to stick the needles in all of them without bending them

[Deleted]  

Are there people on this forum who know physics well?

Problem: Find the force of gravity acting on a body of mass M located at height H above the Earth.

PS:
here decided the problem, according to the solution, at an altitude of 6000 km body weighs half as much as on the surface of the Earth. Strangely enough, space stations do not fall even from a height of 400-600 km.
How to write the full equation of the dependence of gravity on the mass of the body and the height above the Earth?

 

Dim, you can't. You are still young and hopefully you will live to see the time when it will be publicly announced that 9.8 m/s2 stretches all the way to the edge of the Earth's gravitational field.

Jet-propelled aircraft don't know shit about gravity - that's a fact.

 
moskitman:

Dim, you can't. You are still young and hopefully you will live to see the time when it will be publicly announced that 9.8 m/s2 stretches all the way to the edge of the Earth's gravitational field.

Flying jets doesn't know shit about gravity - that's a fact.


Don't bullshit me. And where is this boundary? 9.8 only works at distances small compared to the radius of the Earth.
 
DmitriyN:

How do you write a complete equation for the relationship between gravity and mass and height above the Earth?

Take into account the centrifugal force as well.
[Deleted]  
TheXpert:
Consider also the centrifugal force.
Yes, I'm already calculating with it. I'm trying to calculate the strength of yesterday's pipe. I want to know what the maximum height of the steel pipe can be.
 
sand:

Don't be absurd. And where is that boundary? 9.8 only works at distances small compared to the radius of the earth.

and have you been there??? at the border? and on a fixed platform with scales and kilos of sugar (fluff, lead, turkey, ...)?

The Earth, like any (almost) other celestial body has a clearly (not to be confused with 'sharply')) delineated sphere of gravity, beyond the boundary of which the solar one exclusively acts.

Read(you) the internet, not physics by Hans_Christian_Andersen. :) Bo physicists from G_HH_A are still flying on jet propulsion... :)))