We give below again a copy of our post of March 01, 2021, 03:35:45 PM.

======================

======================

Let us shorten our previous explanations (of February 26, 2021, 04:01:00 PM) by jumping directly to PART 3 (and having a brief glimpse at a small section of PART 2).

----------------------------------------

So let us start our shorter explanations.

----------------------------------------

1) Firstly, please have a look for a while at PART 2 and at the related link

https://youtu.be/aVOfWLDrYwA from 00:00 to 00:03. This is only for getting a notion about the limits of the segment "s", that is, how this segment "s" is situated in relation to (relative to) the zigzag section.

----------------------------------------

2) Now let us focus on PART 3 and on the related link

https://youtu.be/pPGPktU_kpo . The experiment is carried out in a space station under weightlessness conditions. Friction is negligible as the only exception is the friction inside the two straight-line channels of the segment "s". (The inside surfaces of the straight-line channels of the segment "s" are made rough thus able to generate friction (and heat, respectively).)

----------------------------------------

3) The mass of each blue component is Ma.

-----------------------------------------

4) The mass of each black component is Mb.

-----------------------------------------

5) There are four couples blue ball/blue rod. Each blue ball is firmly attached to the related blue rod thus forming one united whole.

-----------------------------------------

5A) The mass of each blue ball is negligible (if compared to Ma or to Mb), but not equal to zero.

-----------------------------------------

5B) The mass of each blue rod is negligible (if compared to Ma or to Mb), but not equal to zero.

-----------------------------------------

6) From 00:00 to 00:03 the two blue components move simultaneously and uniformly. Each blue component's linear velocity is V' as V' = const. The two black components are at rest.

------------------------------------------

7) At 00:03 the four blue balls enter simultaneously (a) the "upper" black component's smooth zigzag channels and (b) the "lower" black component's rough straight-line channels of the segment "s", respectively.

------------------------------------------

From 00:03 to 00:15 the four blue balls move (a) inside the "upper" black component's smooth zigzag channels and (b) inside the "lower" black component's rough straight-line channels of the segment "s", respectively.

-------------------------------------------

9) At 00:15 the four blue balls exit simultaneously (a) the "upper" black component's smooth zigzag channels and (b) the "lower" black component's rough straight-line channels of the segment "s", respectively.

-------------------------------------------

10) The force of friction inside the two rough channels of the segment "s" is chosen in such a manner (we could use for example a variable roughness and the related variable force of friction, respectively) that:

-------------------------------------------

a) the blue components decelerate in one and same manner, that is, their decelerations are one and same and equal one to another;

-------------------------------------------

b) the black components accelerate in one and same manner, that is, their accelerations are one and same and equal one to another.

-------------------------------------------

11) From 00:15 to 00:17 the two blue components move simultaneously and uniformly. Each blue component's velocity is V" as V" = const.

-------------------------------------------

12) From 00:15 to 00:17 the two black components also move simultaneously and uniformly. Each black component's velocity is V"' as V"' = const.

-------------------------------------------

13) Therefore for the "upper" zigzag modification we can write down that

(Ma) x (V') = ((Ma) x (V'')) + ((Mb) x (V''')) (1)

(1/2) x (Ma) x (V') x (V') = ((1/2) x (Ma) x (V'') x (V'')) + ((1/2) x (Mb) x (V''') x (V''')) (2)

-------------------------------------------

14) And for the "lower" straight-line modification we can write down that

(Ma) x (V') = ((Ma) x (V'')) + ((Mb) x (V''')) (1)

(1/2) x (Ma) x (V') x (V') = ((1/2) x (Ma) x (V'') x (V'')) + ((1/2) x (Mb) x (V''') x (V''')) + Q (3),

where Q is the heat, which is generated while the two blue balls move inside the two rough channels of the segment "s" in the "lower" modification.

------------------------------------------

15) It is evident that (a) the system of equations in item 13 and (b) the system of equations in item 14 cannot be true simultaneously.

------------------------------------------

16) And it directly follows from the previous item 15 that either (a) the law of conservation of linear momentum is not correct or (b) the law of conservation of mechanical energy is not correct or (c) both the law of conservation of linear momentum and the law of conservation of mechanical energy are not correct simultaneously.

------------------------------------------

NOTE. Please refer, if necessary, to our first post of Sat Jul 28, 2018 12:41 and to the two related links

https://mypicxbg.files.wordpress.com/2018/04/pages_01-12.pdfhttps://mypicxbg.files.wordpress.com/2018/05/figs01-08.pdf------------------------------------------

Looking forward to your answer.