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  2.7. Force elements with the increasing mass of mobile elements

 

The task represented in a Fig. 1 can be a little bit modified.

 

Varipend. Áåçîïîðíîå ïåðåìåùåíèå. Ñèëîâîé ýëåìåíò ñ íàðàñòàþùåé ìàññîé ïîäâèæíûõ ýëåìåíòîâ.

Fig. 22

Around of the center of mass of a massive body , on a circle of radius R the system of mobile elements moves with constant speed. Elements are put forward from some "source" in total mass (at the initial moment of time), connected with a body . The system of bodies is distributed continuously and in regular intervals. Through time after the beginning of promotion of elements, i.e. after end of a running cycle, all trajectory of movement of mobile elements will be filled by these elements.

To repeat a running cycle, not breaking position of the center of mass of all system, it is necessary simultaneously and to move mobile elements to a point from which elements are put forward on a working trajectory in regular intervals.

For the working period the closed mechanical system represented in a Fig. 22 will move the same as also system in a Fig. 1, on distance

, where

 

 

(see the formula (23),(24))

Corresponding plots of moving of the center of mass of the case of system and the center of mass of all system as a whole are resulted in a Fig. 23 and a Fig. 24:

Varipend. Áåçîïîðíîå ïåðåìåùåíèå. Ïåðåìåùåíèå "êîðïóñà" ñèëîâîãî ýëåìåíòà ñ íàðàñòàþùåé ìàññîé ïîäâèæíûõ ýëåìåíòîâ.

Fig. 23

 

Varipend. Áåçîïîðíîå ïåðåìåùåíèå. Ïåðåìåùåíèå öåíòðà ìàññ ñèëîâîãî ýëåìåíòà ñ íàðàñòàþùåé ìàññîé ïîäâèæíûõ ýëåìåíòîâ.

Fig. 24

Two plots presented  on Fig.23 and Fig 24, collected in one plot:

Red color designates a trajectory of moving of the center of mass of all system,  dark blue - moving of the case ( Mc ).

 

 



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