Please help in this mechanics question involving bug

Физика Механика
1

Please provide a solution for this problem.
OA и OB — две нити, шарнирно соединенные в точке O. OA = OB. М — середина горизонтальной доски АВ. Насекомое находится в точке А. ОМ = 10 см. Вся система находится в состоянии покоя. Теперь система освобождается, и насекомое перемещается из точки А в точку Б так, чтобы дощечка не вращалась. Найдите время, за которое насекомое доберется до точки В?

OA and OB are two threads hinged at O. OA = OB. M is midpoint of horizontal plank AB. An insect is at A. OM = 10 cm. The whole system is held at rest. Now, system is released and the insect moves from A to B in such a way that the plank doesn’t rotate. Find the time taken for insect to reach point B?

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2

The insect has a very very small mass. It can be ignored.

3

no, it can’t

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4

but the problem statement says that insect can be assumed as point mass

5

but point mass still has the mass

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6

oh so with mass how will we solve? could you send the solution, if possible?

7

initially, the system is held at rest, thus the plank is inclined (so you can find the relationship between the inclination angle and mass ratio via expressing sum of torques = 0)

then the insect moves because of friction force (and mg\sin\varphi) that, apparently, can be arbitrarily changed in such way that plank doesn’t rotate

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8

ok i’m trying

9

sorry, but i’m unable to understand how will it be inclined and in what direction do we have to assume its inclined? could you explain?

10

yeah, i found this contradiction right now too. if insect starts from the left side, then it should rotate plank clockwise in any case. lemme think

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11

yeah, i have tried using this approach before, no luck that is why asked solution here.

12

i mean I tried equating torques = 0 and but could get correct answer…

13

Isn’t the plank horizontal initially? So when it is released, it rotates anticlockwise, due to gravity, but bug rotates it clockwise

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14

i tried using, torques by two tension forces = torque by weight of insect (assuming axis thorugh mid point of plank)…

15

i figured it out guys, i understood…

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16

there will be Simple harmonic motion (small oscillations) with amplitude as half of planks length. The time will be pi/10 seconds.

17

that the plank is horizontal by the problem statement and change of angular momentum equals m\dot v \cdot OM?

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18

i did not think this way, i just equated torque by friction and normal force on plank

19

I think it is more convenient to use axis through O because in this case the only non-zero torque is by weight of the bug

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I think the next ideas are correct, but I am not quite sure. So in order to plank not to rotate there shoud be another force that produces torque \tau = mgx. If the bug moves with some acceleration, then it is pushed by plank, and bug itself pushes the plank (we can apply Newton’s thrid law here because plank does not rotate)[1].

  1. the last part of the solution is left to the reader as an assignment :upside_down_face: ↩︎

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20

you wont believe it, but i did the same as yours, i even assumed x as the distance… we think alike :sweat_smile:

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