Doubt from relative motion



A similar question regarding the acceleration of insect is in quora:


Imagine we faviquicked the legs of that case velocity
Of insect=velocity of rod
Now after time t velocity of rod in free fall is=0+gt
Now if insect is allowed to move downward direction
Then velocity of insect in time t is u+gt
Then how u+gt be costant...IT IS MY OPINION NOT SOLUTION

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Ok but can this affect acceleration of rod?


Cause of accelaration is due to force of gravity
Now F=G(mass of rod+mass of insect)×(mass of earth)×1/(distance)square
In one sense i think the c.g of (rod+insect) change due to movement of insect in accelarating frame(the downward moving
rod) value of g may change in microscopic scale...

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In such a case, there will be an acceleration present in insect, as you incorporated the term gt?

@Ankith_2020 the acceleration should be g only, is the answer A?


Acceleration=g is present in option A . Answer is B i.e acceleration is more than g


If c.g changes then distance between earth and (rod+insect) system gracitational force change...result g changes...MY OPINION


That will be a very small change sir, and I don't feel there is such minuteness to be taken into account in this question.


Thank you sir scan and detect the right answer..


IMO acceleration of rod with respect to ground should always be g because external force acting on system is constant. There will be little variations because according to Newton law of motion all parts of system should have identical acceleration.

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What is IMO


In my opinion



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Is the rod frictionless?
If not, then B is correct.


There is nothing mentioned in question I think rod has friction as insect will not able to crawl on frictionless surface. Now I am getting the question , the force on rod is not only because of gravity but because of insect also . Correct me if I am wrong. And we can't take rod and insect both as a system because acceleration of both are different and one of restriction of taking two object as a system is both should have same acceleration.

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What you can say about the acceleration of the insect is only with respect to the ground frame here. Since there is no net force acting on the insect in the ground frame, other than friction and gravity, its acceleration remains zero, and so the friction precisely equals to m_{insect}g. If we then consider the rod, so there are two forces acting on it, the friction and the gravity and hence : F_{net}=m_{rod}g+m_{insect}g which makes sure that the acceleration of the rod is more than g.

Talking solely about the acceleration of insect with respect to the rod wouldn't make sense here as we don't know all the constraints, but yeah surely the rod and the insect won't have the same acceleration and hence we cannot take them as a system.

But @Ankith_2020 do you think having the same acceleration only makes the condition for not taking them as a system?

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For taking a system I think this is only restriction



Yes, so you mean that there should be no relative acceleration between the two, but there is one more requirement, which is the reference frame in which we are observing the phenomenon.

So here if you see in the question you asked, if suppose wrt the ground frame, we consider the insect and the rod as a single system, then the net force acting on the system is just gravity and hence the acceleration of the system is g only.

Now we have for any system : F_{ext}=\sum_i m_ia_i where the accelerations a_i are relative to the frame in which we are considering the system to exist.

So here, considering the ground frame, we have that : (m_{insect}+m_{rod})g=m_{rod}a_{rod}+m_{insect}a_{insect}. Now given that there is no acceleration of insect wrt the ground frame and hence we get that the acceleration of the rod wrt the ground frame is more than g.

Now, considering the two bodies as a system in the ground frame could occur because the net force acting between them due to their interactions was zero, if we considered them as a single entity wrt the ground frame. If, however we come to the frame of the rod, then we cannot do the same as there is the pseudo force acting on the insect due to the rod's acceleration and hence we cannot proceed the same way.

So, if you don't wanna take into account the friction and all, so I think the aforementioned solution is better. Do let me know if you have any further queries.

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@Churchil_2018 Thanks for clearance.

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