IIT JEE , AIEEE Forum - Physics , Mechanics - Challenge- A multimechanical question

tarinbansal

I am posting a new type of ques here and its a multimechanical ques as it contains all the concepts of mechs viz, Kinematics,NLM,momentum,Collision,rotation.

In the figure, the 2 balls are are rolling without slipping. They undergo a perfectly inelastic collision at t=0. Find the time t taken by the total mass to stop after collision.

Given-Coefficient of friction=

.

Find the answer in terms of the given variable viz, M1,M2,R1,R2,V1,V2,

.

Yeh ques kar liya, samjho mechanics finish.

blackjack

nice ques dude.............

Ksudha_iit

first conserve momentum...find the velocity and then conserve angular momentum ....before they start pure rolling and friction will help it ...for starting pure rolling ...and in that time factor can b ecalculated ...by integrating it :)

its kinda lengthy question involiving all concepts....i shall giv eit a try...just post the answer just check it out ...if mine doesnt match thn i shall approach u again ..

Werewolf

Tarin, can u post your solution because any solution you post I can definately find some fault in it , since your question carries a lot of bugs.

Werewolf

Bug 1 : Is there friction between the two spheres ?

Bug 2 : What is the relation between M1 M2 (M1>M2 or M1<M2)and R1 R2(R1>R2 or R1<R2) ....its needed so that we can find which mass will stop first as these factors decide their angular accelerations.

Bug 3 : Atleast post the answer if not the solution.

Bug 4 : its high time now , and u should consider posting solution also.

Werewolf

we can solve this problem easily if its given that their angular accelerations are also equal....if their angular acc are different they will need different times to stop and in that case both spheres will stop at different times and not simultaneously....i bet u must be thinking that they will stop at same time otherwise problem is easy .....they will stop at same time when their ang acc are also equal like their linear acc

anchitsaini

i think tarin has made up this question on his own !!!!

tarinbansal

Bhai,
They are undergoing perfectly inelastic collision.
And as they are in same line, the whole mass wud not be able to roll now and it wud slide on the ground like a simple body given a velocity on a surface with friction. And will ultimately stop after some time. U just need to find that time to stop.

Werewolf

EXPLAIN :And as they are in same line, the whole mass wud not be able to roll now

everyone knows that the spheres will still have their own independent rotational motion.

tarinbansal

Bhai,

After a perfectly inelastic collision, the 2 bodies stick together.

Just look at the figure-

after collision, the total mass will move together. Now I dont think it will roll.

If U still think it will roll, then take the condition that it is not rolling, it is sliding now.

But I am quite sure that such a mass cant roll now.

Werewolf

What do u mean they stick together , they don't stick together , in technical terms they after the collision tend to have same velocity direction and magnitude....its that in general talk we say that they stick togather ...they dont get stick togather with a glue yaar so that they cant even rotate

tarinbansal

Buddy, maine ab tak jitne ques solve kiya hain and jahan bhi padha hai, I hav always seen and used that after PERFECTLY INELASTIC collision, the 2 bodies move as a single body with same velocity.

And I introduced this in this ques with this approach only.

Werewolf

u r talking of linear collisions only where the acc of the two bodies after the collision are equal so there is no problem .....but here it is rotational collision where angular acc also cums into play and if that different for the two bodies they will need different times to stop separately

Werewolf

tarin bro , pls provide answer to this question.

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