Q1.A string of bob is attached to a block kept on frictionless surface (bob is hanging ) an impulse is imparted to bob to give it velocity v0 describe motion of block.
33Notice One interesting thing.......
If a force of any magnitude is applied to a disk at R/2 above COM it will do pure rolling on stationary surface without help of friction or other force, as that F is itself capable of providing acc and ang acc, a=αR
for any body(hoolow or solid sphere or disk) (on a stationary surface) if Force F is applied at a distance x above COM such that x=Ic/mR then it will do pure rolling without any frictional help.....
33assuming both masses to be same.
Let ad (+x direction)be acc of COM of disk and α(In clockwise sense) be its angular acc and ap be acc of plznk(+x direction). For pure rolling......
Acc of point of contact=ad - αR.
Acc of point of contact of plank=ap
ad - αR=ap
Now ad=(F2+F3)/m
ap=F1/m
From COM of disk. MR2/2.α=F3R/2
α=F3/mR
ad - αR=ap
(F2+F3)/m - (F3/mR)*R = F1/m
=> F1=F2
and it doesnot depend on F3
62"Sky said"
F1 HAS NO EFFECT ON DISC.
F2 N F3 PRODUCED ACC a2 N a3 (forward)...
from torque equation, F3.R/2=0.5mR^2.(a3/R) => a3=F3/m..
now,
at point of contact, a2+a3 - a3(due to rotation) = a1(due to acc of plank) (considering masses of both same=m)
so. a1=a2 => F1=F2
NOW EXPLAIN ME THE MISTAKE :(
1arrey so wat is the correct choice????????
this question is eating up my head!!!!
i have been thinking about it for the last two days....
Adding to Nishant's Post ...
Look, this is what will happen :-
at time t=0, both will be at rest.
after impulse is applied, the bob will get a horizontal velocity.
As soon as the bob is displaced from its position, the tension in the string will have a horizontal component also.
Now lets consider the forces at upper block:-
There is no horizontal force to balance the horizontal component of T, coz the surface is frictionless.
( Note: If friction was present, it could had balanced it )
So the Block will also start moving forward.
62no sky, i dont think that is the right choice...
there will be force on the bob in the downward direction... due to gravity.
This will have a horizontal component. This force will cause the bob to move backwards..
Once the bob is in the backward direction, it will cause a force on the mass in the backward direction due to tension. The block may start to move back..
1i think its (b).
the impulse will create tension in the string... which will have a horizontal component... n so the block will move forward without change of direction...
33Ok the options given were:
writing equations and describing its motion is not practical in tests.....
a) block will perform oscillatory motion
b) block will not change its direction of motion.
c) Kinetic energy of the system is conserved
d) none
62may not be..
But i have not tried to think either... ! :)
But it will be something more than an shm.. bcos the blcok is not fixed...
unless u write down some equations it will all be guesswork :) right?
1waaaaaaaat yaaar??? all contradictory answers!!
i am confused!!
maine to yahi sochi thi.... fir toh ans (b) hi hona chahiye... hai naa??
62no sky.. there is an impulse..
so u need to consider a lot of other things...
i will give u an example.. try giving a velocity to one end of a string with balls on both ends... will these balls just satrt to move ...
i think abhishek wants smoe more details :)
i mean think a bit more than u have...
1since there is no external force on the system, so total momentum should remain conserved..
so, the vel of the block should be v in the opp direction... n it should continue to move...as no friction....
1first will be at rest.
then it will move suddenly. on constant velocity.
what is answer?
33bada tention hai, maine to first sight insitinct se b mara tha exam me par ab bana ke dekhta hun aur raat tak soln batane ki koshish karunga....
62Arrey now i am getting the feeling ki B hi hona chahiye!
damn.. pata nahi i will have to look more into this as well!
contd ...
sorry for the delayed post [1]
As far as the answere is concerned ...
The answer will be (D)
Explanation:-
The Block will accelerate at first no doubt ...
but when the bob is returning back & crosses its mean position, the tention in the string will be more.(coz the block is still moving in forward direction)
This will cause the Block to retard to 0 velocity & then change its direction of motion.
Option A is wrong ... coz the block will not oscillate, as it will travel in forward direction for more time than in backward direction.
Option B is wrong ... as explained above
Option C is wrong ... coz the total energy PE + KE of the system will be constant.
Hence the correct option will be D
1then y a is wrong??
after changing direction,,, it can agn change direction...
if no, y not?
62no bcos the center of mass of the system will always have a forward velocity.
33i have got (b)
i got the following soln... considering masses of both to be same for easy calculation...
I doubt that.
Because the Block itself is accelaration.
So if you are considering from reference point of Block,
you need to add the Pseudo Force.
That I dont think you have taken that into account.
33My mistake............
but phir bhi jab bob return kar raha hai how velocity of block can change the direction then momentum of the system will be in -x direction but should be mv0 in +x as there is no net external horizontal force on the system
