IIT JEE , AIEEE Forum - Physics , Mechanics

lokeshsardana

sumbody reply ..............................i m waiting.............

where r all masterminds of this site???????

rooney

Take a chill pill man. Relax. Someone will surely give a reply. I will read your doubt now.

rooney

http://www.goiit.com/posts/list/30/mechanics-challenge-3-32895.htm

Check the question. and here is a great soln given by freneid's prof.

Let us consider that F2>F1.now let m1 be displaced to the ryt by x1 and m2 to the ryt by x2.therefore net displacement of m1 wrt m2=x1-x2.this is also the elongation of the spring.so we get the concept that the relative disp. of the 2 blocks is the elongation of the spring.let us denote it by Srel.then dSrel/dt=Vrel of the two blocks.in position of max.elongation the Vrel=0.now consider the fbds of the 2 blocks.
T-F1=m1a1.
F2-T=m2a2.
solving a1 and a2 we get a1=T-F1/m1
a2=F2-T/m2
therefore rel accn.=a2-a1.
now write above accn.=VdVrel/dSrel and put T=kSrel....integrate with limtis Srel=0, Vrel=0 and Srel=x,Vrel=0 where x is max elongation.

lokeshsardana

@rooney,
pls find the final answer which is accelerations of the blocks of my question asked in starting of forum..........in which only single force is acting................

although ur question is slightly diff. from mine but well done dude from this an elementary idea has been generated..................

tarinbansal

Yes both the accelerations will be same.
You can even understand it logically.
At max extension both the blocks should have same velocity becoz if thier velocities are different then one of the block will have some velocity w.r.t the other and hence the condition of max extension will not hold good.
Now when we have decided that they should have same velocities, its obvious that their individual acceleration should be same, Becoz all motion,veloctiy and acc are in same direction and any difference in acc between the 2 blocks will change their velocities.

Hope you understood. If not nudge me.

lokeshsardana

@tarin

sorry dude............you are wrong.............

accelerations of both will be different................

tarinbansal

What????????
But why?

rooney

coz Force on 1 mass is F - kx and on the other is only kx.

tarinbansal

But have you read my explanation?
I mean if their acc are diff, then their velocities will be different and for max elongation, velocities must be equal.

rooney

Acceleration can be different even if velocities are same.

tarinbansal

Arre yaar,
When the direction of motion,velocties and acc is same.
Then won't diff acc change the magnitude of velocities?

waterdemon

Sorry for the delay ..saw this query now.

If you want to do it by method of getting the acceleration
of both the blocks and then doing it rather than foll. the
process of taking the system as a whole then try the foll.
methods that are mentioned below:

First derive the equations as follows:

If the block on RHS moves by x₂ then lets say block on
LHS will move by x₁ distance.
So the force on either bolcks will not be equal.

F₁ - Kx = m₁a ....(1)

Kx - F₂ = m₂a ....(2)

x₂ - x₁ = L + x
where x is the elongation in the spring
where L is the Original length.

a₂ - a₁ = a .........(3)
Here a is the acceleration when there is maximum elongation

Now follow the steps as metioned:
1)Reduce the differential eqn. which will have a dependent
variable as elongation of spring that is "x".

Also this should be known:
1)When the spring has maximum elongation both blocks will
have same velocity.
2)Separation Speed will be "zero"/
3)Rate of change of elongation with respect to time will be
equal to "zero".

dx/dt = 0

Hope it is useful.
Cheers!!!@@@!!!

tarinbansal

So waterdemon, Was I correct?
I also said the same thing that their relative velocity should be zero.
SO they should have same accelerations.

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