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Cool goIITian

Joined:	9 Oct 2007
Post:	73

21 Oct 2007 11:47:54 IST

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help me hc verma 31 sum friction

None

a small mass m kept at the left end of a larger block of mass M and length L .the system can slide on a horizontal road ,The system is started twards right with initial velocity v.The frriction coefficient between the road the bigger block is and betwween the blocks is/2 Find the time elapsed before the sammler block seperates from the biggerblock...GIVE THE FULL SOLUTION

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waterdemon

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Joined: 11 Jun 2007

Posts: 1048

21 Oct 2007 14:37:50 IST

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Here is the solution :

Given the diagram-

There will be relative motion between the block and plank
and plank and road.So at each surface limiting friction will act.

The direction of friction forces at different surfaces are as given by me in Diagram.

f₁ = umg/2

f₂ = u(m+M)g

Retardation of The block of mass "m" :

a₁ = f₁/m = ug/2

Retardation of The block of mass "M" :

a₂ = f₂-f₁/M = ug(m+2M)/2M

Since ,

a₂ > a₁

Therefore Realtive acceleration of "m" wrt "M" is:

a_r = a₂ - a₁

a_r = ug(m+M)/2M

Initial Velocity of both "m" and "M" os "v".So there is no
relative initial velocity.So,

Applying S = (1/2)at²

As per above sum it becomes:

L = (1/2)a_rt²

L = (1/2)[ug(m+M)/2M]t²

From solving above we get :

t² = 4ML/ug(m+M)

So Time elapsed before the plank seperates from the

block :

T =

4ML/ug(m+M)

Hope you find it useful.

plZ do rate me if useful.

Cheers!!!!!!!!!!!@@@!!!!!!!!!!

waterdemon

Forum Expert

Joined: 11 Jun 2007

Posts: 1048

21 Oct 2007 14:54:05 IST

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Hey Vichu I have answered it now you can look at the solution
I rechecked it twice so ............took some time for check.

Cheers!!!!!!!!!@@!!!!!!!!!!

viswesh Nrayanan

Cool goIITian

Joined: 9 Oct 2007

Posts: 73

21 Oct 2007 15:37:04 IST

Like 0 people liked this

COOL MAN!!!!!!!!!

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