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Discussion Response Post to: help me hc verma 31 sum friction

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waterdemon (3810)

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total posts: 1048
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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!!!!!!!!!!!@@@!!!!!!!!!!

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