- #1

cooldudeachyut

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## Homework Statement

Two block M

_{1}and M

_{2}rest upon each other on an inclined plane. Coefficient of friction between surfaces are shown. If the angle θ is slowly increased, and M

_{1}<M

_{2}then

Options :

1- Block A slips first.

2- Block B slips first.

3- Both slip simultaneously.

4- Both remain at rest.

## Homework Equations

Taking frictional force between the two blocks as f

_{1}and between the block B and inclined plane as f

_{2}, the equations for limiting values f

_{1max}and f

_{2max}:

f

_{1max}= μ

_{2}M

_{1}gcosθ

f

_{2max}= μ

_{2}(M

_{2}+M

_{1})gcosθ

## The Attempt at a Solution

For Block A :

I only considered the case where f

_{1}reaches its limiting value, hence I get this inequality as the condition when block A may start slipping,

M

_{1}gsinθ - μ

_{2}M

_{1}gcosθ ≥ 0

Which is equivalent to,

tanθ ≥ μ

_{2}

For Block B :

Again, I only considered the case where f

_{2}reaches its limiting value but cannot figure out what's the magnitude/direction of f

_{1}on this block. So I assumed f

_{1max}to act on this block in the direction up the slope as this basically provides least resistance and also complies with block A's case which may as well be the "limiting factor" for the case where block B slips, giving my inequality as,

M

_{2}gsinθ - μ

_{2}(M

_{2}+M

_{1})gcosθ + μ

_{2}M

_{1}gcosθ ≥ 0

Which is again equivalent to,

tanθ ≥ μ

_{2}

I'm confused how to proceed now as I think both blocks should start slipping simultaneously however the answer provided is option 2, i.e., block B will slip first.