(a) Find the acceleration of the two block shown in figuer (b) Find the friction force between alll contant surface

Explanation

Let as first calculate the limiting and kinetic friction between varius surface between `3 kg` and ground

`f_(t_(1)) = f_(k_(1)) = mu_(1) (2 + 3) g = 0.1 xx 5 kg = 5 N`
Between `2 kg` and `3 kg`
` f_(t_(2)) = f_(k_(2)) = mu_(2)2g = 0.2 xx 2 kg = 4 N`
Let us first assume that both block move together with common acceleratia a.
`a = (5 + 10 - f_(k_(1)))/(2 + 3) rArr a = (15 - 5)/(5) = 2ms^(-2)`
Now let us see how much friction is required between 2 and `3 kg` for common acceleration a
`5 - f_(2) = 2a rArr 5 - f_(2) = 2 xx 2 rArr f_(2) = 1 N`
Since `f_(2) lt f_(t_(2))`

1. Both blocks will move together with common acceleration `a = 2 ms^(-2)`
Friction between `2 kg` and `3 kg = f_(2) = 1 N` friction between `3 kg` and ground `= f_(k_(1) = 5 N`