Question

For the arrangement shown in Fig. find the minimum and maximum value of the horizontal acceleration a of the system so that the block does not slide on the wedge.

Answer 1

If we define our coordinate system so that the y-direction is up and x-direction is down, then we have

y-direction: $Nsin\theta +fsin\theta -mg=0$

x-direction:$Nsin\theta -fcos\theta =ma$

then

$Ncos\theta +fsin\theta =mg$

Since $tan\theta >\mu$

we know that $f=\mu N$

Then

$N(cos\theta +\mu sin\theta )=mg$

$N(sin\theta -\mu cos\theta )=ma$

$a=\frac{g(sin\theta -\mu cos\theta )}{cos\theta +\mu sin\theta }$