Question

a wooden block of mass 20kg slides without acceleration down a rough inclined plane which makes an angle of 20° with the horizontal. find the acceleration of the block when the inclination of a plane is increased to 30°

Answer 1

any query related to it ask in comment section.

at last it should be
1-tan20°√3=2a

Answer 2

where fg=m.afgma is the force due to gravity. Now as θ increases fg_inclfg_incl increases where fg_inclfg_incl is the component of force along the inclined plane and it is given by

fg_incl=fg∗sinθfg_inclfgsin

Now for θ=60∘60

fg_incl=fg∗sin60∘=0.866∗fgfg_inclfgsin600.866fg

Since the box only starts sliding at 60∘60, the static frictional force is 0.866∗fg0.866fg

The coefficient of friction is greater than 11 when force is less than 0.866∗fg0.866fg and as force exceeds that value past 60∘60, the coefficient drops to less than one and comes to a fixed value (like 0.75) as velocity builds up.