A block of mass m slides down the plane inclined at an angle `60^@` with an acceleration g/2. Find the co-efficient of kinetic friction.

Explanation

Let the mass of the block be m. The forces on lthe block are ure.

a. mg downward by the earth (gravity),
N normal force by the incline and
c f up the plane friction by the incline.
Taking components paralel to the incline nd writing Newton's second law
`mg sin 30^0-f=mg/4`
or, `f=mg/4`
There is no accelertion perpenducular to the incline.
Hence,
`N=mg cos 30^0 =mg sqrt3/2`
As the block is slipping on the incline, friction is `f=mu_kN`.
So, `mu_k f/N=mg/(4mgsqrt3 /2)=1/(2sqrt3)`.