A block of mass `5 kg` rests on a rough horizontal surface. It is found that a force of `10 N` is required to make the block just move However , once the motion begains, a force of only `8 N` is enough to maintain the motion find the coefficient of kinetic and static friction between the block and the horizontal surface

Explanation

The maximum frictional force `f_(max)` acting on the block over the surface is given by
`f_(max) = mu N`

where `N = mg ` since block is in equilibrium.
`rArr mu = (f_(mazx))/(mg)= (5)/(2 xx 10) = 0.25`
Since the applied horizontal force is `F = 4 N rArr F lt f_(max)` we know that when `F lt f_(max)` the block does not slide. Hence friction force will be static nature.
`:.` The friction force on the block is `f = 4` Newton