A block of mass 2.5 Kg is kept on a rough horizontal surface. It is found that the block does not slide if a horizontal force less than 15 N is applied to it. Also it is found that it takes 5 seconds to slide through the first 10 m if a horizontal force of 15 N is applied and the block is gently pushed to start the motion. Taking `g=10 m/s^2`, calculate the coefficient of static and kinetic friction between the block and the surface.

Answer

`0.6 ; 0.52` .

Explanation

Here, `m = 2.5 kg, F = 15 N`
`mu_(s) 0= (F)/(R) = (F)/(mg) = (15)/(2 .5 xx10) =0.6`
From `s =ut + (1)/(2)at^(2)`
`10 = 0 + (1)/(2) xx a(5)^(2),a = (20)/(25) = 0.8ms^(2)`
Using Newton s 2nd law `F - mu_(k) mg = m a`
`mu_(k) = (F -ma)/(mg) = (15 - 2.5 xx 0.8)/(2.5 xx10) =(13)/(25) = 0.52` .