A block of mass 10kg pushed by a force F on a horizontal rough plane moves with an acceleration of `5ms^(-2)`. When force is doubled, its acceleration becomes `18 ms^(-2)` Find the coefficient of friction between the block and rough horizontal plane. `(g = 10 ms^(-2))`.

Explanation

On a rough horizontal plane, acceleration of a block of mass .m. is given by `a=P/m - mu_(k) g`……. (i)
Initially, P=F, `a= 5ms^(-2)`
`5=F/10 - mu_(g) (10)`……..(ii) `(therefore m=10 kg)`
When force is doubled i.e., `P = 2F, a = 18 ms^(-2)`
`18 = (2F)/10 - mu_(K)(10)`......(iii)
Multiplying Eq (ii) with 2 and subtracting from Eq. (iii)
`8 = mu_(k) (10) rArr mu_(k) = 8/10 = 0.8`