A block of mass 10 kg 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)).

A block of mass 10 kg pushed by a force F on a horizontal rough plane

1.	A block of mass 10 kg 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)).
Answer» Solution :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 = 5 `ms^(-2)` `5=(F)/(10)-mu_(k)(10) ""` ……..(II) `(because m = 10 kg)` When force is doubled i.e., P = 2 F , 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`