the coefficient of friction between a block of weight 15N and a horizontal board on which it is resting is 3.0find the horizontal force which will just remove the block and the force acting at an angle of 30 with the horizontal which will just move the block.

Answer 1

In the first case, the horizontal force needed to move the block is the (static) friction coefficient multiplied by the weight. That would be 45.0 N.

In the second case, the required friction force F is given by the formula
(Weight - Fsin30)*mu = F cos30
F[sin30*mu + cos30]= 15*mu
F = 15*mu/[1.5 + 0.866] = 19.0 N