a block of mass 2 kg is pushed against a rough vertical wall with a force of 40N,coeff of static friction=0.5..another horizontal force of 15N,is applied on block in a direction parellel to wall.will the block move?if yes, in which direction?if no,find frictional force exerted by wall on block.

Dear Tushar

max static friction force that can be exerted by wall on block is =0.5*40 =20 N

since applied horizontal force 15 N is less than max static force so block will not move

so friction force exerted by wall on block is =15 N

Sir,

     There are 2 forces parallel to wall,one vertical due to gravitation(20 N) and another horizontal force of 15 N.Now friction will oppose both of them so we shoudnt ignore gravitation force in calculation of friction.Force due to gravitation was there before exerting horizontal force of 15 N so friction in vertical direction is 20 N.Now as we apply horizontal force of 15 N there will be no friction opposing it so block will move in that direction.This is one fo my approach.

Another one(it may be vague) is that we can distribute max. friction in both directions proportion to the forces exerted in those directions.But i am nt sure abt this method.

plz clarify my doubts. 

Sir,

If we assume that block is at a height from the ground then we should include gravitation force also  in calculation of friction.There are 2 forces in perpendicular direction.One weight of 20 N and another horizontal force of 15 N.Before exertion of 15 N force weight waas there so friction of 20 N will be there to balance the weight.Now as we apply horizontal force of 15 N there will be no friction to balance as it max friction itself is 20 N which is balancing the weight.So block will move in the direction of horizontal  force with acceleration of 7.5 m/sec^2.

plz clear my doubts.