Minimum Force on block for its non slipping against Friction on vertical wall and between two hands

To keep a block pressed against vertical wall or between two hands with out slipping, we need to apply some force and we need to under stand the role played by the frictional force. Let us imagine a block of mass on a vertical rough wall with coefficient of friction.The weight of the block always acts in the downward direction. Because of the weight, body tend to slip in the downward direction along the vertical surface and we want to arrest it.

Let us apply a horizontal force on the face of the block.This force is applied by you on the block. In tern, the block applies the same force on the vertical surface of the wall and it acts like action.The wall applies the reaction on the block in opposite direction.This is normal to the surface of the contact. Thus frictional force and normal reaction or perpendicular to each other.

As the body slides down in the downward direction due to its weight, the frictional force acts in the upward direction.For the equilibrium, we frictional force shall be balanced by the weight of the body. Here frictional force is product of coefficient of friction and normal reaction. Normal reaction in this case is nothing but the applied force in terms of magnitude.

By equating them, we can get the value of minimum force required to keep the block in the state of rest against the vertical wall.

We can also discuss the same case when the block is not pressed against the wall and it is pressed in between two hands.The only difference in this case is that the normal reaction is the sum of this two forces applied by the two hands.

We can calculate the minimum force required even in this case also as shown below and it is only half of the previous case.