$A$ force $\vec{F} = \hat{i} + 4\hat{j} \text{ N}$ acts on the $1 \text{ kg}$ block shown in the figure. The coefficient of friction between the block and the surface is $\mu = 0.3$. The force of friction acting on the block is:

The coefficient of static friction between a wooden block of mass $0.5\, kg$ and a vertical rough wall is $0.2$. The magnitude of the horizontal force that should be applied on the block to keep it adhered to the wall will be $N$ $\left[ g = 10\, m/s^2 \right]$.

$A$ block of mass $1 \, kg$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.5$. The magnitude of the force acting upwards at an angle of $60^{\circ}$ from the horizontal that will just start the block moving is

Why is the coefficient of static friction considered a property of the surfaces in contact?

$A$ block of mass $M$ rests on a rough horizontal table. $A$ steadily increasing horizontal force is applied such that the block starts to slide on the table without toppling. The force is continued even after sliding has started. Assume the coefficients of static and kinetic friction between the table and the block to be equal. The correct representation of the variation of the frictional force $f$,exerted by the table on the block with time $t$ is given by

$A$ block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The minimum value of the coefficient of friction between the block and the surface for which the block will remain in equilibrium is