Static and Dynamic Friction

Consider on a rough horizontal surface a block is kept. A horizontal force just strong enough to move the block is acting on it, the force is maintained for $2$ seconds and then removed. The total distance moved by the box is '$S$' meters. What is the value of '$6S$'?$\left({\mu }_s=0.2, {\mu }_k=0.15, g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A plank is rotating in a vertical plane about one of its fixed end $\mathrm{A}$ with a constant angular velocity $\omega =\sqrt{2} \mathrm{rad} {\mathrm{s}}^{-1}.$ A block of mass $\mathrm{m}=2 \mathrm{kg}$ is placed at a distance $l=1 \mathrm{m}$ from end $\mathrm{A}$ (see figure) which is hinged. The block starts sliding down when the plank makes an angle $\theta =30°$ with the horizontal. If coefficient of friction between the plank and the block is $\mu$ and given that ${\mu }^2=\frac{k}{25}$. Find the value of $k$.

If $100 \mathrm{N}$ force is applied on the block. Then, frictional force acting on the block will be (in Newton),

A block $A (5 \mathrm{kg})$ rests over another block $B\mathit{ }(3 \mathrm{kg})$ placed over a smooth horizontal surface. There is friction between $A$ and $B$. A horizontal force $F_1$, gradually increasing from zero to a maximum, is applied to $A$, so that the blocks move together without relative motion. Instead of this, another horizontal force $F_2$, gradually increasing from zero to a maximum, is applied to $B$, so that the blocks move together without relative motion. Then,

${\mathrm{M}}_{\mathrm{A}}=3 \mathrm{kg}, {\mathrm{M}}_{\mathrm{B}}=4 \mathrm{kg}$ and ${\mathrm{M}}_{\mathrm{C}}=8 \mathrm{kg}$. The coefficient of friction between any two surface is $0.25$. The pulley is frictionless and the string is massless. $A$ is connected to a wall by a massless rigid rod. 

A person holding a bag starts sliding freely from a point A on a frictionless inclined plane while his bag starts falling down vertically from the same point. The final speeds of the man $\left(V_M\right)$ and the bag $\left(V_B\right)$ on reaching the ground after falling through the same height should be such that

If a body of mass $m$ is moving on a rough horizontal surface of coefficient of kinetic friction $\mu$, the net electromagnetic force exerted by the surface on the body is

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move?

A block of mass $m$ is kept on an inclined plane of a lift moving down with an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$. What should be the coefficient of friction for the block to move down with constant velocity relative to lift? The angle of inclination of the wedge is $30°$. $g=10 \mathrm{m} {\mathrm{s}}^{-2}$

A block $A$ of mass $m$ is placed over a plank $B$ of mass $2m$. Plank $B$ is placed over a smooth horizontal surface. The coefficient of friction between $A$ and $B$ is $\frac{1}{2}$. Block $A$ is given a velocity $v_0$ towards the right. Acceleration of $B$ relative to $A$ is