Friction

The upper half of an inclined plane with inclination $\mathrm{\varphi }$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is

Find the value of pushing force $P$ just to move the block. If the coefficient of friction between block and floor is given as $\mu =0.6$ 

Blocks $A$ and $B$ shown in the figure are connected with a bar of negligible weight. $A$ and $B$ each has mass $170 \mathrm{kg}$, the coefficient of friction between $A$ and the plane is $0.2$ and that between $B$ and the plane is$0.4$. What is the total force of friction between the blocks and the plane $\left(g=10\mathrm{ }\mathrm{m}{\mathrm{s}}^{-2}\right)$

What does the slope of the graph of friction force versus normal force represent?

The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$ ) inclined plane is $F_1$ while the minimum force needed to prevent it from sliding down, is $F_2.$ If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta =2\mu$, then the ratio $\frac{F_1}{F_2}$ is

In figure, the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and of $B$ is$m$. What is the maximum horizontal force $F$ can be applied to the block $B$ so that two blocks move together?

A block of mass $10 \mathrm{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5.$ If a horizontal force of $100\mathrm{ }\mathrm{N}$ is applied on it, then acceleration of the block will be
$(\mathrm{T}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{ }\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$

A massive platform of mass $M$ is moving with speed $v=6 \mathrm{m} {\mathrm{s}}^{-1}.$ At $t=0,$ a body of mass $m\left(m<<M\right)$ is gently placed on the platform. If coefficient of friction between the body and platform is $\mu =0.3$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}.$ Then, the distance covered by body is $\dots \dots \mathrm{m}.$

Two blocks $\mathrm{A}$ and $\mathrm{B}$ of equal masses are released from an inclined plane of inclination $45°$ at $t=0$. Both the blocks are initially at rest. The coefficient of kinetic friction between the block $\mathrm{A}$ and the inclined plane is $0.2$ while it is $0.3$ for block $\mathrm{B}$. Initially the block $\mathrm{A}$ is $\sqrt{2} \mathrm{m}$ behind the block $\mathrm{B}$. At what time in seconds will their front faces come in a line, (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Can the coefficient of friction be more than one?

A solid hemisphere rests in equilibrium on a rough ground and against a smooth wall. The curved surface touches the wall and the ground. The angle of inclination of the circular base to the horizontal is ${30}^{\circ }$ , The minimum coefficient of friction required between ground and hemisphere is $\mu$. What is the value of $32\mu$?

Two blocks $A$ and $B$ are as shown in figure. The minimum horizontal force $F$ applied to the block $B$ for which slipping just begins between $B$ and ground is :

A box is kept on an inclined plane making an angle $\theta$ from the horizontal and coefficient of friction $\mu$. If $F_1$ is the minimum force required to start pushing it above the plane and $F_2$ to prevent it from sliding. Find the ratio $\frac{F_1}{F_2}$ if $\mathrm{tan\theta }=2\mu$.

A motor cyclist rides around the well with a round vertical wall and does not fall down while riding because

In figure, the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and of $B$ is$m$. What is the maximum horizontal force $F$ can be applied to the block $B$ so that two blocks move together?

A block of mass $M$ is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu$ and the acceleration due to gravity is $g$, the minimum force required to be applied by the finger to hold the block against the wall is:

A block of mass $10 \mathrm{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5.$ If a horizontal force of $100\mathrm{ }\mathrm{N}$ is applied on it, then acceleration of the block will be
$(\mathrm{T}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{ }\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$

When a body slides down from rest along a smooth inclined plane making an angle of ${30}^{\mathrm{o}}$ with the horizontal. It takes time $20 \mathrm{s}$ . When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it takes times $20 p\mathrm{s}$ , where $p$ is some number greater than $1$. The coefficient of friction between the body and the rough plane is

A block of mass $m$ rests on a rough inclined plane. The coefficient of friction between the surface and the block is $\mathrm{\mu }$. At what angle of inclination $\mathrm{\theta }$ of the plane to the horizontal will the block just start to slide down the plane?