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

A book of weight $20 \mathrm{N}$ is pressed between two hands and each hand exerts a force of $40 \mathrm{N}$. If the book just starts to slide down. Coefficient of friction is $\mu$. Find the value of $4\mu$.

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 book of weight $20 \mathrm{N}$ is pressed between two hands and each hand exerts a force of $40 \mathrm{N}$. If the book just starts to slide down, then the coefficient of friction is:

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 block is placed over a plank. The coefficient of friction between the block and the plank is $\mathrm{\mu }=0.2$. Initially both are at rest, suddenly the plank starts moving with an acceleration $a_0=4 \mathrm{m} {\mathrm{s}}^{-2}$. The displacement of the block in $1 \mathrm{s}$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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 :

The flying plane offering the least frictional force should be

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