Friction

Consider a car moving along a straight horizontal road with speed of $72 \mathrm{km} {\mathrm{hr}}^{-1}$  . If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is  (taking $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A heavy uniform chain lies on a horizontal tabletop. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is

A conveyor belt is moving at a constant speed of  $2 \text{m }{\text{s}}^{-1}$.  A box is gently dropped on it. The coefficient of friction between them is  $\mu =\mathrm{0.5.}$  The distance that the box will move relative to belt before coming to rest on it taking  $g=10\mathrm{m}{\mathrm{s}}^{-2}$, is

The coefficient of static friction, ${\mu }_s,$  between block $A$ of mass $2 \mathrm{kg}$ and the table as shown in the figure is $0.2$. The maximum mass value of block $B$ so that the two blocks do not move is (The string and the pulley are assumed to be smooth and massless $g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A block of mass $1 \mathrm{kg}$ is placed on a truck which accelerates with acceleration  $5 \mathrm{m} {\mathrm{s}}^{-2}$.  The coefficient of static friction between the block and truck is $\text{0.6}$. The frictional force acting on the block is

A block of mass $2 \mathrm{kg}$ rests on a rough inclined plane making an angle of $30º$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7.$ The frictional force on the block is

In the figure masses $m_1, m_2$ and $M$ are $20 \mathrm{kg}, 5 \mathrm{kg}$ and $50 \mathrm{kg}$ respectively. The coefficient of friction between $M$ and ground is zero. The coefficient of friction between $m_1$ and $M$ and that between $m_2$ and ground is $0.3.$ The pulleys and the strings are massless. The string is perfectly horizontal between $P_1$ and $m_1$ and also between $P_2$ and $m_2.$ The string is perfectly vertical between $P_1$ and $P_2.$ An external horizontal force $F$ is applied to the mass $M.$ Take $g=10 {\mathrm{ms}}^{-2}.$

(a) Draw a free-body diagram for mass $M,$ clearly showing all the forces.
(b) Let the magnitude of the force of friction between $m_1$ and $M$ be $f_1$ and that between $m_2$ and ground be $f_2.$ For a particular $F,$ it is found that $f_1=2f_2.$ Find $f_1$ and $f_2.$ Write equations of motion of all the masses. Find $F,$ tension in the string and acceleration of the masses.

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

A horizontal force of $10 \mathrm{N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is –

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 block of mass $1 \mathrm{kg}$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\mathrm{m}{\mathrm{s}}^{-2}$. Find the frictional force acting on the block.