Static 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 $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

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 $2 \mathrm{kg}$ 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

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by,

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.

A block $A$ with mass $100 \mathrm{kg}$ is resting on another block $B$ of mass $200 \mathrm{kg}.$ As shown in figure, a horizontal rope tied to a wall holds it. The coefficient of friction between $A$ and $B$ is $0.2$ while coefficient of friction between $B$ and the ground is $0.3.$The minimum required force $F$ to start moving $B$ will be

Consider the situation shown in the figure. The wall is smooth but the surfaces of blocks $\text{A}$ and $\text{B}$ in contact are rough. The friction on $\text{A}$ due to $\text{B}$ in equilibrium

Consider the system shown in the figure. The wall is smooth, but the surfaces of blocks $A$ and $B$ in contact are rough. The friction on $B$ due to $A$ in equilibrium is

In the given diagram, what is the minimum value of horizontal external force $F$ on block $A$ so that block $B$ slides on the ground?

A block of mass$m$ is at rest relative to a stationary wedge of mass $M$. The coefficient of friction between the block and the wedge is $\mathit{\text{μ}}$. The wedge is now pulled horizontally with an acceleration $a$, as shown in the figure. Then, the minimum magnitude of $a$ for the friction between the block and the wedge to be zero, is

The magnitude of frictional force acting between the block and the inclined plane, as shown in the figure, is (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

For a truck with $14$ tyres, only rear $8$ wheels are power driven and can produce acceleration. These $8$ wheels support half the entire load. If the coefficient of friction between road and each tyre is $0.6$, the maximum attainable acceleration by this truck would be (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius $R$. Coefficient of static friction between the sand layers is $\mu$. Maximum volume of the sand that can be piled up in the form of cone without slipping on the ground is

`An object of $6 \mathrm{kg}$ is in the state of limiting equilibrium on an inclined plane having angle of inclination $30°.$ Now if the angle of inclination is increased to $60°,$ then the extra force along the plane to be applied on the object, to keep it in equilibrium will be (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Find the minimum value of $\mathrm{m}$ so that the block $(10 \mathrm{kg})$ do not move :-

Find the acceleration of body $A \& B$ as shown in figure. If friction is present between $A \& B$ only and applied force $F$ is less than limiting friction.

For next three question please follow the same

An engineer is designing a conveyor system for loading lay bales into a wagon. Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 kg. The center of gravity of each bale is at its geometrical center. The coefficient of static friction between a bale and the conveyor belt is 0.60, and the belt moves with constant speed. The angle $\text{β}$ of the conveyor is slowly increased. At some critical angle a bale will tip (if it doesn't slip first), and at some different critical angle it will slip (if it doesn't tip first).

Find the second critical angle (in the same conditions) at which it slips.

If the coefficient of friction between A and B is $\mu$, the maximum acceleration of the wedge A for which В will remain at rest with respect to the wedge is

Three blocks are kept as shown in figure. Acceleration of $20 \mathrm{kg}$ block with respect to ground is