Dynamic Friction

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

A block of mass $0.1 \mathrm{kg}$ is held against a wall by applying a horizontal force of $5 \mathrm{N}$ on the block. If the coefficient of friction between the block and the wall is $0.5,$ the magnitude of the frictional force acting on the block is (take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

Two block $A$ and $B$ of equal masses are placed on a rough inclined plane as shown in figure. When (and where) will the two blocks come on the same line on the inclined plane if they are released simultaneously? Initially the block $A$ is $\sqrt{2}m$ behind the block $B$. Co-efficient of kinetic friction for the blocks $A$ and $B$ are $0.2$ and $0.3$ respectively $\left(g=10m{s}^{-2}\right)$

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.

Masses  $M_1,M_2\mathrm{and}{M}_3$ are connected by strings of negligible mass which pass over massless and frictionless pulleys  $P_1\mathrm{and}{P}_2$  as shown in the figure. The masses move such that the portion of the string between  $P_1\mathrm{and}{P}_2$ is parallel to the inclined plane and portion of the string between  $P_2\mathrm{and}{M}_3$ is horizontal. The masses  $M_2\mathrm{and}{M}_3$  are $4 \mathrm{kg}$ each and coefficient of kinetic friction between the masses and the surfaces is 0.25. The inclined plane makes an angle of  $37°$  with the horizontal. If the mass  $M_1$  moves downwards with a uniform velocity, find the tension in the horizontal portion of the string.  $\left(g=9.8 m s^{-2}, \sin 37°=\frac{3}{5}\right)$

In the diagram shown, the blocks$\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}$ weight, $3 \mathrm{kg}, 4 \mathrm{kg} \mathrm{and} 5 \mathrm{kg}$ respectively. The coefficient of sliding friction between any two surface is $0.25$. A is held at rest by a massless rigid rod fixed to the wall while $\mathrm{B}$ and $\mathrm{C}$ are connected by a light flexible cord passing around a frictionless pulley. Find the force $F$ necessary to drag $\mathrm{C}$ along the horizontal surface to the left at constant speed. Assume that the arrangement shown in the diagram, $\mathrm{B} \mathrm{on} \mathrm{C} \mathrm{and} \mathrm{A} \mathrm{on} \mathrm{B}$, is maintained all through.  $(g=9.8\mathrm{m}{\mathrm{s}}^{-2})$

A skater weighing $70 \mathrm{kg}$ throws a stone of mass $3 \mathrm{kg}$ with a velocity of $8 \mathrm{m}/\mathrm{s}$ standing on ice. Coefficient of kinetic friction is $0.02$. The distance through which he moves back is:

Consider a car moving on a straight road with a speed of $100 \mathrm{m} {\mathrm{s}}^{-1}.$ The distance at which car can be stopped is $[{\mu }_{\mathrm{k}}=0.5$]

Two cars of unequal masses, use similar tyres. If they are moving at the same initial speed, the minimum stopping distance

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 block of mass$M=5 \mathrm{kg}$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When the force $F=40 \mathrm{N}$ is applied, the acceleration of the block will be

A $60 \mathrm{kg}$ body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are $0.5$ and $0.4$, respectively. The acceleration of the body is

For two given surfaces, the value of the coefficient of friction is the highest for:

A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, then

Minimum force to keep a body stationary on a vertical wall.

(i) A body of mass $m$ is kept on a vertical wall as shown in figure the maximum value of $F$ to keep the body stationary on vertical 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
$(\mathrm{T}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{ }\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$

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