Friction

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 $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the acceleration of $A \& B$.

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,

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 horizontal turn table rotates with its axis at the uniform rate of 2 revolutions per second.Find the maximum distance from the axis at which a small body will remain stationary on the turn table .If the coefficient of static friction between the turn table and body is $0.8$.Assume $g={\mathrm{\pi }}^2 {\mathrm{ms}}^{-2}$

A horizontal force of  1 N is needed to keep a block of mass $0.25 kg$ sliding on the horizontal surface with a constant speed. Find the coefficient of sliding friction.$(g=10 m{s}^{-2})$

A uniform ladder which is$5m$ long has a mass of $25kg$ , leans with its upper end against a smooth vertical wall and its lower end on rough ground. The bottom of the ladder is $3m$ from the wall. Calculate the frictional force between the ladder and the ground . Use $g= 10 m{s}^{-2}$

A 40 kg slab rests on a frictionless floor.A 10 kg block rests on the top of the slab. The static coefficient of friction between the block and the slab is 0.60.,while kinetic friction is 0.40.The 10 kg block is acted upon by a force of $100N$.What is the resulting acceleration of the slab?

A block of mass $m$ is attached to a cart of mass $M$.The coefficient of friction between block and the cart is $\mu$.What is the minimum acceleration of the cart so that the block does not fall ?

A body of mass m is kept on an inclined plane. The force required to just move the body up the inclined plane is double the force required to prevent the body from sliding down the plane.If the coefficient of friction is $\mu$.What is the inclination of the plane?

Two blocks of masses $22kg$and $18 kg$ are connected by a massless rope.They are dragged by a horizontal force of $100 N$.The coefficient of friction between each block and the surface is $0.20$.What is the magnitude of acceleration of the system?

A block of mass $10 kg$  slides down an inclined plane of inclination ${30}^{\circ }$ with an acceleration of $\frac{g}{3}$.What is the coefficient of kinetic friction between the block and the plane.?

A roller of mass $500 kg$ is attached by a light horizontal chain to a tractor of mass $500 kg$. Assume the force of friction exerted by the ground to be $1000 N$ .If the system has a forward acceleration of $2m{s}^{-2}$.Calculate (i) the tension in the chain.

A roller of mass $500 kg$ is attached by a light horizontal chain to a tractor of mass $500 kg$. Assume the force of friction exerted by the ground to be $1000 N$ .If the system has a forward acceleration of $2m{s}^{-2}$.Calculate (i) the total force required for motion.

A train of mass 400 tons climbs up an incline of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$49$}\right.$ at the rate of $36 km{h}^{-1}$.The force of friction is $4kg at per ton$. Find the powerof engine.

A body of mass $2kg$ collides with a horizontal weight spring of force constant $4N{m}^{-1}$. The body compresses the spring by $1m$ from rest position. Find the speed of the block at the instant of collision? Given that the coefficient of kinetic friction between the body and the surface is $0.1$.

A mass of 2 kg rests on a horizontal plane. The plane is gradually inclined until at an angle with the horizontal, the mass just begins to slide.What is the coefficient of static friction between the block and the surface?

A body of mass $20 kg$ is resting on a table.  A light string is attached to it and passed over a smooth pulley at the edge of the table and a mass $3 kg$ is attached at the free end.  What is the acceleration of the system of the coefficient of kinetic friction between the mass and the table is $0.04$ ?  What is the tension in the string? 

A block of mass $15 \mathrm{kg}$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5 \mathrm{m} {\mathrm{s}}^{-2}$ for $20 \mathrm{s}$ and then moves with uniform velocity. Discuss the motion of the block as viewed by an observer is moving with the trolley.