Friction Questions

There are two inclined surfaces of equal length ($L$) and same angle of inclination $45^{\circ }$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (${\mu }_k$) between the object and the rough surface is close to:

A uniform rod of mass $20\text{kg}$ and length $5\text{m}$ leans against a smooth vertical wall making an angle of $60^{\circ }$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10{\text{m/s}}^2$):

Assertion: Frictional forces are conservative forces.Reason: Potential energy can be associated with frictional forces.

A block $B$ is pushed momentarily along a horizontal surface with an initial velocity $v$. If $\mu$ is the coefficient of sliding friction between $B$ and the surface, block $B$ will come to rest after a time:

A body of mass $1\text{kg}$ is thrown upwards with a velocity $20\text{m/s}$. It momentarily comes to rest after attaining a height of $18\text{m}$. How much energy is lost due to air friction? ($g=10{\text{m/s}}^2$)

A block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies:

A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if:

A belt moves at $2\text{m/s}$. A box is dropped on it ($\mu =0.5$). Distance the box moves relative to belt before coming to rest on it is:

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by:

A system consists of three masses $m_1,m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is: (Assume $m_1=m_2=m_3=m$)

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^{\circ }$, the box starts to slip and slides $4.0\text{m}$ down the plank in $4.0\text{s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively: