Friction on an Incline

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is ______.

(g = gravitational acceleration)

A block of mass 5 kg is moving on an inclined plane which makes an angle of $30^\circ$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{\sqrt{3}}{2}$. The force to be applied on the block so that the block will move down without acceleration is ______ N. $(g = 10\text{ m/s}^{2}).$

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^\circ$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ______

A block takes $t$ time to slide down a plane inclined at $45^\circ$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$. The value of $\alpha$ is ______.

A cubic block of mass $m$ is sliding down on an inclined plane at $60^\circ$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

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 $2\text{ kg}$ brick begins to slide over a surface which is inclined at an angle of $45^\circ$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

A block of mass $m$ is placed on a surface having vertical cross-section given by $y = x^2/4$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

A block of mass $5\text{ kg}$ is placed on a rough inclined surface as shown in the figure. If $\vec{F_1}$ is the force required to just move the block up the inclined plane and $\vec{F_2}$ is the force required to just prevent the block from sliding down, then the value of is: [Use $g = 10\text{ m/s}^{2}]$

A given object takes $n$ times the time to slide down $45^\circ$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $45^\circ$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is:

In the given arrangement of a doubly inclined plane two blocks of masses $M$ and $m$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $m$, for which $M = 10\text{ kg}$ will move down with an acceleration of $2\text{ m/s}^{2}$, is: (take $g = 10\text{ m/s}^{2}$ and $\tan 37^\circ = 3/4)$

A block of mass 2 kg is placed on inclined rough surface AC (as shown in figure) of coefficient of friction $\mu$. If g = 10 m s${}^{-2}$, the net force (in N) on the block will be:

A block of mass $m$ slides down the plane inclined at angle $30^\circ$ with an acceleration $\frac{g}{4}$. The value of coefficient of kinetic friction will be:

Consider a block kept on an inclined plane (incline at 45${}^\circ$) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane($\mu$) is equal to:

The time taken by an object to slide down 45${}^\circ$ rough inclined plane is n times as it takes to slide down a perfectly smooth 45${}^\circ$ incline plane. The coefficient of kinetic friction between the object and the incline plane is:

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta$. The magnitude of the contact force will be:

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t(\sqrt{2}+1)$ s. The value of t is ___________.

(use $g = 10\text{ m/s}^{2}$)

An inclined plane is bent in such a way that the vertical cross-section is given by $y = \frac{x^2}{4}$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

When a body slides down from rest along a smooth inclined plane making an angle of 30${}^\circ$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $\alpha$T, where $\alpha$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{\alpha^2-1}{\alpha^2}\right)$ where x = __________.

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30${}^\circ$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$ if the time of ascent is half of the time of descent. The value of x is __________.

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is: [Take g = 10 m/s2]

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms${}^{-}$2)

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $30^\circ$. The external force required to take the same body up the plane with the same acceleration will be: (g = 10 m/s2)

A given object takes n times more time to slide down a $45^\circ$ rough inclined plane as it takes to slide down a perfectly smooth $45^\circ$ incline. The coefficient of kinetic friction between the object and the incline is:

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $\mu$min between the mass and the inclined surface such that the mass does not move is:

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°, the box starts to slip and slides 4.0 m down the plank in 4.0 s.

The coefficients of static and kinetic friction between the box and the plank will be, respectively

A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{x^3}{6}.$ If the coefficient of friction is $0.5,$ the maximum height above the ground at which the block can be placed without slipping is:

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while 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 body starts from rest on a long inclined plane of slope 45°. The coefficient of friction between the body and the plane varies as $\mu = 0.3x$, where x is distance travelled down the plane. The body will have maximum speed (for $g = 10$ m/s${}^{2}$) when $x$ =

A smooth block is released at rest on a $45^\circ$ incline and then slides a distance $'d'$. The time taken to slide is $'n'$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A block rests on a rough inclined plane making an angle of $30^\circ$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\text{ N},$ the mass of the block (in $\text{kg}$) is $(\text{take } g = 10\text{ m/s}^{2})$

A block has been placed on a inclined plane with the slope angle $\theta$, block slides down the plane at constant speed. The coefficient of kinetic friction is equal to

Starting from rest, a body slides down a $45^\circ$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is