Factors Affecting Friction Force

Q. While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure

1. larger normal force
2. smaller Normal force
3. smaller coefficient of friction
4. larger coefficient of friction

Q.

Why does frictional force gets increase when two surfaces in contact are polished beyond a certain limit?

Q. A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, the frictional force $f$ versus $P$ graph will look like:

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Q. A block of mass $m$ is placed on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the inclined plane. The direction of force pointing up the plane is taken to be positive. As force $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, then the graph of frictional force $f$ versus $P$ graph will look like:

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Q. (A) A mass of 4 Kg rests on a horizontal plane . The plane is gradually inclined until at an $angle\theta ={15}^o$ with the horizontal, the mass just beings to slide, What is the coefficient of static friction between the block and the surface?
(B) Two blocks of masses 1 Kg and 2 Kg are connected by an intextensible string which passes over a frictionless pulley as shown in the figure.calculate the acceleration of these blocks

Q. A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_1=mg(\sin \theta -\mu \cos \theta )$ to $P_2=mg(\sin \theta +\mu \cos \theta )$, the frictional force $f$ versus $P$ graph will look like:

1. 
2. 
3. 
4. 

Q. In figure, a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough is ${\mu }_k.$ What is the acceleration of the crate in terms of ${\mu }_k,\theta$ and g?

1. $g(\sin \theta -\sqrt{2}{\mu }_k\cos \theta )$
2. $g(\sin \theta -\frac{{\mu }_k\cos \theta }{\sqrt{2}})$
3. $g(\sin \theta +\sqrt{2}{\mu }_k\cos \theta )$
4. $g(\sin \theta +\frac{{\mu }_k\cos \theta }{\sqrt{2}})$