$A$ block of mass $2 \ kg$ is placed on a rough horizontal surface. If a horizontal force of $20 \ N$ acting on the block produces an acceleration of $7 \ m \ s^{-2}$ in it,then the coefficient of kinetic friction between the block and the surface is $(g = 10 \ m \ s^{-2})$.

$A$ block of mass $50\, kg$ slides over a horizontal distance of $1\, m$. If the coefficient of friction between their surfaces is $0.2$,then the work done against friction is ......... $J$.

$A$ block of mass $5 \,kg$ is pulled by a force $F$ as shown in the figure. If the coefficient of friction is $0.1$, then the force needed to accelerate the block to $3 \,m/s^2$ to the right is close to (in $\,N$)

$A$ block of $7\,kg$ is placed on a rough horizontal surface and is pulled by a variable force $F$ (in $N$) $= 5t$,where $t$ is time in seconds,at an angle of $37^{\circ}$ with the horizontal as shown in the figure. The coefficient of static friction between the block and the surface is $\mu = 1$. If the force starts acting at $t = 0\,s$,find the time at which the block starts to slide. (Take $g = 10\,m/s^2$)

$A$ block of mass $10\, kg$ starts sliding on a surface with an initial velocity of $9.8\, m/s$. The coefficient of friction between the surface and the block is $0.5$. The distance covered by the block before coming to rest is: [use $g = 9.8\, m/s^2$].........$m$

$A$ $300 \ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20 \ m/s$. $A$ motor maintains the belt's constant speed. The belt initially slides under the crate,with a coefficient of friction of $0.400$. After a short time,the crate is moving at the speed of the belt. During the period in which the crate is being accelerated,find the work done by the motor which drives the belt.