In the given figure,the acceleration of the block of mass $M = \frac{10}{3} \, kg$ is (given $g = 10 \, ms^{-2}$,$\mu = \frac{1}{3}$,$F = 50 \, N$,and $\theta = \sin^{-1}(\frac{3}{5})$):

$A$ $60 \, kg$ mass is dragged on a horizontal surface by a rope for a distance of $2 \, m$. If the coefficient of friction is $\mu = 0.5$,the angle of the rope with the surface is $60^\circ$,and $g = 9.8 \, m/s^2$,then the work done against friction is ........ $J$.

When a body is moving on a surface,the force of friction is called

$A$ body of mass $2\, kg$ is being dragged with uniform velocity of $2\, m/s$ on a rough horizontal plane. The coefficient of friction between the body and the surface is $0.20$. The amount of heat generated in $5\, s$ is ........ $cal$ $(J = 4.2\, J/cal$ and $g = 9.8\, m/s^2)$

$A$ $300 \ kg$ 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.

$A$ cylinder of mass $10\,kg$ is sliding on a plane with an initial velocity of $10\,m/s$. If the coefficient of friction between the surface and the cylinder is $0.5$,then before stopping,it will travel a distance of ............. $m$.