What is the maximum force $F$ that can be applied on block $m_1$,so that both $m_1$ and $m_2$ will move together? There is no friction between $m_1$ and the horizontal table. The coefficient of friction between $m_1$ and $m_2$ is $\mu$.

$A$ block of mass $1\, kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\, m/s^2$,the frictional force acting on the block is ........ $N$.

In the figure,the coefficient of friction between the floor and block $B$ is $\mu_1 = 0.2$ and between blocks $A$ and $B$ is $\mu_2 = 0.3$. The masses are $m_A = 20 \text{ kg}$ and $m_B = 40 \text{ kg}$. Find the maximum horizontal force $F$ that can be applied to block $B$ so that both blocks move together. (in $\text{ N}$)

Find the acceleration of the $10\,kg$ block when a force $F = 30\,N$ is applied as shown in the figure. The coefficients of friction are $\mu = 0.1$ between the blocks and $\mu = 0.3$ between the $5\,kg$ block and the ground. (in $,m/s^2$)

Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between the bottom block and the table is $\mu = 0.1$. Find the force $F$ that must be applied to the $0.8 \text{ kg}$ block such that it attains an acceleration of $5 \text{ m/s}^2$. (Assume acceleration due to gravity, $g = 10 \text{ m/s}^2$.) (in $\text{ N}$)

$A$ system of two blocks of masses $m = 2 \; kg$ and $M = 8 \; kg$ is placed on a smooth table as shown in the figure. The coefficient of static friction between the two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\dots \; N$.