First slide

Two block problem

Question

A block of mass m is placed on another block of mass M which itself is lying on a horizontal surface. The coefficient of friction between the block of mass M and horizontal surface is $μ_{1}$ and that between the two blocks is $μ_{2}$ . What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?

Moderate

Solution

Maximum acceleration of m by friction = their maximum common acceleration
$\begin{array}{l} \frac{μ_{2} mg}{m} = \frac{F - μ_{1} (M + m) g}{M + m} \\ solving we get, \\ F = (M + m) (μ_{2} + μ_{1}) g \end{array}$

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