Two blocks of mass 10 kg each are placed on a smooth horizontal surface, as shown in the figure. The coefficient of friction between the blocks is 0.2. Initially the blocks are at rest. A time varying horizontal force $F = (20 t) N$ is applied on the upper block. Find the value of t (in s) when slipping takes place between the two blocks.

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Detailed Solution

The limiting friction force between the blocks $f = 0.2 (10 g) = 20 N$ The maximum possible acceleration for the lower block is

$a = \frac{f}{10 kg} = \frac{20 N}{10 kg} = 2 m / s^{2}$

The blocks will move without slipping till acceleration of the upper block reaches the value a $= 2 m / s^{2}$ This happens at time t given by $20 t - 20 N = (10 kg) (2 m / s^{2}) gives t = 2 s$

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