Pseudo Acceleration and Pseudo Force Concepts NCERT Example 4.7

Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the co-efficient of static friction between the box and the train's floor is 0.15.

When the train is accelerating with an acceleration of 'a'  in the forward direction, the block on the floor will try to slip backwards with the same acceleration 'a' or $a_{pseudo}$. The friction on the block is what will help the block to keep going forward with the train. However if the $F_{pseudo}$ is greater than the $F_{friction}$ then the block will slip backwards. So the condition for maximum acceleration of the train allowed so that the block will remain stationary or move along with the train is,

$F_{pseudo} \le F_{friction}$

$m a_{pseudo} \le \mu_{s} N$
$m a_{pseudo} \le \mu_{s} mg$

$ a_{pseudo} \le \mu_{s} g$

$ a_{pseudo} \le 0.15 \times 10$

$ a_{pseudo} \le 1.5 m/s^2$

If the train accelerates higher than 1.5 $m/s^2$ then the block will slip backwards.

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