Question #1984f

1 Answer
Dec 18, 2014

When the driver of the truck decelerates, the egg crate would experience a fictitious inertial force giving it a tendency to slide forward. However the frictional interaction between the egg crate and the floor would oppose this tendency. Eggs are prevented from damage if sliding is prevented. The egg crate will be prevented from sliding as long as the inertial force (due to the deceleration of truck) is balanced by the static friction.

But the nature of static friction is as follows - For small values of applied horizontal inertial forces, the static friction exactly balances the applied force. As the applied inertial force increases so does the force of static friction. But there is a maximum value for the applied inertial force which can be supported by the static friction. Once the applied force exceeds this value static friction disappears and is replaced with kinetic friction and the object starts moving.

This is expressed by the inequality:

#f_s < f_s^{max} = \mu_s N#

It is the deceleration that matters and the speed of the vehicle does not matter and is only a red herring. As long as the inertial force due to deceleration is less than the maximum value that static friction can

#F_{i"ne"rtial} = ma; \qquad f_s^{max}=\mu_s N; \qquad N=mg#
Maximum Inertial force before sliding : #F_{i"ne"rtial} = f_s^{max}#
#ma = \mu_s mg; \qquad => a = \mu_s g = 0.4\times9.8m.s^{-2}=3.92 ms^{-2}#

So the magnitude of maximum deceleration that can be withstood by the egg crate without getting the eggs damaged is #3.92 ms^{-2}#