The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with `2 m s^(-2)` . At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

Explanation

Acceleration of the box due to friction` = mu g = 0.15 xx 10 = 1.5 m s^(-2)` . But the acceleration of the truck is greater. The acceleration of the box relative to the truck is` 0.5 m s^(-2)` towards the rear end. The time taken for the box to fall off the truck ` = sqrt( (2 xx 5)/(0.5)) = sqrt20 s ` . During this time, the truck covers a distance ` = 1//2 xx 2 xx 20 = 20 m `