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).

The rear side of a truck is open and a box of 40 kg mass is placed 5 m

1.	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).
Answer» Solution : 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 = 20m `