The rear side of a truck is open and a box of 40kg mass is placed 8m away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is μ = 0.1. On a straight road, the truck starts from rest and moves with acceleration 2m s⁻². Find the time (in sec) when box falls off the truck. Take g = 10m s⁻²
Physics · Mixed Chapter
JEE Mains

Question

The rear side of a truck is open and a box of 40kg mass is placed 8m away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is μ = 0.1. On a straight road, the truck starts from rest and moves with acceleration 2m s⁻². Find the time (in sec) when box falls off the truck. Take g = 10m s⁻²

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Maximum friction on the box is μmg, so its maximum horizontal acceleration with the truck is μg=0.1×10=1 m s⁻². The truck accelerates at 2 m s⁻²; the box slips backwards relative to the truck. Step 2: Relative acceleration magnitude =2−1=1 m s⁻². Initial relative speed is zero. Step 3: The box must slip 8 m to reach the open rear: 8=½(1)t², so t²=16 and t=4 s. Answer: 4.