The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end. If μ is 0.15 and g is 10 m s − 2 and the truck starts from rest with an acceleration of 2 m

Question

The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end. If μ is 0.15 and g is 10 m s − 2 and the truck starts from rest with an acceleration of 2 m s − 2 on a straight road, then the box will fall off the truck when it is at a distance of x metre from the starting point. The value of x is

TestHub · Accepted Answer

a = 2 m s − 2 , N = m g For the box's motion w.r.t. truck, ​ ma − μ N = m a BT ​ ⇒ ( ma − μ m g ) = m a BT ​ ⇒ a BT ​ = a − μg ​ ​ = 2 m s − 2 − ( 0.15 ) ( 10 m s − 2 ) = 0.5 m s − 2 ​ ​ s BT ​ = u BT ​ ⋅ t + 2 1 ​ a BT ​ ⋅ t 2 4 = 0 + 2 1 ​ ( 0.5 ) t 2 ⇒ t 2 = 16 ⇒ t = 4 s . ​ After 4 s , the box will fall off the truck. During 4 s , the truck travels, x = 2 1 ​ a t 2 = 2 1 ​ ( 2 ) ( 4 ) 2 = 16 m .

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