A cart loaded with sand having total mass m 0 = 1800 kg moves on a straight horizontal road starting from rest under the action of a force of 120 N . The sand spills through a small hole in the bottom at a rate of K = 0 . 5 kg s - 1 . What will be the value of the velocity (in m s - 1 ) of the cart after 20 min ?

Step-by-step solution

In this case, sand falls on the ground vertically and comes to rest. Hence, horizontal velocity of ejected sand with respect to ground is zero; so F ⁡ ext = d d t mv or F ⁡ ext d t = d mv Which on integration gives F ⁡ ext ∫ t 1 t 2 d t = ∫ d ⁡ mv F ⁡ ext t 2 - t 1 = m ⁡ 2 v 2 - m ⁡ 1 v 1 … i The rate of leakage of sand, K   =   ( – d m d t ) is constant which on integration gives ∫ m ⁡ 1 m ⁡ 2 d m ⁡ = - K ⁡ &#