Question

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg $s^{-1}$. What is the speed of the trolley after the entire sand bag is empty ?

Answer 1

Since the hole is on the floor , that means sand is falling vertically with respect to trolley. Therefore there is no force in horizontal direction hence in horizontal direction momentum is conserved.

Let $M=$ mass of trolley

$m=$ mass of sandbag

$v_1=$ initial velocity

$v_2=$ final velocity ( to be found)

Then $P_1=(M+m)v_1$ when the sand bag is empty the momentum is

$P_2=(M+0)v_2$

Momentum is conserved in horizontal direction so

$P_1=P_2$

$\Rightarrow =v_2=\frac{(M+m)}{M}{v}_1=\frac{300+25}{300}\times 27\times \frac{5}{18}=8.215m/s$