Answer to Question #12298 in Mechanics | Relativity for Som

Question

A trolley of mass 20 kg carries 16 kg grain and moves on a horizontal smooth and straight track at 20m/s.If the grain starts leaking out of a hole at the bottom at time t=0 s at the rate of .5 kg/s,what will be the speed of trolley at t=22s?

Answer 1

Mass of leaked grain: 22 s *0.5 kg/s = 11 kg
After 22 seconds trolley carries mass of grain 16 kg - 11 kg = 5 kg
Total mass before the leakage m1 = 20 + 16 = 36 kg
Total mass after leakage m2 = 20 + 5 = 25 kg
From the momentum conservation law we have:
p1 = p2 or
m1*v0 = m2*v
Then the velocity after 22 seconds will be
v = v0*(m1/m2) = 20 m/s * (36 kg/25 kg) = 28.8 m/s