Question

During a heavy rain,hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s.Suppose 2000 hailstones strike every square meter of a $10m\times 10m$ roof perpendicularly in one second and assume that the hailstones do not rebound.Calculate the average force exerted by the falling hailstones on the roof.Density of a hailstone is 900 $\frac{kg}{m^3}$.

Answer 1

d=1 cm,v=20 m/s,

u=0,p= 900 $\frac{kg}{m^3}$

=0.9 $\frac{gm}{c{m}^3}$

volume=$\left(\frac{4}{3}\right)\pi r^3$

=$\frac{4}{3}\pi (0.5{)}^3=0.5238c{m}^3$

$\therefore$ mass=vp=$0.5238\times 0.9$

=0.4714258 gm

$\therefore$ mass of 2000 hailstone=$2000\times 0.4714=947.857$

$\therefore$ rate of change of momentum per unit area=$947.857\times 2000$

=$19\frac{N}{m^2}$

$\therefore$ Total force exerted=$19\times 100=1900N$