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 10 m × 10 m 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 kg/m3.
Mass of a hailstone, m = Density×Volume
= 900×4/3×ϖ×(Radius)3
= 900×4/3×ϖ×(0.5×10-2)3
= 0.471×10-3kg
Mass of 2000 hailstones, M = 2000×m = 0.942 kg
Average force exerted by falling hailstones per unit area = Rate of change of momentum
= M× (20 – 0)
= 18.84 N ≈ 19 N
Total force exerted on the roof = 19 × area of the roof
= 19 × 10 × 10
= 1900 N