Calculating Momentum Impulse During Thunderstorm

[chessmath]

Thunderstorm During a violent thunderstorm, hail of diameter 2.0 cm falls directly downward at a speed of 25 m/s. There are estimated to be 120 hailstones per cubic meter of air.

(a) What is the mass of each hailstone (density = 0.92 g/cm3)?

(b) Assuming that the hail does not bounce, find the magnitude of the average force on a flat roof measuring 10 m x 20 m flat due to the impact of the hail? (Hint: During impact, the force on a hailstone from the roof is approximately equal to the net force on the hailstone, because the gravitational force on it is small.)



a)I figure out the first part using density and volume of each hailstone.

b) for the second part I say total mass is equal to mass in part a times 120 , then I do not know what is time because F(avg) is equal to change in momentum over t , now what is final velocity and t , If I know final velocity , I know t and vise versa , is there anyone that can help me in this problem?

 

[Ken G]

You need the concept of "momentum flux", to get the rate that momentum passes through a 10x20 area. Note the latter is a force-- the rate of momentum passing through or into that area. Here the momentum is just the mass that passes through that area per second (use its speed and density), times the velocity. It's a bit unusual to think of force as a rate of mass, times a velocity, rather than a mass times a rate of change of velocity, but there you have it. It's a lot like a rocket engine problem, only in reverse.