How Does Hail Impact Force Compare to Rain Despite Similar Mass and Size?

[ericka141]

Homework Statement

"Think of a rainstorm. Each raindrop hits your roof, exerting a certain amount of force for a short time until it comes to a stop. Now think of a hailstorm instead. All of the raindrops are now hard little ice pellets of the same size and mass. Using common sense and what you know about momentum, how would the total force of the hailstorm striking the roof of your house compare to the equivalent rainstorm."

The Attempt at a Solution

I was POSITIVE that the force would be the same, since both the size and mass are the same and it seems like it's assumed that velocity is the same as well. However, that was the incorrect answer.
Momentum = mv
I'm not sure if it's even possible to find out the velocity of each particle, as it doesn't give any information on how they're different in velocity, only that they're the same mass and size- therefore the same drag constant and weight.

 

[UltrafastPED]

Actually hailstones are larger than raindrops: they accumulate as they freeze, and can become quite large! We get hail frequently enough where I live: it comes with violent thunderstorms.

For your actual problem as given note that the raindrops hit the roof, and then slide off - each one contributes momentum p = mv; so the total momentum over a short time is Np, where there were N raindrops.

For the little hailstones they hit the roof, then bounce off ... they are hard objects. Due to the bounce you get double the momentum, so you now have 2Np for the total momentum.

If you allow some of the momentum to be absorbed by the roof tiles or fracturing of the hailstone, then it will be some number greater than 1 (because they do bounce) but less than 2 (due to loss of momentum upon impact).

The total force is approximately the total momentum divided by the "short amount of time".

 

[ericka141]

So the answers I have to choose from are:

a. The force from the hailstorm and the rainstorm would be almost the same. Incorrect
b. The force of the hailstorm would be close to twice that of the rainstorm.
c. The force of the hailstorm would be close to four times times that of the rainstorm.
d. The force of the rainstorm would be close to twice that of the hailstorm.
e. The force of the rainstorm would be close to four times that of the hailstorm.

Would the force of the hailstorm be close to twice that of the rainstorm in that case?

 

[UltrafastPED]

Yes.