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Hail bounces off the roof of the car with a velocity of +15 m/s

Physics Sep 10, 2020

Hail bounces off the roof of the car with a velocity of +15 m/s. Ignoring the weight of the hailstones, what is the force exerted by the hail on the roof.

Expert Solution

Let's assume that the hailstones reflect off the roof elastically, so that the change in vertical velocity is 30 meters/second. Suppose that during the hailstorm the mass flux of the hail is J.

J is the mass per square meter per second that is raining down. If the area of the roof is A then the mass that is hitting the roof per second is j*A. It may be that j*A is given in your problem (it has units of kg/second). I will work out the problem in terms of j*A

Suppose that the average mass of a single hail stone is m. Then the number of hailstones that are hitting the roof per second is j*A/m. All these hailstones change their velocity by 30 meters/second. Each hailstone changes its momentum by 30 meters/second times m. The total change in momentum of all the hailstones per second due to the collisions with the roof is thus:

j*A/m * 30 meters/second * m = j*A*30 meters/second

Change in momentum per unit time is force, so, this is the force exerted on the roof. Note that j*A has units of kg/second, so you get the correct units of the force: kg meters/second^2.

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