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Homework answers / question archive / Hail bounces off the roof of the car with a velocity of +15 m/s

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

Physics

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.

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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.