When a rain falls from the sky, what happens to its momentum as it hits the ground? Is your answer also valid for Newton‘s famous apple?

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crmhaske | College Teacher | (Level 3) Associate Educator

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To answer this question, the momentum (p) equation will be invaluable:

p = mv

With the rain drop, m is the mass of the rain drop, and v is its terminal velocity (zero acceleration) through the air.

When the rain drop hits the ground the momentum changes.  This can be conceptualized by taking the derivative of the momentum equation with respect to time.  Remember that "d" simply means "change in":

dp/dt = m (dv/dt)

Since dv/dt is the change in velocity over time which is acceleration we can replace it with "a" for acceleration:

dp/dt = ma

And as we know, F = ma

Because the drop decelerates when it hits the ground, F = ma tells us an impact force is created.  This impact force causes the raindrop to break apart and splatter in all different directions on the ground.

However, the conservation of momentum rule (momentum of the whole drop is equal to the sum of the momentum of the splattered drops) is not valid in this case because there are energy loses due to the impact force.

This effect seen with the rain drop is likely what you would see with an apple.  Depending on the apple's coefficient of elasticity (e), the ratio of bounce to splatter will differ (an e=1.0 would mean a perfect bounce, where as an e=0.5 would mean some splatter, and thus, momentum loss due to the impact force).

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