HELP! momentum question?

Question

when rain falls from the sky, what becomes of its momentum as it hits the ground?
is your answer also valid for newton's famous apple? Explain
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the first one i know...but the second one..what the hell is it talking about??

this is a question from my textbook.

i know the apple story!!
i just don't know how to answer this freaky question!!

Answer 1

Momentum = p = mv; where m is the mass of a raindrop and v is its terminal velocity as it falls through the air. Terminal velocity is when the raindrop is no longer accelerating as it falls. This happens when the air drag (D) on the drop exactly offsets the weight (W) of the drop.

On impact with the ground, we have a change in momentum dp/dt = m dv/dt as the raindrop comes to a halt. dp/dt just means a change in momentum (dp) over a change in time (dt). Similarly, dv/dt means a change in velocity (dv) over that same change in time (dt). But dv/dt = acceleration; so we have dp/dt = m dv/dt = ma = force. So when that drop hits the ground and decelerates, a force of impact is created.

Clearly a raindrop does not just stop when it hits the ground; it will likely splatter. Some of that drop continues on, but in widely scattered parts going in different directions. Those splatters also have momentum; in fact, according to the conservation of momentum law, if there were no energy losses when splattering, the sum of all the momenta of all the splatters would equal the momentum of the raindrop just before hitting the ground.

But, and this is a big BUT, there are energy losses. That impact force, which caused the splattering in the first place, is the source of the energy losses. So, to answer your question directly, some of that initial momentum before impact is lost due to the impact force. In which case the sum of the splatter momenta will be less than the momentum of the whole drop before the impact.

The answer to the apple question is, as in many physics questions, it depends. First, the apple is unlikely to hit terminal velocity; so there will be a net force acting on it all the way from the branch to the ground. That means, the apple, unlike the raindrop, will be accelerating all the way to the ground.

Second, unless it is rotten to the core, the apple is unlikely to splatter. In fact, it may not even bounce if, for example, it falls onto a deep grassy area. Thus, whatever momentum remains will be resident in the whole apple, M mass, rather than a lot of parts.

Finally, the amount of momentum after the impact depends on the coefficient of elasticity (e) of the apple with the ground. If e = 1.00, all the momentum before impact will still be there after impact. That follows because, by definition, e = p(after)/p(before); where the p's are momentum before and after impact.

And my personal experience with apple trees and apples is that e < 1.00; this assertion stems from the observation that, when apples do bounce, they don't bounce very high. Clearly, the momentum after impact is not as great as the momentum before.

And this loss comes from the same kind of impact force the raindrop experienced. And that force is again due to the change in momentum dp/dt = m dv/dt = ma. So, the "famous" apple and the raindrop do in fact exhibit the same fate for their respective momenta. That is, the momenta before impact will likely be greater than the momenta after impact.

BTW, myth says that Newton got his idea for his famous gravity relationship when an apple fell from the tree he was sitting under at the time. It's not clear that really happened, but it makes a good story.

Answer 2

You don't know about newton's famous apple? Mayhaps you should READ the textbook. I am sure that they will mention that apple at least once. Then think of the comparison between the apple and a rain drop and that is your answer.

Answer 3

Well, the momentum of a raindrop hitting the ground is imparted to planet Earth. The law of momentum conservation leaves very little doubt about that :)

Answer 4

Angular momentum is likewise a scalar. besides the fact that: angles themselves at the instant are not vectors. you may instruct that angles a, b and c, in the event that they're orthogonal to a minimum of one yet another, supply distinctive reulting angles for a+b+c vs. a+c+b, as an occasion.

Answer 5

it is only the potential energy(energy by its state) which is converted into kinetic energy(nothing but energy by its velocity).................obviously gain in velocity increases the momentum since momentum=M*V(here M=dm differencial mass of the rain drop)......................ur apple question is no where related to the rain drop because its that which is related to gravity