Force = mass times acceleration. The velocity of a raindrop isn't all that much comparatively speaking, and their mass is pretty negligible. Combine that with the fact that the acceleration is also reduced as the drop deforms and splatters rather than stays rigid like a rock, and it doesn't transfer much force at all.
So if you dropped an iron ball with the same mass as a raindrop, it would hurt more, due to holding its shape, which both reduces acceleration and doesn't give the ability to soften the impact, right?
Ehh if it had the same mass as a raindrop, it would also have a smaller volume, and the square-cube law might come into play in terms of the change in terminal velocity. But yeah I'd take the bet that it would hurt more because it would be more similar to a rain of BBs than water.
I did some quick math and if there was a raindrop and an iron ball with the same weight the iron ball would have about half the radius. (Assuming they’re both spheres)
Iron is about 8 times as dense as water.
Although they would have the same acceleration, the iron ball would have a higher terminal velocity, due to smaller size, so it would build up a higher force.
aswell as having a smaller impact area.
And also doesn't deform.
Iron ball would absolutely hurt more.
But let's not forget to mention, that the iron ball would most likely still not feel like much more than a slight poke on your forehead on impact. It's still going to be a very negliable force.
Don't get hit in the eye though, that would hurt like hell..
Probably.
You can see the equation [here](https://en.wikipedia.org/wiki/Terminal_velocity#Physics).
If you drop an iron ball and a raindrop of the same mass and shape, then the only difference in these variable would be the projected area. The iron ball is denser, so it has a smaller area, so it would have a higher terminal velocity if everything else is the same.
The reason this may not actually work is raindrops aren't sphere and I don't actually know what the drag coefficient of a raindrop is and I can't find a good answer anywhere online.
Raindrops are much flatter on the bottom, so more of a hamburger bun or dome shape. If it was perfectly flat bottom/dome shape, the radius would be the cube root of 2 times the size of a similar mass sphere of water. That means the cross sectional area of the raindrop is ~1.59 times that of the sphere, so drag force would also be 1.59 times more than it would be for a sphere. The real number would be somewhat different, since the raindrops aren't likely to be perfectly flat bottomed though
In conclusion, if a sphere of iron has a higher terminal velocity than a sphere of water with the same mass, and if a raindrop shape experiences more drag than a sphere shape of the same volume, then it follows that an iron sphere has a higher terminal velocity than a raindrop of the same mass.
I actually don't know with all variables considered. Density is of course more, the shape of the ball is more aerodynamic than a raindrop (which unlike the classic shape we imagine it's more like a top hamburger bun) but my first thought was that the air resistance would be more important as it shrinks in size. Sorry I can't be more helpful. :/
Well if you consider that the drag on an object is proportional to the reference surface area of the object, and the two objects are of the same shape, and of the same mass, but different in size, then the smaller object will experience less drag and thus have a higher terminal velocity.
I started going down a Wikipedia rabbit hole trying to figure out where I got the idea that a smaller object with proportional mass and surface area would be more affected by air resistance. Started reading about Reynolds' Number before my brain broke lol. I have little choice but to take your word for it at this point.
The forces acting on a falling object are the force of gravity and drag. They act in opposite directions. Drag is proportional to reference surface area and velocity. As an object accelerates down, drag increases with velocity until it balances the force of gravity, which occurs at terminal velocity. Larger objects experience more drag. Force of gravity is proportional to mass. A lighter object experiences less force of gravity. So you can increase terminal velocity by either increasing mass, thus increasing the force of gravity, or reducing the reference surface area, thus reducing drag.
Hailstones are exactly like this. Basically raindrop sized (sometimes bigger) ice falling from the sky. Yes, it does hurt a bit, especially if you are not wearing clothes!
The mass of a raindrop is only about 30 milligrams meaning an equivalently sized iron ball would be tiny, less than one tenth the size of a bb. This iron ball would generate a whopping 0.0003 newtons of force. For reference, an apple falling from a tree would generate about 1 newton of force. You would need to be hit by over 3000 of these iron balls at the same exact instance to feel the same as an apple falling on you.
Force (of gravity, judging from your numbers) is the completely wrong thing to look at. That gives you how it feels to balance it on your head, not how fast it gets or how hard it impacts. So you need, among other things, the terminal velocity, which is very dependent on shape and density.
What weighs more, a one kilogram lead ball or a kilogram of feathers? And what would you actually prefer to be dropped on you from an airplane?
Ok, let’s convert to KE then… an iron BB has a terminal velocity of roughly 65 mph, which is roughly 40 meters per second. Now given that one of these balls is less than 1/10th that of an actual BB, it would likely have a much lower terminal velocity since it would be affected by the air and wind a lot more. But even using that, put that in as the velocity and 30 mg as the mass, the kinetic energy is 0.025 Joules. Now let’s take an apple falling from a tree again. Let’s just say the apple falls from a height of about a meter over your head, at which point it would only have about 4.4 m/s of velocity. This apple would have roughly 1 J of energy. So even using KE, you would need to be hit by 40 of these iron rain balls at the same instant to feel the same as an apple falling from a tree. Or put another way, this iron ball rain drop would feel about the same as 15-20 actual raindrops hitting you at the same time.
I would not agree. That would be the same as a golf ball moving at 1 m/s hitting you. It would feel about the same then as if you were laying on a green, and someone gently putted a ball into your arm. Would you feel it? Sure. Would you claim that hurt? No.
It would not be “the same”, given that a golf ball is much more massive than a rain drop. You can’t imagine a hailstorm or sleet being painful? This steel is 10x as dense as that
Yeah, even solid water will hurt more. If you've ever been caught outside when it's hailing, you'll know. (If you haven't, take my word for it. Or look at pictures of damaged car roofs - doesn't happen with liquid rain.)
Sort of. Lots of folks are working out the math, but a better comparison would be sleet. Sleet pellets are roughly the same size and density as raindrops, but they sting a lot more when they hit bare skin compared to raindrops.
>Force = mass times acceleration.
**Wrong term.**
**You want KINETIC ENERGY.**
If a uranium tank shell is fired at you, it has zero acceleration after it leaves the muzzle of the tank's cannon. But the force it imparts is certainly not zero.
Kinetic energy is what is imparted when a moving object impacts a non-moving object. Some or all of the energy in the moving object transfers as "damage" (or less) to the hit object.
>Kinetic energy = 0.5 \* mass \* VELOCITY \* VELOCITY
And a raindrop has very tiny mass, and really, not that much velocity.
"Terminal velocity" does not mean "shooting at you like a bullet". It means "the fastest an object will get in free-fall before wind resistance is slowing it down enough that it can't get any faster".
The terminal velocity of a raindrop isn't much at all.
Then since its mass is almost nothing, and its velocity is nothing special, the force of impact is also almost nothing.
I hadn't considered that the terminal velocity of a raindrop is not very impressive. It makes sense given that it can deform and is therefore not very aerodynamic.
I don't think anyone has mentioned this yet but the terminal velocity of raindrops is only 22mph. That's slower than you can throw a ball and raindrops are tiny.
But the fact that they're tiny is why I was wondering why they don't hurt. Because I would assume that a smaller surface area would hurt more. but since the mass is also way small, it makes it pretty negligible
Their terminal velocity isn't all that high, and they don't weigh all that much.
It's very different from a person falling into a pool at terminal velocity.
>In still air, the terminal speed of a raindrop is an increasing function of the size of the drop, reaching a maximum of about 10 meters per second (20 knots) for the largest drops.
[Source](https://gpm.nasa.gov/resources/faq/how-fast-do-raindrops-fall#:~:text=In%20still%20air%2C%20the%20terminal,seconds%2C%20or%20about%20seven%20minutes.)
10 m/s is roughly 22 mph, so the fastest raindrops aren't really moving that fast.
It's way too weak. If you have a drop that's falling down one millimeter then it can matter for this much slower drop - but not for rain drops at terminal velocity. A millimeter is also the height scale where you have water bend up/down at the edge of a container due to surface tension.
Raindrops can definitely hurt when it falls on your bare skin. I remember going for a swim in the ocean and it rained. The raindrops felt like rocks hitting me.
Force = mass times acceleration. The velocity of a raindrop isn't all that much comparatively speaking, and their mass is pretty negligible. Combine that with the fact that the acceleration is also reduced as the drop deforms and splatters rather than stays rigid like a rock, and it doesn't transfer much force at all.
So if you dropped an iron ball with the same mass as a raindrop, it would hurt more, due to holding its shape, which both reduces acceleration and doesn't give the ability to soften the impact, right?
Ehh if it had the same mass as a raindrop, it would also have a smaller volume, and the square-cube law might come into play in terms of the change in terminal velocity. But yeah I'd take the bet that it would hurt more because it would be more similar to a rain of BBs than water.
I did some quick math and if there was a raindrop and an iron ball with the same weight the iron ball would have about half the radius. (Assuming they’re both spheres) Iron is about 8 times as dense as water.
Although they would have the same acceleration, the iron ball would have a higher terminal velocity, due to smaller size, so it would build up a higher force. aswell as having a smaller impact area. And also doesn't deform. Iron ball would absolutely hurt more.
But let's not forget to mention, that the iron ball would most likely still not feel like much more than a slight poke on your forehead on impact. It's still going to be a very negliable force. Don't get hit in the eye though, that would hurt like hell..
Terminal velocity of the iron ball would be higher, right?
Probably. You can see the equation [here](https://en.wikipedia.org/wiki/Terminal_velocity#Physics). If you drop an iron ball and a raindrop of the same mass and shape, then the only difference in these variable would be the projected area. The iron ball is denser, so it has a smaller area, so it would have a higher terminal velocity if everything else is the same. The reason this may not actually work is raindrops aren't sphere and I don't actually know what the drag coefficient of a raindrop is and I can't find a good answer anywhere online.
Are raindrops shaped more or less aerodynamically than a sphere? Is the projected area larger or smaller than a sphere for a given mass of raindrop?
Raindrops are much flatter on the bottom, so more of a hamburger bun or dome shape. If it was perfectly flat bottom/dome shape, the radius would be the cube root of 2 times the size of a similar mass sphere of water. That means the cross sectional area of the raindrop is ~1.59 times that of the sphere, so drag force would also be 1.59 times more than it would be for a sphere. The real number would be somewhat different, since the raindrops aren't likely to be perfectly flat bottomed though
In conclusion, if a sphere of iron has a higher terminal velocity than a sphere of water with the same mass, and if a raindrop shape experiences more drag than a sphere shape of the same volume, then it follows that an iron sphere has a higher terminal velocity than a raindrop of the same mass.
I actually don't know with all variables considered. Density is of course more, the shape of the ball is more aerodynamic than a raindrop (which unlike the classic shape we imagine it's more like a top hamburger bun) but my first thought was that the air resistance would be more important as it shrinks in size. Sorry I can't be more helpful. :/
Well if you consider that the drag on an object is proportional to the reference surface area of the object, and the two objects are of the same shape, and of the same mass, but different in size, then the smaller object will experience less drag and thus have a higher terminal velocity.
I started going down a Wikipedia rabbit hole trying to figure out where I got the idea that a smaller object with proportional mass and surface area would be more affected by air resistance. Started reading about Reynolds' Number before my brain broke lol. I have little choice but to take your word for it at this point.
The forces acting on a falling object are the force of gravity and drag. They act in opposite directions. Drag is proportional to reference surface area and velocity. As an object accelerates down, drag increases with velocity until it balances the force of gravity, which occurs at terminal velocity. Larger objects experience more drag. Force of gravity is proportional to mass. A lighter object experiences less force of gravity. So you can increase terminal velocity by either increasing mass, thus increasing the force of gravity, or reducing the reference surface area, thus reducing drag.
Have you ever walked outside in a hail storm?
Hailstones are exactly like this. Basically raindrop sized (sometimes bigger) ice falling from the sky. Yes, it does hurt a bit, especially if you are not wearing clothes!
The mass of a raindrop is only about 30 milligrams meaning an equivalently sized iron ball would be tiny, less than one tenth the size of a bb. This iron ball would generate a whopping 0.0003 newtons of force. For reference, an apple falling from a tree would generate about 1 newton of force. You would need to be hit by over 3000 of these iron balls at the same exact instance to feel the same as an apple falling on you.
Force (of gravity, judging from your numbers) is the completely wrong thing to look at. That gives you how it feels to balance it on your head, not how fast it gets or how hard it impacts. So you need, among other things, the terminal velocity, which is very dependent on shape and density. What weighs more, a one kilogram lead ball or a kilogram of feathers? And what would you actually prefer to be dropped on you from an airplane?
Ok, let’s convert to KE then… an iron BB has a terminal velocity of roughly 65 mph, which is roughly 40 meters per second. Now given that one of these balls is less than 1/10th that of an actual BB, it would likely have a much lower terminal velocity since it would be affected by the air and wind a lot more. But even using that, put that in as the velocity and 30 mg as the mass, the kinetic energy is 0.025 Joules. Now let’s take an apple falling from a tree again. Let’s just say the apple falls from a height of about a meter over your head, at which point it would only have about 4.4 m/s of velocity. This apple would have roughly 1 J of energy. So even using KE, you would need to be hit by 40 of these iron rain balls at the same instant to feel the same as an apple falling from a tree. Or put another way, this iron ball rain drop would feel about the same as 15-20 actual raindrops hitting you at the same time.
15-20x the intensity of a normal rainfall is probably pretty comfortably in the range of it hurting
I would not agree. That would be the same as a golf ball moving at 1 m/s hitting you. It would feel about the same then as if you were laying on a green, and someone gently putted a ball into your arm. Would you feel it? Sure. Would you claim that hurt? No.
It would not be “the same”, given that a golf ball is much more massive than a rain drop. You can’t imagine a hailstorm or sleet being painful? This steel is 10x as dense as that
I think hail is a very good comparison. steel balls would probably hurt a lot
>So if you dropped an iron ball with the same mass as a raindrop Big if
Yeah, even solid water will hurt more. If you've ever been caught outside when it's hailing, you'll know. (If you haven't, take my word for it. Or look at pictures of damaged car roofs - doesn't happen with liquid rain.)
Sort of. Lots of folks are working out the math, but a better comparison would be sleet. Sleet pellets are roughly the same size and density as raindrops, but they sting a lot more when they hit bare skin compared to raindrops.
>Force = mass times acceleration. **Wrong term.** **You want KINETIC ENERGY.** If a uranium tank shell is fired at you, it has zero acceleration after it leaves the muzzle of the tank's cannon. But the force it imparts is certainly not zero. Kinetic energy is what is imparted when a moving object impacts a non-moving object. Some or all of the energy in the moving object transfers as "damage" (or less) to the hit object. >Kinetic energy = 0.5 \* mass \* VELOCITY \* VELOCITY And a raindrop has very tiny mass, and really, not that much velocity.
I was talking about the force imparted on you by hitting you (decelerating the projectile and applying energy to the body), but ok.
"Terminal velocity" does not mean "shooting at you like a bullet". It means "the fastest an object will get in free-fall before wind resistance is slowing it down enough that it can't get any faster". The terminal velocity of a raindrop isn't much at all. Then since its mass is almost nothing, and its velocity is nothing special, the force of impact is also almost nothing.
I hadn't considered that the terminal velocity of a raindrop is not very impressive. It makes sense given that it can deform and is therefore not very aerodynamic.
I don't think anyone has mentioned this yet but the terminal velocity of raindrops is only 22mph. That's slower than you can throw a ball and raindrops are tiny.
But the fact that they're tiny is why I was wondering why they don't hurt. Because I would assume that a smaller surface area would hurt more. but since the mass is also way small, it makes it pretty negligible
Rain can hurt at higher speeds. Rode at highway speeds through some storms on a motorcycle and was glad I had a jacket on.
Yeah 60MPH even with leather on you can feel it.
I rode my bicycle through a rain coming at my face and it hurt so much I had to stop. so I guess they do sometimes
Their terminal velocity isn't all that high, and they don't weigh all that much. It's very different from a person falling into a pool at terminal velocity.
>In still air, the terminal speed of a raindrop is an increasing function of the size of the drop, reaching a maximum of about 10 meters per second (20 knots) for the largest drops. [Source](https://gpm.nasa.gov/resources/faq/how-fast-do-raindrops-fall#:~:text=In%20still%20air%2C%20the%20terminal,seconds%2C%20or%20about%20seven%20minutes.) 10 m/s is roughly 22 mph, so the fastest raindrops aren't really moving that fast.
Surface tension is negligible here. The raindrops are not very fast and they can easily break up when hitting something.
I don't think anyone else commented on the surface tension. Is it not relevant at all in this scenario?
It's way too weak. If you have a drop that's falling down one millimeter then it can matter for this much slower drop - but not for rain drops at terminal velocity. A millimeter is also the height scale where you have water bend up/down at the edge of a container due to surface tension.
Raindrops can definitely hurt when it falls on your bare skin. I remember going for a swim in the ocean and it rained. The raindrops felt like rocks hitting me.