The Stone and The Water
A stone falls into the water and water drops are splashed. Why do the water drops fly upwards? Does the maximal height reached by the drops depend (primarily) on the size of the stone or on its speed? What is the maximal height?
Labels: SharedPuzzle
posted by Vago at
6:18 AM
16 Comments:
What's the question? Seems more like a basic homework question.
The height depends on size, shape, speed, and mass of the stone, and varies from extremely near zero height to any height at all. The maximum height can be many miles given enough mass with enough speed.
yeah i agree with steve...all the variabes can alter the hight..take size and speed for instance...you throw a pebble into a pond at high speed the splash may still be small...you then throw a big boulder in at a much slower speed it will still make a much larger splash.
The height reached by the highest-flying ejected droplet is greatest when the depth of the target liquid is equal to the radius of the hemispherical crater formed by the impact of the incident drop.
yes, the above person touched on another unaccounted for variable. The depth of the water. This can be from millimeters to meters deep. If the water is very shallow than the water won't splash as high as it would if it was a little deeper.
I think the answer to the first question: "why do the drops fly upward?" goes to one of Newton's principles. Every action has an equal and opposite reaction. The force pushing down will be equaled by a force pushing up (water drop).
I think I've missed a trick with this one. Do water drops fly directly upward? Is that possible? If the mass of the stone hits the water surely it is physically impossible for it to go directly up because the stone is in the way?? The primary driver as everyone has alluded to is the mass/size - but due to the direction the droplets fly at (between 91-179 degrees) surely their is a maximum height?
last anon: The droplet can shoot directly upwards due to (at least) two effects: hydrodynamic properties of the stone (the water must go around the stone in some way and and is partially prevented from going outward because the surrounding water prevents it), and once the stone is submerged the empty space above it will have water rushing in from all sides (once water collides in the middle, it will be forced upwards since air has lower density than water thus it can't easily splash "down".
My list was not intended to be exhaustive: for example, height is also dependent on humidity, dew point, temperature, surface smoothness of the stone, etc.
Yes, a jet does shoot directly upward. Actually two jets are formed when water rushes to fill the cavity made by the falling object. One shoots up and another shoots down.
http://www.npr.org/templates/story/story.php?storyId=100333707
I'm sure there are even better videos of this effect, but look especially at the 4th coin drop...
http://www.youtube.com/watch?v=Nk_Rqj6_qFo
Alright could someone connect this to the law of conservation of momentum? As the last question asks about how to find the height, not what it depends on.
Also it is NOT a HW question, and the other explanations are very good thx.
Conservation of momentum is easy to apply to billiard balls, hard to apply in this case. Once the stone hits the water, much of the momentum is directed outward, and most of the upward momentum is only achieved once the water refills the area vacated by the stone. There isn't going to be a clean equation to define the height the water will attain unless you hold lots of variables constant. In practice, the best way to figure this out is through experimentation in an environment similar to the one you're expecting. If you're thinking of a roundish stone dropped from a reasonable height into a pool of stationary water, then the maximum droplet height will be a few feet or less.
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Yes Steve I agree that it would be easier, but my question statess t find out through some method the height through a formula or an equation. That is the toughg part i couldnt do hence I asked this question here.
I do not want a practical experiment, i want a theoretical and if you want you can assume any shape, mass, orientation, etc. of the stone, but i would like HOW it can be found out. NOT experimentally, and i do NOT want what it depends on eiter.
The actual working out is what I want. Just take any numbers you see fit and whatever you need and solve it theoretically. Take anything, I just want to know how it can be got.(And here HAS to be a way, there is almost nothing that science cammot prove theoretically but can be proved practically only.
Yes Steve I agree that it would be easier, but my question statess t find out through some method the height through a formula or an equation. That is the toughg part i couldnt do hence I asked this question here.
I do not want a practical experiment, i want a theoretical and if you want you can assume any shape, mass, orientation, etc. of the stone, but i would like HOW it can be found out. NOT experimentally, and i do NOT want what it depends on eiter.
The actual working out is what I want. Just take any numbers you see fit and whatever you need and solve it theoretically. Take anything, I just want to know how it can be got.(And here HAS to be a way, there is almost nothing that science cammot prove theoretically but can be proved practically only.
@abdeali-There is no formula that can predict the number of typographical errors in a post, however we can observe their occurrences and pass judgement. So you are wrong.
Also, THERE ARE NO ROBOTS IN LORD OF THE RINGS!
...jeez
Conservation of energy, 1/2mv^2= mgh + (friction force)+ (sound force) and any other force you want to add on. If energy can't be destroyed and created then conservation of energy would be a good choice to use
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