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Author Topic: PUZZLE -- Falling Raindrops  (Read 1414 times)

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Offline Neil Obstat

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PUZZLE -- Falling Raindrops
« on: September 06, 2018, 08:50:02 PM »
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  • .
    Which raindrops fall faster, the small ones or the large ones? 
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    (Explain your answer using verifiable physical principles, if possible.)
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline Felicitas

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    Re: PUZZLE -- Falling Raindrops
    « Reply #1 on: September 06, 2018, 08:59:54 PM »
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  • Same.
    9.8 m/sec squared.. rate of falling object absolute velocity...

    I wouldn't place any bets on my answer. My high school years seem so far away..
     :jumping2:


    Offline Maria Regina

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    Re: PUZZLE -- Falling Raindrops
    « Reply #2 on: September 06, 2018, 09:27:17 PM »
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  • .
    Which raindrops fall faster, the small ones or the large ones?
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    .
    (Explain your answer using verifiable physical principles, if possible.)
    It might depend on what state the water is in. We do not live in a vacuum, so gravity will affect the velocity of frozen water vs water vapor.

    If the water is frozen, the size has increased to that of baseballs, and the wind is strong, then that hail would strike the earth with a greater velocity, which could break windows, damage ceramic tiles on roofs, and even kill people.
    Lord have mercy.

    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #3 on: September 06, 2018, 09:37:33 PM »
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  • .
    Nothing special.
    Ordinary about sea-level (14 psi absolute), room temperature, clear day. 
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #4 on: September 06, 2018, 09:43:19 PM »
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  • Same.
    9.8 m/sec squared.. rate of falling object absolute velocity...

    I wouldn't place any bets on my answer. My high school years seem so far away..
     :jumping2:
    .
    That's a good start, but falling rain has more than acceleration due to gravity to affect its terminal velocity (hint hint).
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.


    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #5 on: September 06, 2018, 09:45:52 PM »
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  • It might depend on what state the water is in. We do not live in a vacuum, so gravity will affect the velocity of frozen water vs water vapor.

    If the water is frozen, the size has increased to that of baseballs, and the wind is strong, then that hail would strike the earth with a greater velocity, which could break windows, damage ceramic tiles on roofs, and even kill people.
    .
    "Rain drops," as in liquid water. That excludes frozen because then it would be hail or sleet, or snowflakes, not rain DROPS.
    But wind is a good thing to keep in mind -- that's making progress!
     
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #6 on: September 06, 2018, 10:04:57 PM »
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  • .
    Not to confuse the topic, but for comparison sake here is another puzzle involving falling objects:
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    A baseball is tossed upwards into the air. 
    Which takes longer, its flight up or its drop back down?
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline Maria Regina

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    Re: PUZZLE -- Falling Raindrops
    « Reply #7 on: September 06, 2018, 10:29:20 PM »
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  • .
    "Rain drops," as in liquid water. That excludes frozen because then it would be hail or sleet, or snowflakes, not rain DROPS.
    But wind is a good thing to keep in mind -- that's making progress!
     
    Ah yes! Vectors.
    Wind sheer can drive rain up, move it in a circle (tornadoes) slam it down to the earth, or even move it sideways and back.
    Lord have mercy.


    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #8 on: September 06, 2018, 11:39:47 PM »
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  • .
    Wind is a relative term. The problem doesn't mention any wind (sideways or crosswind) but neither does it say the drops are falling at different times. So we can most simply presume the large drops are falling alongside the small drops and an observer can simply watch their progress to see which is falling faster. Such a scene might be found at night, in the falling rain, standing outside under a street light that makes the falling raindrops prominently visible, even as they're falling. Again, presume no wind so they're falling pretty much straight down toward the ground. But in any case, from the point of view of the rain drops, they're experiencing "wind" merely by the fact that they are falling, that is, "wind" blowing upwards against the drops, in other words, air resistance.
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    This same air resistance is what causes the rain drops to slow their rate of descent, such that they attain a "terminal velocity" which is constant speed, and this constant speed can vary from drop to drop depending on the only other variable, namely, the size of each drop. So the question can be reduced to this: Which drops have a greater terminal velocity, the small drops or the large drops?
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline Neil Obstat

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    Re: PUZZLE -- Falling Raindrops
    « Reply #9 on: September 07, 2018, 03:19:32 AM »
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  • .
    Air resistance is an important factor in problems like these. Either it is supposed to be considered or it is not, but the puzzle needs to be worded to make that clear. The simplest way is to say, "without considering air resistance..." Otherwise, working the puzzle cannot presume that no air resistance ought to be included.
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    Consequently, the two puzzles above make no mention of air resistance, however, the correct solutions not only must consider air resistance, but as it turns out, air resistance is entirely what those two puzzles are all about! There would be no correct solutions without considering air resistance. In the first case, air resistance has a specific physical effect on the movement of the rain drops which is a function of the DIAMETER of the drops. Smaller drops necessarily have a smaller diameter, and larger drops have a larger diameter. As the drops of water fall, the buffeting effect of the relatively still air they're running into causes minor distortions of the shape of the drops, perhaps even causing the drops to separate into two or more smaller drops; or wayward drops might bump into other wayward drops causing them to combine into one or more larger drops. But for simplicity's sake, we ought to keep just two different sizes of drops in mind, one larger and one smaller, as the puzzle is worded that way.
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    Regarding the baseball, as it ascends it encounters air resistance which has the effect of slowing down the velocity of the ball in a similar way that the force of gravity has on the ball: they are both forces of resistance to the upward motion of the baseball, but obviously, air resistance (or friction) is small compared to the greater force of gravity. It's smaller but still significant. When a major league pitcher throws a fast ball, its velocity is greatest the instant it leaves his hand and due to air friction the speed of the pitch slows down as it approaches the catcher. Likewise, the puzzle ball being thrown vertically into the air has more air resistance from the very start than it does near the top of its ascent as it slows down to zero. At the apex of its flight, the baseball's initial kinetic energy is completely exchanged for potential energy which is defined by the ball's weight times the distance upwards that it has traveled. The force of air resistance starts at its maximum and decreases to its minimum as the ball goes upward, but the force of gravity remains practically constant the whole way. To be precise it decreases slightly as the ball gets further from the earth's center but the change is too small to be significant, and therefore can be disregarded. Then on its descent, the baseball encounters the same friction in reverse order starting at zero and gradually increasing to its maximum at the bottom of its fall. But that maximum at the end is still less than the initial maximum air resistance had been against the ball when it was first thrown. The whole point is, the velocity of the ball as it returns to the elevation from which it was first thrown must be less than the initial velocity it had when it was thrown, since some amount of kinetic energy has been lost going up AND coming down, due to air resistance. In contrast, if it had been thrown in a vacuum, there would have been no air resistance, so the ball would not have lost any total energy due to its movement, consequently the time it would take to ascend would be the same as the time it would take to fall back down.
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    To demonstrate the importance of air resistance, here is another puzzle that disregards it:
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    A large stone is 100 times heavier than a small rock, but when dropped at the same time, they fall with the same acceleration (ignoring air resistance). Why doesn't the large stone accelerate faster? Is it because of its weight, its energy, its surface area or its inertia?
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    Effectively, this puzzle could be worded to have the stone and the rock falling in a vacuum. But the effect of air resistance is so small in this case, that it really makes a minuscule contribution, and therefore for simplicity can be disregarded. Nonetheless, "ignoring air resistance" should be included to make this official. The air resistance effect on the rain drops and the baseball are far more significant due to the less density of water and ball compared to the greater density of the rocks. Generally, rocks are 3 times heavier than the same volume of water and baseball-sized rocks are about twice the weight of a baseball. Density is a function of unit mass divided by unit volume.
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.

    Offline TKGS

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    Re: PUZZLE -- Falling Raindrops
    « Reply #10 on: September 08, 2018, 11:39:45 AM »
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  • .
    Nothing special.
    Ordinary about sea-level (14 psi absolute), room temperature, clear day.
    On a clear day, there are no raindrops.


    Offline Nadir

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    Re: PUZZLE -- Falling Raindrops
    « Reply #11 on: September 09, 2018, 01:48:13 AM »
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  • See if you can figure out what these seven words all have in common?
    1. Banana
    2. Dresser
    3. Grammar
    4. Potato
    5. Revive
    6. Uneven
    7. Assess

    Offline jvk

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    Re: PUZZLE -- Falling Raindrops
    « Reply #12 on: September 09, 2018, 03:49:06 PM »
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  • 2 sets of double letters?

    Offline Struthio

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    Re: PUZZLE -- Falling Raindrops
    « Reply #13 on: September 09, 2018, 04:12:10 PM »
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  • All these words have less than 1000 letters.  Furthermore there is an infinity of other properties they have in common.
    It is absurd to imagine that he who is outside can command in the Church — Leo XIII., Satis Cognitum, 1896

    Offline Nadir

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    Re: PUZZLE -- Falling Raindrops
    « Reply #14 on: September 09, 2018, 06:41:03 PM »
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  • 2 sets of double letters?
    That is a clue to the desired answer. Good try!

    Quote
    Quote from Struthio: 
    All these words have less than 1000 letters.  Furthermore there is an infinity of other properties they have in common.
    Correct but not the specific enough for a gold star.

     

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