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Kinetec energy question

  1. Nov 9, 2007 #1
    1. Which of the following is an example of an object possessing Kinetic energy



    A. a ball rolling downhill
    B. a bird perched in a tree
    C. a stick of dynamite
    D. a boulder resting on a cliff
    E. Water at the top of a dam



    3. Without hesitation I answered E. Water at the top of a dam

    The reason I answered E. It is to my belief that flowing water (/large bodies of water) always has a constant (ever changing) kinetic energy (no matter how small it may be.) If the Water is at the top of a dam, (regardless if the water is over flowing over the dam or the turbines are on and the water is flowing through the spillways.) The water that is moving against the dam will always have kinetic energy.
    4. Proof: KE = (1/2)M * V^2 and for reference (V = [tex]\sqrt{(4/3)gh}[/tex] ) for the velocity of the ball rolling down hill. In order for an object to have Kinetic energy it must have mass and velocity. Water has mass and if you were to measure the waters velocity I bet it would be at least a tenth of the objects Ke if given the same mass (assuming we neglect the area of the water all together.) Here are my thoughts on why. Regardless if the dam was on a Lake or a river we must assume that water is flowing from point A to point B (the top of the Dam). Now let’s create two scenarios and freeze frame them.
    For simplicity the two scenarios will involve Scene 1 which will include the Ball and measure its KE in three different Quadrants (1/4, ½ and ¾ the distance traveled down the hill) I want to make the ball rolling down the hill the exact time in which (Scene 2) the body of water is considered at the “…top of a dam.”

    Scene 1. We release a ball with Mass = 1kg from rest on top of a hill of 20 meters. It rolls down our X distance and we freeze frame it (we assume the angle is a perfect 90 degree angle and we are neglecting any air resistance.) T = D/V
    (V1/4 = [tex]\sqrt{(4/3)(9.8) (5)}[/tex] = 8.08m/s
    Ke = (1/2)(1kg)(8.08m/s)^2 = 32.64 J
    T = 5/8.08 = .62s
    (V1/2 = [tex]\sqrt{(4/3)(9.8) (10)}[/tex] = 11.43m/s
    Ke = (1/2)(1kg)(11.43m/s)^2 = 65.32 J
    T= 10/ 11.43 = .875s

    (V3/4 = [tex]\sqrt{(4/3)(9.8) (15)}[/tex] = 14m/s
    Ke3/4 = (1/2)(1kg)(14m/s)^2 = 98 J
    T = 15/14 = 1.07s



    Scene 2. Remember the velocity of any object (for our equation particle of water) is always tangent to the path taken by the object. So the particle of water’s (which is a fluid element) velocity is always tangent to the streamline (the direction headed to the dam.) Also I would like to note that no two streamlines will ever intersect giving off multiple velocities at the same time. The weight of the water is exactly the same as the ball M2 = 1kg. As for its velocity we will obtain the mean from previously recorded velocity of water that exists near a dam and use this data to determine the average velocity if the data seems a bit skewed I will select a sample of the data using a random generator provided by excel. After putting in the numbers I get an average water speed of
    3.2mph = 1.43m/s
    and a speed of
    2.9mph = 1.29m/s
    Without putting up the formulas the KE for both (in order) is as follow (both in a freeze frame at the top of a dam so that it is in contrast to the ball rolling down hill

    KE1 = 1.022 J
    KE2 = .832 J
    If you notice they are exactly as I predicted (given already the common knowledge of about how fast water flows down a stream) the KE is about 1/10th of the ball rolling down hill.

    But Wait A Minute. The question never asked in regards if rather or not the water was the same weight, nor did it say it was the same area or mass. All it asked is “Which of the following is an example of an object possessing kinetic energy” Logically a person would assume that a ball rolling downhill would be the first and correct answer and that all other answers are considered objects possessing potential energy and not kinetic energy. But how big is this ball what is the individual’s initial thoughts on the answers? Initially my thoughts where a bowling ball rolling down the streets of San Francisco, and my initial thoughts of the water was about a billion gallons of water hitting the side of the Hoover dam instantaneously at a undetermined velocity.



    Alright now we have a new format what’s the weight of the water surrounding the top of the Hoover dam. Well we know the density of water to be 1m per 1v. Well we can’t get any easier than a depth of 1 meter. So for simplicity we will use a depth of 1 meter and since we are talking three dimensions and volume we will use the cubic meter. Since we are already talking about the Hoover dam lets use it as the example. The Hoover dam is 379 meters long. So if water was at the top of the Hoover dam joining it adjacently with a volume of 379 cubic meters then by conversion to liters we would get roughly 379,000 Liters, and if we were to convert to Gallons we would get 100121.2gal, and finally if were to convert it from gallons to Kilograms we would get 379,000kg of water. (ok now where’s are little bouncing ball…
    Ok San Francisco right? Well let’s pick an adequate ball? When I was a kid I always wanted to roll a bowling ball down one of the streets of San Francisco from about 9 blocks away to the bay that’s about a half a mile or more. Since we don’t know the exact distance or dimension, let’s use our old 90 degree angle perfect slope. And let’s make our bowling ball 20lbs = 9.07 kilograms. Since we don’t actually know the height of which the ball is initially released let’s do a crazy experiment and see what the Kinetic energy would be from 1 half mile (804.672 meters) up at a 90 degree angle. This time we are going to measure the Ke just before it hits bottom (to avoid any other formulas we are going to assume this means 99.9% of the distance.) Here is our formula V = [tex]\sqrt{(4/3)gh}[/tex] ) and our velocity is…



    V = 102.5 m/s
    And our Ke ? = (1/2)(9.07kg)(102.5)^2 = 47,677 J .
    What about our water?


    The average speed of the Colorado River that flows through the Hoover Dam is between 1.6 mi/hr and 4 mi/hr (based on multiple resources). For this experiment we are going to give it the later of the two speeds.
    1.6mi/hr = .715264m/s
    Now let’s fill in the equation for KE = (1/2)( 379,000kg)( .715264)^2 = 96,948.69 J
    So our answer is Water at the top of the Hoover dam is roughly equal to 97kJ .versus a bowling ball a half a mile up rolling down a 90 degree angle slope producing roughly 48KJ

    Are these numbers completely accurate? (of course not I never used collisions in two dimensions for the water to dam nor did I use Ideal fluids in Motion). But I do believe they give a good representation of rather or not Water on top of a dam could be used as an alternative answer.

    Given this information wouldn’t it seem reasonable that Water at the top of a dam possesses kinetic energy? If I’m incorrect on this information by all means please show me how I am wrong.

    Sincerely
    AJ
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 10, 2007 #2

    Astronuc

    User Avatar

    Staff: Mentor

    The correct answer to the question is "A. a ball rolling downhill" The ball is clearly moving.

    Water at the top of the dam is somewhat vague. Water at the top of a dam in a reservoir is not moving. For hydroelectric energy production, water is taken through pipes or tunnels at some depth below the surface of the reservoir since the pressure and potential energy increases with depth. Stationary water (stored) behind a dam possess gravitational potential energy with respect to lower elevations beyond the dam.

    Water could be spilling over the top of the dam, but it's not clear that is the inference in the question/problem.

    A bird perched is not moving - so no KE.

    A stick of dynamite is not necessarily moving - so no KE - but it posseses chemical potential energy

    A boulder resting is not moving - so no KE.
     
  4. Nov 10, 2007 #3
    The correct answer to the question is "A. a ball rolling downhill" The ball is clearly moving.

    Water at the top of the dam is somewhat vague. Water at the top of a dam in a reservoir is not moving.


    I disagree completely. Water not moving is called ice, freeze framed instantaneously at the exact moment the water is frozen. Once water is ice it even still continues to move either by melting or by condensing (think of a ball thrown into the air where it stops for a split second just before it begins it’s descend. The only way water does not move is if it is contained in pressure at absolute Zero. Water contains both potential energy and continuous kinetic energy.
     
  5. Nov 10, 2007 #4
    ok let us for arguments sake agree with your answer.

    How would you explain a ball rolling down a hill not having kinetic energy?
     
  6. Nov 10, 2007 #5
    ... you guys didn't even read my full post. Clearly if you had you would see that I am comparing the kinetic energy of a 20lb bowling ball being rolled down a 90 degree angle a half a mile up. Versus the kinetic energy being produced by water at the top of the Hoover dam with a depth of 1m and a width of 396meeters. please it is very important to fully read the post. I am merely stating that water at the top of a dam can just as easily be an alternative choice.
     
    Last edited: Nov 10, 2007
  7. Nov 10, 2007 #6
    It might be helpful to rename molecular kinetic energy "internal energy" or "thermal energy." Then only when some gross volume of water is moving do we say it has kinetic energy. Now we can understand water at the top of a dam, if it is not flowing, to have zero kinetic energy--and quite a lot of thermal energy. Of course, for the water to have no flow, we have to assume that there is no wind, no underwater motions, etc. But physics at this level is all about creating simplifications to approximately model reality, is it not?
     
  8. Nov 10, 2007 #7
    in my defense. I believe that water at the top of a dam produces more kinetic energy than a ball rolling down a hill. And I dumbed down my equations. I said nothing about when water creates small waves up against the top of a dam (and it does always). Water produces kineteic energy when it hits the side of the wall, when the water goes up breifly (as a small wave) when it goes to the left and when it goes to the right and finally when it goes down (sometimes repeating a few times)
     
  9. Nov 10, 2007 #8
    Ajwrighter...unless i missed it, you didnt add the potential energy of the ball...

    the should possess KE and PE since it is motion from a height.

    I agree with Cardini about the simplifications to approximately model reality.

    If I am not mistaken, the kinetic energy you describe at the molecular level of water is unusable therefore neglected? so the approximation would be correct that it has no KE.
     
  10. Nov 10, 2007 #9
    I guess you were just given a poorly worded question. It asks you to assume that there are no waves and is no flow; in reality, there should always be very small velocities of many small volumes of water.

    The thought process you were supposed to have was:

    Bird perched in a tree has potential chemical and gravitational energy,
    Dynamite has potential chemical energy,
    Boulder on cliff has potential gravitational energy,
    Water at the top of a dam has potential gravitational energy,
    Ball rolling down hill has kinetic energy.

    Of course, I would have chosen the stick of dynamite. My preferred inertial frame is the moon considered fixed, so the dynamite has a LOT of kinetic energy. Come to think of it, so does everything else. And the bird more so: in what inertial frame could we ignore its breath and heartbeat? Its blinking?

    I guess I'll have to start making more assumptions and simplifications.
     
  11. Nov 10, 2007 #10
    hmm let me make the question easier then. Water at the top of a dam does it have mass and does it have velocity if not, answer why.
     
  12. Nov 10, 2007 #11
    what about the blood inside the bird? it also possess kinetic energy.
    In my opinion, it doesnt say the water is flowing it just says at the top of the dam. so therefore no velocity.
     
  13. Nov 10, 2007 #12
    Remember that energy is conserved. When the water is at the top of a dam, it contains all potential energy. That is exactly what it stated. Unless if it specifically stated that the water was cascading from the dam, then we can assume that there's kinetic energy involved. The ball rolling down a hill clearly expresses that there is kinetic energy involved. So the answer should be 'A'.
     
  14. Nov 10, 2007 #13

    So what you are saying is that the water isn't moving. Its Ice, correct? Or has time stopped? But we have to assume its not ice and that its water and since water in its natural enviroment is constantly moving we can only assume that water (being a liquid) will always move. When we refer to water as water we think of a liquid form and not ice nor a gass. As a liquid (unless contained at a certain amount of pressure) will always move, Thus the term ball rolling and the word Water are directly related in terms of movement. Prove me wrong. Prove to me that water means stand alone object with no movement at all thus having no velocity. Prove to me that when the water that reaches the top of a dam from some point of origin and at the instant it is considered at the top of the dam has no velocity what so ever.
     
  15. Nov 10, 2007 #14
    um.. if u are persistent about arguing a problem because of details.. then by all means u should probably select the answer. I think the main point of the question was along the lines of-- which one of these objects have MORE kinetic energy relative to its potential energy.

    I mean for your argument's sakes, almost everything we see have some form of kinetic energy when its not on a closed system. BUT the ratio of KE/PE for the ball is FAR more than the KE/PE for the water at the dam.
     
  16. Nov 10, 2007 #15
    also.. i can make an argument that the ball is the size of a building.. and the dam is an experimental dam i made in my backward with tap water..
     
  17. Nov 10, 2007 #16

    Astronuc

    User Avatar

    Staff: Mentor

    No, it is not moving if it is in a reservoir behind a dam. Liquid water can sit still. I doesn't have to be ice.

    Look at water in a cup 'sitting' on a steady table. It is not moving. It has no kinetic energy!

    Now one can argue that everything has kinetic energy because atoms are vibrating and diffusing all the time. However, we consider this thermal energy rather than kinetic energy.
     
  18. Nov 10, 2007 #17
    But it doesn't, infact it asks "Which of the following is an example" and by example all of them posses kinetic energy.

    ok for arguements sake lets say the Question asked instead of
    1. Which of the following is an example of an object possessing Kinetic energy

    it asked

    1. Which of the following contains more Kinetic energy

    Before, I was generous giving the ball a height of a half a mile (which is considered a mountain and not a hill). Now lets give it what the question wants a hill. A hill before it becomes a mountain is 300 meters. Now how about the worlds largest ball? I found one that weighs 8000kg. Now roll that ball down a 90 degree angle at a distance of 300 meters. Now lets compare it to the worlds largest Dam (recently built in China.) its 2,309-meter-long. The average speed of the Yangtze River is about 1.3m/s. the density of water is 1. Now freeze frame a snap shot at which the water is considerd at the top of a dam verses a ball rolling down a hill (lets say the ball is at the very bottom of the roll for maximum KE) This time you do the math. Water still wins
     
    Last edited: Nov 10, 2007
  19. Nov 10, 2007 #18
    Astronuc you have a misconception of reservoirs. The flow of water from the reservoir through the dam is slowed down. At the reservoir the water can be held and released at anytime. However the speed of the water when it hits the dam through the reservoir doesn't slow down unless acted upon by another force. The resrvoir is still filling up it doesnt stop. If you are talking about the type of reservoir where it is simply redirected through piping from the dam itself than sure. but then your no where near the initial dam.

    A dam is a barrier across flowing water that obstructs, directs or slows down the flow, often creating a reservoir

    Reservoir is, most broadly, a place or hollow vessel where something (usually liquid) is kept in reserve, for later use

    thus the water at an instantaneous moment where the water is considered at the top of the dam has a velocity. I need someone else to give me a concrete answere that proves me wrong.
     
    Last edited: Nov 10, 2007
  20. Nov 10, 2007 #19
    Something which often becomes a problem for students in the sciences is trying to relate simplified concepts to specific real-world examples, with all of their complexities and peculiarities. Another is trying to read too far into a question.

    In the first, we often blind ourselves to the forest by introducing a lot of trees, as it were--we can't really deal with the real world; we need simplifications. In the second, we find that we can really pick anything apart into meaninglessness. The water could have kinetic energy, but it doesn't have to have it. Water doesn't have to have any gross motion. We can consider "water at the top of a dam" to mean hundreds of thousands of gallons, but we could also assume it meant exactly what is said--the few moles of water that actually occupy the very top of the water behind the dam. We can assume motion, or we can assume stillness; we can assume large motion or we can assume negligible motion. We can look at the molecular motion that the liquid state guarantees, or we can ignore it; molecular KE is relabeled thermal or internal energy. We can freeze-frame our water, assumed to be moving--but we must consider that in the freeze-frame, the water "on top" may need to be considered to be the infinitesimal cross-section we've frozen. We can assume the water to be flowing over the dam, or we can assume that the dam merely holds back a drying lake--not a river. Each assumption is equally valid. We face unlimited dichotomies, and lose ourselves in our assumptions. Is the water liquid or ice? The problem didn't tell us the state, so either assumption is equally valid. Either also has equal real-world relevance; a dam may contain a small or large amount of water at a small or great temperature. In what reference frame are we measuring energy? &c.

    In order to answer a simple question, we must usually think in simple terms. If the question involves a simplification, by abandoning that simplification we find ourselves answering a substitute question.
     
  21. Nov 10, 2007 #20
    the correct answer is A. Its a simple multiple choice question. It supposed to be worth one mark. Its just a straight foreward question. I agree with Astronuc.
     
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