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Item traveling through water via gravity.

  1. Mar 12, 2009 #1
    I started to post this in the homework area but it is a square peg and that is a round hole.

    My son (6th grade) wanted to observe what would happen when he dropped a marble and a penny into 8inches of water from 20inches above the water and .5 inches above the water.

    With the marble he found that it traveled through the water about twice as fast when dropped from the higher level. The penny though was about 20 % faster from on high. Bottom line is he is having hard time understanding what forces are at work here and how he can explain it to other 6th grade students.

    Any help breaking this down in layman's terms would be appreciated.
     
  2. jcsd
  3. Mar 12, 2009 #2
    I think there are just three forces acting on the objects as they travel through water, although there could be something going on at the instant that the object impacts the water that could add complexity - I'm going to disregard this for now.

    You'll have gravity pulling the object down, and you'll have a bouyant force pushing the object up. This force is equal to the weight of water displaced by the object, so this will be the same regardless of how fast the object is moving. The third one is the drag force, which I suspect is where the difference is.

    This drag force is proportional to the square of the speed of the object, the cross sectional area, and is dependant on the object's shape. The portion that is dependant on the object's shape we call the Coefficient of Drag. Since air resistance is small enough to neglect, we can say the objects will impact the water at the same speed when dropped from the same height.

    If the penny is moving slower, a reasonable conclusion might be that the penny has a higher coefficient of drag, this it slows quicker upon entering the water.

    Since the penny is not symmetric about all of its axis, it's rotation will have a large impact on the drag force. As it rotates, the effective cross sectional area changes. It will also create forces that make it tend to move sideways and rotate more. Another reasonable conclusion might be that because it is rotating and moving side-to-side, some of it's energy is being "wasted" on these other motions, instead of moving downwards.

    -Kerry
     
  4. Mar 12, 2009 #3
    Kerry,

    Thank you, I think this sums up nicely the difference between the two objects. What about the marble by itself when it drops from a higher level why is it so much faster, in science terms that a 12yr old can grasp. Is it possible that if dropped from high enough the marble would shatter and lose its momentum to where the lower dropped marble might beat it to the bottom? Just curious.
     
  5. Mar 12, 2009 #4
    The higher the item is dropped from, the faster it is going when it hits the water. That is why they travel faster through the water when dropped higher. The water should slow the object down, if you had deeper water you would probably notice that they went close to the same speed after the first couple inches slow it down.

    As for shattering, I'm not sure if you mean upon impact with the water or the bottom. It could be possible to shatter the marble if it were going fast enough, but as long as you are dropping it through air drag will give it a terminal velocity. In other words you'll reach some height where the object won't travel any faster the higher you drop it.
     
  6. Mar 12, 2009 #5

    Andy Resnick

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    The marble is easy to discuss becasue of the shape. The speed that the marble (and penny) has at impact is proportional to the square root of the height- 4 times the height doubles the speed at impact to the water.

    Then the marble hits the water, slows down, and reaches a new terminal velocity which depends on the diameter and mass of the marble. What happens in between is fairly complex because of the turbulent flow, splashing, and other dissipative processes that occur.

    The penny is *much* more complicated because the penny can flip, which creates huge changes in the drag force. Consequently, a good experiment to perform would be a marble and a disk with approximately the same diameter and density (a dime?). Also, dropping the disk edge-on vs. face-on would be interesting.
     
  7. Mar 13, 2009 #6
    Perhaps you could do it with two different sized balls. The experiments would be much more consistent than with a disc-shaped object (a penny).

    Like the others said, the penny is very hard to explain due to the flipping. There is magnitudes of difference in drag between the penny traveling horizontally and vertically. It can be compared to someone doing a belly-flop or an Olympic diver. It's obvious how different your results may be.

    If you had differently sized or weighted spheres the experiment would be very interesting. You could drop them from a certain height and show that no matter what the weight or size, they always hit the water at the same time. Then you could also show that a heavier ball will hit the bottom of the water more quickly. This is because there is a greater difference in weight (aka the force of gravity) and buoyant force. As someone else said, the buoyant force (the force that makes the ball want to go up) is proportional to the amount of water it displace (the volume of the object) and is the same no matter what the weight.

    It might be a little much for a 6th grader to conceptually grasp unless you have an extremely gifted child. Still a fun experiment nonetheless.

    But most importantly, make sure your kid has fun doing it! :D
     
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