So this next post is going to be about this video I recently saw on YouTube. Is it about a musical machine that this guy made that makes music with 2000 marbles. Well here is the video.....
So as you can see there is a lot of physics going on here. We are going to look at just a little bit of it. So here we go...
So the first thing we are going to look at is the falling marbles. Now if we assume the the machine is about 2 meters tall which seems to me like that is a pretty good guess. We can find out using some video analysis that the balls fall about .5 meters. Now when the marbles are in the air they are just projectiles. Which as we talked about last time means that gravity is the only thing that effects them and as we also learned last time that means their acceleration should be 9.8 m/s2. After doing a bit of video anaylsis with video tracker (free physics software downloadable here) and plotting the data here.
We find that the acceleration which is 2 times the number in front of x2 which is exactly 9.8 m/s2. So our guess that the machine was 2 meters tall was a good guess it turns out. Now the energy that the ball has before it falls is called gravitational potential energy. When it falls that potential energy gets converted to kinetic energy, the energy of motion. This is due to the conservation of energy. Energy can not be created or destroyed. This conversion is not quite 100% due to air resistance however I think that we can ignore it in this case without too much error in our calculations. We can calculate how much gravitation potential energy something has by knowing it's height and mass along with the acceleration due to gravity. The equation to calculate Gravitational potential energy is...
We find that the acceleration which is 2 times the number in front of x2 which is exactly 9.8 m/s2. So our guess that the machine was 2 meters tall was a good guess it turns out. Now the energy that the ball has before it falls is called gravitational potential energy. When it falls that potential energy gets converted to kinetic energy, the energy of motion. This is due to the conservation of energy. Energy can not be created or destroyed. This conversion is not quite 100% due to air resistance however I think that we can ignore it in this case without too much error in our calculations. We can calculate how much gravitation potential energy something has by knowing it's height and mass along with the acceleration due to gravity. The equation to calculate Gravitational potential energy is...
Where m is mass and g is the acceleration due to gravity and h is the height above some zero point. I really have no idea how much mass one of those marbles has but if you look at the equation for kinetic energy which is...
And then solve for velocity you will realize that the mass will cancel out and you will get....
Which means that one of the marbles will have a velocity of 3.13 m/s when it hits the xylophone. Given that the acceleration due to gravity is 9.8 and it falls for about .5 meters. Now because the guy that made this machine also made 2 other videos that goes though the mechanics of the machine I found out that the marbles are 11 mm diameter steel ball bearings. So if we take the diameter divide it by 2 we get the radius and if you plug the radius in this equation..
You get .69691 cm³ then if you times that by the density of steel (7.85 g/ cm³) then you get 5.47 g per marble. Which means the marble has about 27 J of energy that could be converted to sound. Now how much of that energy is turned into sound and how loud that sound would be if all turned into sound is a much more difficult problem which I will save for another day but I think that this is a pretty thorough analysis of the velocity of the marble and how much energy the marble has at the points of most interest to me. Thanks for reading to the end even if in the middle there it got be to more equations than writing and the fact that the most interesting thing about this post was that there was a really cool video at the beginning of it. I really just wanted to show all my millions of readers the video and to be able to talk about it in a some what physics way. If you are more interested in this machine which I hope you all are then the other two videos that really explain the mechanics of it are here and here and if you just want to hear the music in a loop for 10 hours then there is this video. Which I really don't understand why anyone would do that but there you go.
This is Marble-ous!
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