Thursday, May 12, 2016

A Somewhat Tense Lab

A Somewhat Tense Lab


Procedure (1):


Weight Constant

  1. Make sure that the frequency adjuster and the measurer are synced up. 
  2. Attach the string to the frequency adjuster
  3. Place the 20 kilogram weight on the end of the string that is loose
  4. Put the string through the pulley so that is secured at the end of the table and the weight is hanging off of the table
  5. Shift the frequency so that there are three standing waves
  6. Adjust the tension of the string
  7. When the string reaches a point where there are 3 standing waves, measure the still space in between each standing waves to find the wavelength
  8. Repeat steps 5/6/7 till enough data is collected
  9. Fill in data chart
  10. Multiply the wavelength by the frequency to find the speed of each wave
Data (1):













Graph (1):




Procedure (2):

Weight Shift
  1. Make sure that the frequency adjuster and the measurer are synced up. 
  2. Attach the string to the frequency adjuster
  3. Put the string through the pulley so that is secured at the end of the table and the hanger is hanging off of the table
  4. Place the lowest weight onto the hanger
  5. Adjust the frequency of the wave until there are 3 standing waves
  6. When the string reaches a point where there are 3 standing waves, measure the still space in between each standing waves to find the wavelength
  7. Place the next weight on the hanger
  8. Repeat steps 5/6/7 till enough data is collected
  9. Fill in data chart
  10. Multiply the wavelength by the frequency to find the speed of each wave

Data (2):




Chart (2): 





Analysis:
While the formula to find wave speed is Wave Speed = Frequency x Wave Length, this does not mean wave length and frequency are indicators of where wave speed comes from. Wave speed is less telling of the wave that is moving than it is of the medium it is traveling in. Therefore, it is the density, mass, and tension of the string the wave is traveling through that effect the wave speed. If you were to image the same wave traveling through molasses and water, the waves may have the same frequency and the same wave length, but the speed the wave is traveling at is different. Our data further supports the relationship between the medium the wave is traveling and the wave. When the weight of the object is increased, it is clear that the speed is increasing too. This is because as the weight of the hanger increases, the tension of the string increases as well due to a higher weight pulling on the string. The graph supports this.









Friday, December 18, 2015

Justifiable? The Three Gorges Dam

Justifiable? The Three Gorges Dam

“There’s a kind of a balance sheet of benefits and liabilities that have come out of this project. My sense is that the Chinese government is getting better and better at collecting information about things like this. They know if they don’t fix these problems there will be dire consequences.” 
-Orville Schell

When the Three Gorges Dam (TGD) is mentioned in conversation, its name alone is almost always enough to invoke a grimace. The worlds largest dam, the TDG is internationally recognized and controversial, changing the landscape of what a dam is capable of doing and raised the question of constructional ecological morality. Human rights groups, wildlife preservationists, and many more have all condemned the TGD as a violation of almost all forms of life. Their claims are rationally based; looking at the 1.3 million people displaced (1), the hundreds of species wiped out by the disruption of the river, and entire ecosystems destroyed. Its cost a massive $22.5 billion over the course 17 years to build the 2.3 kilometer long dam blew economists out of the water (2). When looking at this, it makes one question why they built it in the first place. But like all controversial issues, the TGD is not a one dimensional problem. While it has caused problems, the TGD is the worlds largest clean energy producing hydro electric plant, a solution to annual flood seasons that have plagued river towns in China, and a massive boost to the economy. At the core of the debate over the TGD lies one essential question; can eco-friendly hurt one aspect of the environment if it helps another? How much good must something cause to outweigh the bad? The TGD has posed a moral and ecological predicament ranging between its destructive costs and revitalizing benefits. 

Before looking into the effects of the TGD, it is important to look at its history. The idea for a dam to reach across the Yangtze River was first proposed during the early 20th century. The Yangtze River was necessary for trade and agriculture, but also prone to dangerous floods that could wipe out towns. Dr. Sun Yat-Sen, one of China’s early modern industrialists, offered the idea to build a hydroelectric dam across the river to regulate floods and generate electricity. Roughly 30 years after this proposal, China began their first attempt to build the dam. However, due to civil upheaval the proposal fell through and was forgotten till the massive Yangtze Floods of 1953 that resparked interest in the building of a dam. Like the first attempt, the proposal was once again disregarded due to internal conflict and chaos from “the Great Leap Forward”. Finally, in 1994, construction began on the TGD, finishing 15 years later in 2009. Standing 2.3 kilometers long and 139 meters tall, the TGD continues to be a historical and engineering marvel of China. Requiring almost a century of processing, the TGD changed the landscape of the area around the Yangtze River forever. (3)

The first controversial topic of the TGD is its relationship with the people physically living around the Yangtze river. 1.3 million people displaced. It is difficult to even imagine the streams of people leaving any of the numerous cities, towns, or villages that were abandoned with the formation of the TGD. However, the living were not the only ones affected; several historical ruins of ancient China were destroyed and flooded by the building of the TGD (4). In response to the massive forced dispersal of Chinese citizens, the Chinese government promised reparations to those who were moved to replace the loss of a home, livelihood, and for many, the loss of a history. While sweet nothings of repayment were whispered, 20 years later it appears that most of the money has failed to reach those who needed it (5). There is no doubt that the rights of those who were forced to move were sacrificed for the building of the TGD.

While 1.3 million people were moved, they were moved to save lives. The Yangtze River has had a history of dangerous flooding, killing hundreds of thousands in the past centuries. In 1931, floods covered more than 804 square kilometers, destroying towns, farms, cities, and the landscape.The same floods of Yangtze river killed roughly 3.1 million people over a course of several months (6). But these are only two examples from a long history of deadly flooding. It is likely than the Yangtze will continue to flood, and as China becomes more populated, will be increasingly devastating. The TGD is an investment for the future, an investment in the saving of populations to come. 

It is difficult to balance population needs due to the mix of long term and immediate problems. The displacement of people points to immediate problems caused by the building of the dam, but the counter balance of this is the long term goal to save lives from floods. The intricate mixture of impacts is why the number of displacement becomes less relevant, and the larger context of long term life saving comes to context. Ultimately, it begs the question; does the displacement of people now equalize the saving of those who could be killed by floods?

The next negative effect of the TGD is on wildlife. Not only does the dam immediately threaten over 300 species of fauna and flora (7), but also the health of the river itself. Because the dam blocks the flow of water, fish can no longer migrate for breeding. Compounding the threat to the wildlife, the river itself has become polluted from construction. With ancient specifies such as the Yangtze River Dolphin already going extinct partially due to the formation of the TGD, it forces confrontation with the ever growing list of endangered/extinct species sacrificed to the building of this dam.  On top of the fauna in the river, plants on the river banks will also be affected. As sediment and nutrient rich sediment is unable to float downstream, plants will die on the sides from a lack of nutritious soil. (8) The TGD has permanently wiped out species, polluted the river, blocked fish migration, and is actively decaying the soil quality for plants on the river bank. 

But on the other hand, the TGD generates roughly 98.8 billion mWh per year — roughly 3% of China’s overall electricity— completely clean and hydroelectric. By increasing clean energy creation, China loosens their dependence on coal. As goal use goes down, so will acid rain and smog. The sheer amount of electricity generated by TGD is astounding, its 32 generators turn to generate the most electricity of any hydroelectric dam in the world (9). If the word eco-friendly is defined as “having a beneficial effect on the environment or at least not causing environmental damage,” wouldn't significantly reducing the emission of green house gases through a massive clean hydroelectric dam be eco-friendly?

The contrast of clean energy and wildlife destruction shows a deeper flaw in the term eco-friendly. If eco friendly can be having a benefit on the environment, then by that definition the TGD would be eco-friendly. However, the idea of something being eco-reasonable rather than eco-friendly, is a better term. Eco-reasonable would be something that while it does hurt the environment, its benefits provide sufficient advantages to create a net positive. Is clean energy more important than protecting wildlife? Is protecting wildlife more important than clean energy? Who decides which is more relevant? 

While the dam itself cost $22.5 billion, the grand total was far more due to reparations and rebuilding of the dam (10), the TGD was incredibly over budget and expensive. By the time the reparations, construction, movement, and more were finished, the TGD had punched a hole in the economy of China. With arguably misplaced funding, it is debatable how much of the allocated funds were actually spent efficiently on the dam. Besides the loss of money on the dam itself, the TGD affects farming and fishing in the Yangtze river. Farming downstream is considerably reduced due to the lack of sediment flow, causing the nutrients in the ground to not be replaced. Fishing for the entire Yangtze river will be devastated by the dam preventing fish migration, therefore the industry will be ruined. Whether it was the money sinked into the dam itself or the industries destroyed by the lack of unheeded flow, the TGD wrecked numerous economic functions. 

However, the TGD only hurt the economy in the short, but it is arguable that the TGD will have massive rewards in the long run. First off, the TGD will attract tourists because, well, it is a very big dam. People like those type of things. On top of tourism, the electricity generated by the TGD is renewable energy that is endlessly produced by the Yangtze river. Lastly, the calm waters created by the dam will allow easier trade in the damed section. From Chongqing to Sandouping the rivers depth and width has increased due to the stoppage of water (11). This stoppage has allowed bigger trading ships to travel; larger cargo boats can now go up and down the river. Larger cargo boats means more cargo, which means more trade, therefore more money. While China may be hurt in the immediate sacrifices for the building of the dam, it appears that it will succeed in the long term.
Like most of the issues surrounding the TGD, it is about the long term success verse the short term sacrifice. The incredible cost of the TGD is difficult to look past, but years in the future it will pay itself off. Thus the question is whether or not the suffering of the present is worth the success of the future. 

Now that these three conflicts have been laid out, it is up for you to chose how these balance out. What is important is to look at the pros and cons of the TGD with an unbiased and suspicious eye. In the context of the physical relationship with people who live in the area surrounding the Yangtze River, it is the weighing of short term displacement verse long term life saving. 1.3 million people is a lot of people, no one disputes that. However, it is critical to weigh the issue against the history of floods in the Hubei Province. The next contradiction presented was the issue of the environment and eco-friendliness. The Yangtze River has wiped out species, disrupted the ecosystem, polluted the river, and began dissolving the river bank. It has hit the flora and fauna around the river with deafening blows. But eco-friendliness isn't just about wildlife, the environment includes CO2 emissions and clean energy. The TGD has provided an immense amount of electricity for China, 3% of the overall electrical demands; all clean, renewable, and consistent. The TGD allows China to cut down on the use of coal, consequently, massively reducing CO2 emissions, which in turn decreases global warming, smog, and acid rain. Lastly, the conflict of the economic toll on China verse the potential for long term rewards was discussed. The TGD cost $37.23 billion, and in no way can all of it be properly justified.  However, the long term rewards of the TGD is based tourism, ease of trade, and electricity. As the TGD is the largest hydroelectric dam in the world, stretching over 1.4 miles, it has and will continue to be a tourist destination. With the Chongqing to Sandouping section being increased, trade will become easier and more bountiful. Then most obviously, the TGD will continue to be a massive renewable generator of clean energy. It is the duty of the people of the planet to weight these questions and seek to make the best choices. 


----------------------

Citations:
(1) "China's Three Gorges Dam, by the Numbers." National Geographic. National Geographic Society, n.d. Web. 16 Dec. 2015.
(2) "Dam Shame." The Economist. The Economist Newspaper, 06 July 2002. Web. 16 Dec. 2015.
(3) "Three Gorges Dam." About.com Education. N.p., n.d. Web. 11 Dec. 2015.
(4) "Waters of Three Gorges Dam Will Wash Over World Culture." Los Angeles Times. Los Angeles Times, 08 June 2003. Web. 15 Dec. 2015
(5) "Development–induced Displacement, Rehabilitation and Resettlement in India." (2011): n. pag. Web.
(6) "Yangtze River Peaks in China." History.com. A&E Television Networks, n.d. Web. 18 Dec. 2015.
(7) Three Gorges Dam Project, Yangtze River, China (n.d.): n. pag. Web.
(8) Hydrol. Earth Syst. Sci. "2006a, 2007a, 2007b; Chen Et Al., 2008; Xu and Milliman,." (n.d.): n. pag. Web.
(9) "Three Gorges Dam Hydroelectric Power Plant." Power Technology. N.p., n.d. Web. 18 Dec. 2015.
(10 The Three Gorges Shiplock In 2001, and (© Chris De Bode / Panos Pictures. Three Gorges Dam: The Cost of Power (n.d.): n. pag. Web.
(11) "Economic Issues." Economic Issues. N.p., n.d. Web. 18 Dec. 2015.

Sunday, November 8, 2015

Hanging Onto Physics: Hangers, Fixed Weight, Carts, Oh My

Hanging Onto Physics: Hangers, Fixed Weight, Carts, Oh My


Procedural Fun:


Experiment Set Up
Force Diagrams
First, we put the cart onto the rail (which was on top of the table) and the 2 heavy weights into the bed of the cart. Next we put the string through the pulley and connected the hanger to the string so that it was hanging off of the rail. We then put 5 20g weights onto the hanger.  hen the string was secured, we pulled the cart back so that it would be 50 cm (0.5 m) from the bumper. We then let go of the cart and timed how long it took to get to the bumper. We did two trials of this, then would transfer one of the weights from the hanger into the the bed of the cart. Repeated two trails with each round transferring an additional weight to the cart.








Data









It was Garett: Human Error

The only influential impactful form of human error I could think of would be possible timing errors due to the short span of time. The 0.5 meters leaves little room to prepare and time correctly. Other than that, it appears as if there was little chance for human error as the other elements of this lab were very controlled.



Slope of the Trend line: y = 0.91 * x
To Be Direct, Its the Second Law
The relationship between force and acceleration is described in Newtons second law as directly proportional. Force is equal to (mass)(acceleration), which means that in this experiment, because the mass is fixed, that the force and acceleration are directly related. The slope of the graph is 0.91, which should be 1, reflects the direct proportionality of the the acceleration and force.






























Wednesday, October 14, 2015

What the Frick is Going on with Fracking?

What the Frick is Going on with Fracking?
An Investigation into Energy Use


"Wikimedia Upload." Wikimedia Upload. N.p., n.d.Web. 14 Oct. 2015.

What is Fracking?

Before we delve into the effects and practicality of fracking, it is important to first understand what fracking is. Fracking is the process of drilling into the earth to form a well, then propelling a mixture (composed mostly of water) to break the shale shelf. When the shale breaks, it releases natural gas trapped below the earth, as the natural gas escapes it is harvested (1). Fracking is a highly efficient, low cost approach to capturing natural gas in mass quantities. However, fracking can also poison the ground and nearby water sources, creating environmental havoc. The term "fracking" is an abbreviation for hydraulic fracturing, but gained popularity as a name for the process as fracking gained notoriety in the news. 



Why is Fracking Controversial?

Fracking is not inherently bad, it is not some evil system of mining for natural gas that automatically destroys the environment around it. The issue surrounds a fluctuating rate of failure, and when it fails, fracking can displace masses of wildlife and people. While a study at Cornell warns that 40% of the fracking wells in Pennsylvania (specifically the Marcellus Shale Region) will most probably leak methane or other harmful chemicals, it also notes that only around 6% of the wells that are currently active have leaked (2). What does this mean? Are we on the precipice of fracking induced destruction? Is 6% larger than it appears? One of the main problems with the issue of fracking is that it is difficult to answer those questions in a completely decisive way. 



"Greenhouse Gas Emissions Lowest in 20 Years, Thanks to Natural Gas."ExxonMobils Perspectives

 Blog Greenhouse Gas Emissions Lowest in 20 Years Thanks to Natural Gas Comments. N.p., n.d. 
Web. 15 Oct. 2015.
Fracking: A Solution

"
Fracking Lies, Myths and Statistics: BS Detector." Fracking Lies, 
Myths and Statistics: BS Detector.N.p., n.d. Web. 15 Oct. 2015.
First off lets look at the positives of fracking; what is the appeal? Fracking is low cost, speedy, low carbon impacting, and extremely profitable business. It has had an undeniable effect on establishing the U.S as a provider of natural gas, allowing businesses to tap into the national abundance. Natural gas use lowers international dependence on other countries for energy, allowing the U.S to hold more cards in the game of diplomacy. Furthermore, techniques such as fracking have allowed an immense increase in the  harvesting of hydrocarbons, so much so that the price of oil has dramatically plummeted (3). Natural gas also has a much lower degenerative effect on the environment, as burning it is near harmless. We have reached a 20 year low in CO2 emissions, arguably from the increased use of natural gas as a cleaner alternative. As use of natural gas goes up, the use of coal and other more poisoned energy forms go down, a point that will later be explored into more detail. Other than the oddly climate beneficial effect (take note of the word climate, not environment), fracking helps the American economy. It has been predicted that natural gas will spark a 3% increase in the US's GDP by 2020, as well as creating a predi-cted 3.6 million jobs (4). With statistics like this, it is hard to see why fracking could be bad; but it is important to note that this is a part of the problem surrou-nding fracking, it is a polarizing technique with very definitive pros and cons.


Fracking: A Wrecking Ball
"These concerns include the potential for groundwater and surface-water pollution, local air quality degradation, fugitive greenhouse gas (GHG) emissions, induced seismicity, ecosystem fragmentation, and various community impacts. However, the scale of hydraulic fracturing operations is much larger than for conventional exploration onshore. Moreover ... [drilling] often literally in people’s backyards." -Annual Review of Environment and Resources (5)
As stated in the Annual Review of Environment and Resources, there is a vast array of complaints that stem from fracking. The first is water pollution due to cracks in the wells that can cause the water mixture used in fracking to poison the local aquifers and bodies of water. The water mixture contains many toxic and carcinogenic chemicals that when ingested or introduced to the water supply can prove catastrophic. When this occurs, wildlife suffers and families are often forced to move, scarring the environment. Similarly, fracking can release these deadly chemicals into the air, dispersing into the air quality of the area (6). While fracking and natural gas are better than other hydrocarbons, natural gas is ultimately still more dangerous than solar or other clean energy sources. Fracking has also been blamed for increasing the rate of earthquakes due to its destructive breaking of shale formations, loosing the rock and leaving areas more susceptible to seismic activity (7). Lastly, the physical closeness of these dangerous effects to environmental systems and communities poses a substantial threat. Fracking is not a light matter, posing serious environmental, ethical, and life threatening dangers.




U.S. Energy Information Administration, Annual Energy Review 2011,

Tables 1.3, 2.1b-2.1f , 10.3, and 10.4.
 The Prologue Ends Pt. 1: What is the Chart of Energy Consumption?

At first, this graph appears to be very complex, but upon further inspection it becomes increasingly simple. The right side sources are the different medians used to generate power. The sources are in descending order of use, with the most used being petroleum and the least being nuclear electric power. On the opposite side of the sources are the sectors. Sectors are general divisions within an economy. The lines connecting each are percentage lines. These show the percent used and the percent given, respectively sectors and sources. For those reading this who already understand what this infographic means and question why I spelt out what each aspect of it meant, the information locked within this graph is incredibly important.  Having a graph is step 1, understanding the graph is step 2.



The Prologue Ends Pt. 2: Analysis of the Chart of Energy Consumption 

When I first looked at the source side, my eyes zeroed in on natural gas. Why is this chart important in relation to fracking and the course society should take with handling it? Natural gas is in second place for the most used, demonstrating the point that it has become established as an essential aspect of energy consumption in the United States. While one could argue that fracking should be banned for its environmental effects, it is hard to rationalize this in front of the statistics saying that natural gas is effectively the second most needed resource in regards to energy consumption. Fracking is an essential process the cheapness, accessibility, and usability of natural gas in the United States. By banning its extraction method, natural gas prices would soar; thus ultimately hurting the Residential and Commercial Sector the most because it currently gets 75% of its energy from natural gas. Banning is unnecessarily harsh, as we earlier noted that the actual percent of leaks is relatively small (6% in Pennsylvania). However, that does not mean the current state of fracking wells is ideal. It could be argued that stricter regulation (checking wells to ensure that they are appropriately sealed and maintained), preventative legislation (confines are how close to people the wells can get as to reduce the possibility of forcing families away), and prosecution for damages (strengthen punishments for violations) would each help round out the issues surrounding fracking. Regardless of the pivotal role fracking plays in the current state of the American economy, lets say, hypothetically, we ban fracking. In return, a different source of energy is turned to. We would not be able to fill the void with petroleum as the price would increase without the check of abundant natural gas. The next place to turn to would be coal, an incredibly high CO2 emitting hydrocarbon that would do far more damage to the atmosphere than natural gas. Banning fracking ultimately hurts each aspect that banning it would be good. If you want to ban fracking to save the environment, it hurts far more to reinstate coal as a primary energy source due to its disastrous effects on the atmosphere. Banning fracking would destroy the delicate balance of energy we have reached. 


"Maps: Exploration, Resources, Reserves, and Production - Energy Information
Administration." Maps: Exploration, Resources, Reserves, and Production -
 Energy Information Administration. N.p., n.d. Web. 15 Oct. 2015.

Looking to the Future: Brighter, Gustier, Cleaner?

Is banning fracking a viable way to fix the issues it causes with the environment? Absolutely not. Natural gas is an efficient, effective, and cheap alternative to harsher hydrocarbons. However, this is not the final state of energy consumption. For the moment these points stand true, fracking is too essential to the economic success of our nation, as well as serving as a type of buffer on hydrocarbon emission. But as clean energy continues to make strides, it is not unreasonable to hope for the eventual implementation of a fracking free world. Till then, chose the shale region you live on wisely. 
















Citations:
(1) "What Is Fracking and Why Is It Controversial? - BBC News." BBC News. N.p., n.d. Web. 14 Oct. 2015.
(2) "Four of 10 Wells Forecast to Fail in Northeastern Pa. | Cornell Chronicle." Four of 10 Wells Forecast to Fail in Northeastern Pa. | Cornell Chronicle. N.p., n.d. Web. 14 Oct. 2015.
(3) "10 Reasons Fracking Improves American Lives - Drillinginfo." Drillinginfo. N.p., 05 Oct. 2012. Web. 14 Oct. 2015.

(4) "America's Energy Seen Adding 3.6 Million Jobs Along With 3% GDP."Bloomberg.com. Bloomberg, n.d. Web. 15 Oct. 2015.
(5)  Annu. Rev. Environ. Resour. 2014. 39:327–62
(6) 2014, December. Fracking Fumes: Air Pollution from Hydraulic Fracturing Threatens Public Health and Communities (n.d.): n. pag. Web.
(7) "Injection-Induced Earthquakes." Injection-Induced Earthquakes. N.p., n.d. Web. 15 Oct. 2015.











Sunday, September 20, 2015

A Rolling Marble Gathers No Moss


A Rolling Marble Gathers No Moss: 
The Ramp Lab

Procedure:

Procedure:
1) Decide on 3 different types of ramps with varying arrangements to test (see picture)
 2) For each ramp type release the marble from the edge of the tallest book 
4) Start timer as the marble exits the ramp and begins rolling across the table
5) stop timer as the marble reaches 1.5 meters
6) Repeat twice for each Ramp Type/Height

Synopsis of the Procedure:
Our group decided our three ramp types (pictured) and combined two tables to make space for our ramp. We chose one marble to consistently use, as well as establishing where the ramp would always end. After setting up the ramp, we placed the meter sticks for the total of 2 meters, with the intention of only measuring 1.5 meters. We started with Ramp Type 1 Height 1, and proceeded to do two trials for each height of each Ramp Type. I would release the marble at the edge of the highest textbook, the marble would roll down the ramp, my partner Garrett would start the stopwatch as the marble began rolling onto the table, Garrett would stop the stopwatch as the marble passed 1.5 meters, and our other partner Allison would then write down the data. We repeated this process for the entirety of the trials with the same materials.


What do these graphs tell us?

When looking at these graphs it becomes very apparent that the height of the graph is far more important than its form. Across every type of ramp, there is a noticeable increase in speed for each height. The location of the points on these graphs tell us that height of a ramp and speed at the end of a ramp are directly related. It could also be assumed that there is a not a connection between length of ramp and speed at the bottom of a ramp. There appears to be very little evidence of a connection between the two, and if there is one, it is probably
negligible. It should be noted there is a break in this pattern between Ramp 1 Height 2 and Ramp 1 Height 3 where it appears that their averages are the same. However,  it is debatable as to whether this discrepancy actually roots from a possible mis-click on the timer or another form of human error. Disregarding this once instance, it appears from the data and the graphs that their is a strong link between height of a ramp and the speed at the bottom of the ramp.





Speed

Height

Ramp Type

1.03

2

1

1.05

2

1

1.46

3

1

1.29

3

1

1.42

4

1

1.39

4

1

1.05

2

2

1.17

2

2

1.43

3

2

1.17

3

2

1.46

4

2

1.53

4

2

1.1

2

3

1.06

2

3

1.24

3

3

1.24

3

3

1.74

4

3

1.53

4

3

0

0

N/A



An Exponentially Important Graph


With an exponential trendline in place, it becomes incredibly visible that ramp height and the speed at the bottom of the ramp are exponentially related. What this means is that as ramp height gets higher and higher, regardless of the length of the ramp, the speed of the marble will increase even more. A drop down the curve of King-Da-Ka at Six Flags and a roll down an equally tall, but longer, ramp will yield the same speed (although I am sure the wait time to get on King-Da-Ka and the time it takes to slide down an incredibly long ramp would be about the same). By the end of the longer ramp, you will generate the same amount of speed as King-Da-Ka because, as proven in this lab (and disregarding all friction/other slowing factors), length of ramp is not important, height is.




A Straight Line: Speed Squared


Speed squared, the diagonal line, what does that mean and why is it important? Before we look at speed squared, lets first investigate the relationship between another similar phenomenon, radius squared and its relationship to a circle's area. The graphical pattern between radius and area of a circle is an exponential curve, but more importantly, when the radius is squared, it becomes a diagonal line with a constant; a constant that roughly equals 3.14, and is commonly abbreviated with the symbol π. Following the formula for a line (y=mx+b), with a y-intercept of zero, the equation of the graph of radius squared to area becomes A=πr^2+0, or more commonly known as A=πr^2. When we take this approach to the graph of speed squared, in a world of perfectly accurate statistics and data on a high school lab, we should get H=9.8s^2+0, or H=9.8s^2. Just like radius squared, this number is not random, 9.8 m/s^2 is the approximate value of earths gravitational pull, the force that would act on a marble rolling down a ramp. The relationship between speed at the bottom of ramp squared and height of the ramp are connected by the gravitational force, forming a perfect diagonal line.