Sunday, December 24, 2023

Why Would Gyges Act Justly When It Was Much Easier To Act Unjustly?

 Final Paper, Introduction To Ethics, Fall 2023

Student: John Gibson

Professor: John J Kagg

University Of Massachusetts, Lowell, Dec 09, 2023

Why Would Gyges Act Justly When It Was Much Easier To Act Unjustly?

My study buddy, Dutt, a very intelligent man with wisdom, posed the question during brainstorming in Introduction To Ethics class. Dutt has good judgments on when to speak and when to keep silent. The question was well received in class. This essay is my attempt to answer my study buddy’s question.


News headlines like “Elizabeth Holmes sentenced to 11 years in prison for Theranos fraud” are common in science and engineering businesses (Allyn, 2023). Elizabeth Holmes is a Stanford Chemical Engineering Department-trained engineer who should know best about conducting engineering businesses. Many other engineering school graduates from the University Of Massachusetts system may end up in jail if Elizabeth Holmes is in jail. How other “regular” engineers steer clear of trouble, prosper, and have fulfilling lives is a mystery. I am a computer tech worker specializing in small data center setup and maintenance. My affiliation is Cisco Certified Internet Expert, ranking ID number 18497. People in my trade practice “erring on the safe side” and sometimes exaggerate their work's difficulty and problem scope to obtain earmarks on budget and schedule. In engineering-oriented ethics classes, such as Engineering And Ethics, most engineers are trained, by trade, encouraged to use their instincts trainings to reason the long-term outcome of career conduct options. Exaggerations of the difficulty and problem scope of work orders are bound to possible reality, not outright lies. Elizabeth Holmes surrendered to federal prison in May earlier this year, but no one in the office gossiping ever talks about it. Christmas office luncheon came and went. People got alcohol and blacked out and woke up—still no talks about it.

My thesis is that engineers, engineering professors, and professionals are tight-lipped, shrouding the whole issue in mystery. Talking about it should demystify it.

In engineers' minds, I can only assume that the Gyges’ ring is deemed a cheating scheme, a gimmick to be tossed away immediately by instinct and never talked about again. There are advantages to having physics and math instincts in philosophy. Instincts Trained instincts react fast. Calculus classes train professional engineers to figure out, fast, the slopes of a curve with a continuously changing slope when the distance between two points on the x-axis is infinitesimally small. No human or instrument can see the infinitely small distance between two objects, but Rene DesCarte’s “I think, therefore I am” shows reasoning can be true beliefs, in stark contrast to “seeing is believing.” However, trained engineers perform all the calculations and all the reasoning within split seconds without conversing with anyone around and sometimes without even a pencil or a piece of paper—all done by mental math. Maybe I am still a trainee engineer, and Gyges’ ring doesn’t have to be outright dismissed as a gimmick to me. I can look into the legends and stories of the invisibility ring and talk about it. I think I am at the sweet spot of being less tight-lipped and still keeping my job when I say something wrong.

Six Thousand Years Ago - No Answer

In my opinion, the tight-lipped psyche may be correlated to the rigid social structure of the past, at least in the collective consciousness of the Western world. The Roman soldiers and citizens threw slave gladiators into the coliseum to be killed by the beasts; slaves were not allowed to rebel. In J.R.R. Tolkien’s Lord Of The Rings, hobbits were stereotyped to have large feet and presumably didn’t intermarry with humans. And, for an immortal Elf to marry a human, the Elf needs to give up their immortality (Jackson, 2003), illustrating the attempts to partition the groups rigidly. A rigid social structure may give a sense of powerlessness for social movement, and hence withdraw and tight-lipped quiet life.

I rented Peter Jackson’s adaptation of J.R.R. Tolkien’s Lord Of The Rings in a trilogy of films over the Thanksgiving recess, averaging about three hours per installment. Chronologically, of the stories’ action time, the three films are Lord Of The Rings: The Fellowship of the Ring, The Two Towers, and The Return of the King, according to J. R. R. Tolkien's letters of correspondence with publishing outlets, the story of the ring of invisibility power started six thousand years ago (Tolkien, page 708iv). There were twenty rings, hence the plural “Rings,” but only one out of the twenty rings gives invisibility superpower in the three films. This special ring is the One Ring. This setup was similar to Gyges’ ring, where only one ring conveyed invisibility. There were numerous scenes where the invisibility was depicted. One of the most memorable was in The Fellowship of the Ring, with CGI manipulation, Frodo, the ring bearer, accidentally tossed the One Ring in the air, then accidentally wore it and became invisible. 

The similarity between Gyges’ ring and the One Ring was uncanny. In both mythologies, the wearer interacted with the physical world unimpeded, including senses of touch, during invisibility. For example, near the end of The Two Towers, Frodo left footprints on the dusty stone floor. The creature Gollum followed the footprints to locate the invisible Frodo, fought the invisible Frodo by touch, and bit off the One Ring forcefully.

The wearer behaved unjustly in both Gyges’ and One Ring’s stories. The original wearer of the One Ring was Sauron, who used the ring to control the races of dwarfs, men, and elves. The unjust acts by Sauron were described as “cruelty” and “malice” in the screenplay of The Fellowship of the Ring (Jackson, 2002). They were depicted as arsons and displaced families in the film.

The contrast between Gyges’ ring and the One Ring was that the One Ring had explicit corrupting power while Gyges’ ring allowed the wearer to act justly or unjustly by himself or herself. The One Ring was created by Sauron and only served Sauron’s spirit after his physical body was destroyed. Any other wearer of the One Ring became an instrument of the evil spirit of Sauron; as Frodo said, “The Ring will not save Gondor. It has only the power to destroy” (Jackson, 2003).

The burden of morality of the One Ring was apparent and inevitable. The One Ring was said to communicate telekinetically, with global positioning capability, of its location to Sauron whenever worn. The wearer was then pursued by Nazguls, servants of Sauron, and the wearer’s life was in peril when Nazguls tried to take back the One Ring by force. Frogo, the ring bearer, was stabbed by a Nazgul once, which gave Frogo permanent pain in the shoulder for the rest of his life. The film's target audience included younger age groups, so outward pain directly conveyed the morality problem metaphorically.

The morality problem of the One Ring followed the same logic as Gyges’ ring despite the differences in story-telling techniques. The burden of the One Ring bearer was their constant struggle to reframe themselves from using the ring’s superpower and becoming a servant of evil. To manifest such a burden explicitly, the film transformed the people and creatures near the ring into different tormented forms in numerous scenes. For example, the beautiful forest elf princess Galadriel became a green hag fading out of physical existence for a few brief seconds when she was alone with Frodo and the One Ring, intending to give Frodo the gift of Earendil light but inevitably placing herself in proximity and convenience to take the One Ring for herself. The burden of Gyges’ ring was the obligation to wage, just or unjust, wars and fight battles after becoming the king of Lydia. Kings were winners of political-military battles and must continue their winning streaks to maintain the kingship. The person with invisibility was not invincible, and the ring's wearer could still be injured. In One Ring, Sauron’s finger that wore the ring was cut off during a battle. Gyges also died in battle after becoming a king in legends (Bury, 1975).

Both Gyges and Frodo succumbed to the burden of morality, unfortunately. In the legend of Gyges, Gyges used the ring for unjust acts, killing the old king of Lydia to claim the throne for himself. In One Ring story, the film used plot twists to obscure Frodo’s failure in the scene at the volcano summit to toss the ring into the lava river to destroy it. Frodo was incapacitated by dehydration and exhaustion before reaching the summit of the volcano Mount Doom and was carried by Samewise to the summit. It was questionable how Frodo could stand on his own feet in front and above the lava river, hence the excuse for the immoral act of claiming the ring for his own and putting on the ring to become the servant of the evil of Sauron’s spirit, albeit only for a few seconds. It was repeatedly planted in the film that a few seconds' lapse into evil was not a true moral failure, such as Galadriel’s few seconds' lapse and quick recovery when gifting Earendil light to Frodo. However, Frodo's failure to voluntarily toss the One Ring into the volcanic lava was evident. Tossing the ring into the lava river was an accident, not voluntary, when Gollum and Frodo fought and wrestled to take the ring from each other in front of the lava river.

Frodo failed the morality test. There was no answer: Why would Gyges act justly when it was much easier to be unjust? The only sentence Froda said before he put on the invisibility ring to become a servant of evil was, “The ring is mine.” There was no reasoning, inner dialog, or argument, just a 4-word statement, nearly silent.

Twenty-seven Hundred Years Ago - Still No Direct Answer

I watched Yale University professor Tamar Gendler’s YouTube presentation to refresh my memory about Gyges' legend (Gendler, 2012). The legendary Lydia king Gyges claimed the throne of Lydia around 680 BCE (Bury, 1975).  2023-(-680)=2703. Glaucon, Plato’s cousin in Plato's Republic, retold the story. The shock I received when I first read Republic’s translated text about Gyges was the ample freedom given to Glaucon to argue that justice was a social contract even though Socrates and Plato do not agree with Glaucon. As a writer, Plato spent pages upon pages and hours upon hours of time recounting Glaucon’s words which confused me as to whether Plato supported or opposed Glaucon’s view. Parchments would be expensive to document an idea a writer didn’t agree with, and Plato spared no money in documenting Glaucon’s words and possibly even elaborating upon it. I later learned that Philosophy was about charitable debates, and giving the opponent ample freedom to make their argument was possibly the tradition established by Socrates and Plato. There was no question that Gyges used the invisibility ring for evil in the legend, as evident in the book Republic’s text and as presented by Yale University professor Tamar Gendler (Gendler, 2012). So, there was still no answer to the question: Why would Gyges act justly when it was much easier to be unjust?

Gyges’ failure to act justly or throw away the ring was similar to Frodo’s and Sauron's failure in Lord Of The Rings. What kind of burden did one endure by cheating in a more realistic setting, such as murdering a king in Gyges’ legend, The advancement Plato’s Republic made was the realistic setup, as opposed to the fantasy writing that is the Lord Of The Rings?. In the real world, there was no magic power to turn a person pale green, like elf princess Galadriel, when cheating. One thing modern people could cheat perfectly was doing online transactions. Militaries hack enemy states online, and people book tickets and buy goods online with discount cheating techniques. Ideally, they should do all transactions on public WiFi so that all activities are not traced back to the home modem. Airlines had an anti-skip-lagging policy against booking a cheap flight to a less desirable destination and leaving the flight at a desirable point that was a flight connection. It was burdensome to try to evade detection, though. For example, I could put on the invisibility ring to go through the airport security gate to the flight, and airline staff would mark me as a “no show.” I could go to the plane’s lavatory while invisible, emerge as a visible passenger, and take the flight. But I had to be careful in booking the flight during peak days and seasons because the airline could overbook the flight and reassign my seat to another passenger if I was marked as a “no show,” when I emerged from the bathroom, I wouldn’t have a seat. 

To give ample room for Glaucon’s argument, Yale University professor Tamar Gendler created a table of Glaucon’s logic showing that acting justly was on par with taking medicine, which was only instrumental in Figure 1 (Gendler, 2012). Taking medicine normally would make a person heal from sickness, just like acting justly normally would steer a person away from criminal charges. When there was a way to act unjustly perfectly, Gyges opted to act unjustly and still became a great king. Likewise, if there was a way to avoid medicine perfectly and still be healthy, people would skip their medication and stay healthy. Dr. Tamar Gendler proceeded to present the University Of Kansas’s psychology research that showed that when not monitored, most people took advantage of anonymity to give themselves more lottery tickets than to an anonymous partner equally participating in the same psychology test task (Gendler, 2012). Undoubtedly, most people were immoral, as detected in the psychology test, so governments monitored citizens with drivers' records, and constitutions of modern states tended to make checks and balances in government structures. Plato and Socrates discussed the property of justice in the real world. The real world was more complicated than logic tabulations. Cheating in the real world had burdens on cheaters. So, in addition, Plato and Socrates had more words to say about the meaning of justice. The intrinsic good was different from the instrumental good. Yes, justice and checks and balances were often only as good as bitter medicine, but acting justly had intrinsic goodness, like being able to see clearly to enjoy the view of nature. If everyone acted justly, there would be no more theft and robbery, crimes would cease, and people would live well hypothetically in Kallipolis. There was a connection between the humble Hobbit, Frodo's lifestyle, and intrinsic goods. They both meant peace. They both mean living within their means. Frodo was entrusted with the duty of bearing the One Ring, not wearing it, and carrying it to the volcano to get it properly destroyed. Powerful wizards in Lord Of The Rings, such as Gandalf, were not entrusted with the duty of the ring bearer because powerful wizards chased after instrumental goods to gain ever more power. The concept of intrinsic good brought to light the possibility of rejecting the extrinsic good and instrumental pursuit of power, money, and lust.

But I trust Dr. Tamar Gendler’s research showed that plenty of people acted unjustly when unmonitored in all psychological tests, even if it was possible to reject extrinsic goods.

After exhausting all the words Plato and Socrates say in the Republic, the Republic’s city-state, Kallopilis, was a hypothetical country. Still, there was no direct answer to the question: Why would Gyges act justly when it was much easier to be unjust? According to Glaucon's dialogues, there were pages upon pages of inner reasoning as to why justice is merely a social contract. That was still not enough. There was not enough transcendental reasoning for Gyges to act justly.

One Hundred Seventy Years Ago - An Answer And A Disjunction

David Thoreau studied philosophy and science from 1833 to 1837 at Harvard College and was considered trained to become a scientist before the term “scientist” was coined, according to Andrea Wulf’s essay “Walden Wasn’t Thoreau’s Masterpiece” (Wulf, 2017). The term “scientist” was coined in 1834, while David Thoreau’s study at Harvard started in 1833 (Wulf, 2017). David Thoreau was not tight-lipped and wrote more than two million words in his nature journals. According to Andrea Wulf, the journals were “true ecological” journals before the term “ecology” was coined (Wulf, 2017). The term “ecology” was coined in 1866, while David Thoreau started the journals two years after he left Walden Pond in 1849. 2023-1849=174. According to Andrea Wulf's essay, David Thoreau was a few years younger than Charles Darwin and studied Darwin’s essays. There could be some sense of empowerment when David Thoreau was the first generation of Harvard graduates to be called “scientist.” In my experience in writing prose-form biological science experiment reports, I felt less tight-lipped when I used words like “goal of this study was achieved” in the conclusion section of my DNA molecule modification-assembly lab report (Gibson, 2022). Science professors praised my assertive writing style and gave me high grades. I got an A for the report and felt like the king of science. It was not hard to imagine the joy and sense of empowerment David Thoreau experienced when he figured out the germination temperatures of different plants and the timing of frog trumping concerning plant productivity. David Thoreau started journaling about nature before he went to live by Walden Pond (Wulf, 2017), and he felt that he was a “monarch” in terms of personal sovereignty in the Chapter “Where I Lived, and What I Lived For” of Walden (Thoreau, 1995). I use a Linux computer’s “wc” program to count the number of words in the book Walden, and there are more than one hundred thousand words. There is likely more than a generous amount of inner dialogue.

This new monarch king differed from Gyges’ or Frodo’s experience in the Lydian or Gondor wars, respectively. There was no war to wage against any enemy in 1845-1847 for David Thoreau. I had no perpetual streaks of goals to pursue in 2022 because the semester ended soon after the lab report was submitted, and I went back to study engineering. It was just the sense of empowerment from natural science. 

This new monarch king differed from Kallipolis of The Republic because Walden was non-fiction in the genre, Walden Pond in Concord was just 30 miles south of Lowell, and my lab report was true and real, both by “seeing is believing” and reasoning for true belief. But nothing hypothetical at all.

David Thoreau would not need to use an invisibility ring as Gyges did when David Thoreau was already a sovereign monarch in the Walden world. When asked what I would do if I had the invisibility ring, I answered, “I toss it away.” 

If David Thoreau were forced to wear the invisibility ring and become invisible, he would not be able to interact with the farmers who tried to sell farms to him. David Thoreau would not feel the sense of monarch when he released the “ten dollars” hold of the land after the farmer regretted the sale in the Chapter “Where I Lived, and What I Lived For” if he was invisible.  If I were forced to wear the invisibility ring and become invisible, I would not be able to receive an A-grade for my work because I would be marked absent for the lab experiment. After all, the lab teaching assistant would not be able to see me if I was invisible. In either case, nothing would be done unjustly by either David Thoreau or me. It would be a senseless loss of empowerment with invisibility when David Thoreau and I both wanted to feel present and be seen.

However, there were disjunction problems, as Andrea Wulf pointed out in “Walden Wasn’t Thoreau’s Masterpiece” of the process of pursuing natural sciences. David Thoreau doubted and questioned himself if he should immerse himself in microscopy, studying for the tiniest details of organisms, when he said he pursued “heaven’scope” (Thoreau, 1995). The studying of the tiniest things, the quantum realm, could be an endless pursuit require more computing power than what exists on Earth. The DNA assembly I made, was only inferred as a success, and I have no quantum physics knowledge to know how the electrons move to make the assembly that was actually performed by a life E. coli bacteria. “Inference” means guessing, by definition. For engineering students, many classmates know that memorizing formulas is unavoidable to pass exams. The integration formulas of trigonometry and logarithms were too time-consuming to be derived and figured out during an exam. Memorization is sometimes disguised as reasoning. And quantum physics-related equations are probability-based. What was “impossible” in one engineer’s guess might be possible in another’s. Despite the setbacks, David Thoreau would not stop talking and writing until six months before his death (Wulf, 2017).

Seven Months Ago

Elizabeth Holmes surrendered to Bryan Federal Prison Camp, Texas, on May 30th, 2023, with tightly sealed lips. I sifted through news outlets and could not find statements made. Stanford Business School’s news report “What Can We Learn from the Downfall of Theranos?” stated that the culture of secrecy in Theranos brought down their business, by reporter Sachin Waikar (Waikar 2022). There is some contrast between the openmindedness of ecology journalism and the tight-lipped corporate world. Secrecy means silence, bottling up problems to himself or herself. Gyges killed the old Lydian king in total secrecy. In stark contrast, ecologists and environmentalists like Greta Thunberg are very outspoken people. Greta Thunberg talked about her truancy in the European Parliament Economic And Social Committee and published her speech “You're Acting Like Spoiled, Irresponsible Children” (Thunberg, 2020). 

The Wall Street Journal investigating reporter John Carreyrou gave a speech about his findings with colorations collaborations with whistleblowers at the University Of Corolada Colorado, Denver, shortly before Elizabeth Holmes was sentenced in 2019 (Ramsdell, 2019). The word “secrecy” was brought up again, but John Carreyrou stressed that Elizabeth Holmes had no “intent” to defraud investors or malicious intent, at least initially. The Silicone Valley anticipated a “female Steve Jobs” to join the ranks of great inventors and visionaries, who were all men. Blood testing technology, demanding high precision, and purity, might be more complex than DNA assembly modification that is an E. coli bacteria bath of industrial mutagenic chemicals. An undergraduate should not be expected pressured to lead an industry where workers have Ph.D in chemistry; many are older men. Elizabeth might not be able to speak up freely in technical matters against workers with decades more experience. But she was entrusted to the position of the CEO of Theranos, where not being in charge was not an option. The I don’t know can’t figure out if she became more oppressed or depressed she became over time, but the more silent she became more secretive, according to Carreyrou. Greta Thunberg made speeches in the European Parliament at age sixteen. Elizabeth Holmes went to federal prison for eleven and a quarter years at age thirty-nine, silently.

(And everything becomes a mystery.)


Figures

Figure 1. Tabulation of Glaucon’s argument. Credit: Gendler, T. (2012, April 5). 2. The Ring of Gyges: Morality and Hypocrisy (Gendler 2012).

Works Cited

Allyn, B. (2022, November 19). Elizabeth Holmes sentenced to 11 years in prison for Theranos fraud. NPR. https://www.npr.org/2022/11/18/1137606060/elizabeth-holmes-sentenced-11-years-prison

Bury, J. B., & Meiggs, R. (1975). A history of Greece to the death of Alexander the Great.

Gendler, T. (2012, April 5). 2. The Ring of Gyges: Morality and Hypocrisy [Video]. YouTube. Retrieved December 10, 2023, from https://www.youtube.com/watch?v=xTGc1Pyp-Jc

Gibson, John (2022, May 2). Micro-scale PAMP/KAN Recombinant Plasmid production. https://nocomputerbutphone.blogspot.com/2022/05/micro-scale-pampkan-recombinant-plasmid.html

Jackson, P. (Director). (2002). The lord of the rings: The fellowship of the ring [Film]. USA: New Line Cinema.

Jackson, P. (Director). (2003). The lord of the rings: The two towers [Film]. USA: New Line Cinema.

Ramsdell, T. (2021, December 1). Theranos: A cautionary tale of ethics and entrepreneurship. CU Denver Business School News. https://business-news.ucdenver.edu/2019/05/24/theranos-a-cautionary-tale-of-ethics-and-entrepreneurship/

Thoreau, David. The Project Gutenberg eBook of Walden, by Henry David Thoreau. (n.d.). https://www.gutenberg.org/files/205/205-h/205-h.htm#chap03

Thunberg, G. (2020). No one is too small to make a difference: Expanded Edition. National Geographic Books.

Tolkien, J. R. R., & Carpenter, H. (2023). The letters of J. R. R. Tolkien. HarperCollins.

Waikar, Sachin. What Can We Learn from the Downfall of Theranos? (2022, November 22). Stanford Graduate School of Business. https://www.gsb.stanford.edu/insights/what-can-we-learn-downfall-theranos



Thursday, December 21, 2023

Motion In Free-Fall

 


Cover page

Student name: John C Gibson

Course number: PHYS.1410L , Section 811

Instructor name: Benjamin MacConnell

Date of experiment: Sep 13, 2023

Partner’s name: (no partner)

Title of experiment: 

Motion In Free-Fall


Objective: Measuring gravity acceleration. Using a paper strip with a hammering timer, the free fall of a weight is recorded with its traveling motion. The hammering strikes ink onto the paper strip, which is measured for the spacing of the ink marks. Velocity and acceleration due to gravity are calculated by fitting the measured data points to equation curves.


Introduction

The distance of travel equation for free fall due to gravity acceleration is 

 y = y0+ v0 t + 1/2a t2

, where y0 is the starting point displacement from the origin,

v0 is the initial velocity of the object,

t is time, which is 1/40 = 0.025 seconds in this experiment,

 a = g , which is acceleration by gravity, which is what we want to measure in this experiment if we choose our coordinate system to point y downward toward the center of the earth, as illustrated in the figure on the right.


The falling object’s initial displacement is 0 in this chosen coordinate. This coordinate system is chosen for convenience because the acceleration due to gravity is positive, the same sign as “a,” and the displacement is always positive. 


Derivation:

The falling object is pulled by the earth’s gravity toward the center of the earth. When the falling distance is much smaller than the earth's radius, the pulling force is constant, and the acceleration is constant. We express this constant as “a” in this equation.

v = v0 + a t


The free falling distance from the starting position y0 should be expressed as so,

vav= (y - y0) / t 

Furthermore, the vav for a constantly accelerating body is the geometric average of the instantaneous velocity across the time interval, shown in the above velocity-versus-time plot, expressed as so,

vav= (v0 + v) / 2


Combine the last 2 equations, (y - y0) / t = (v0 + v) / 2 

Multiply both sides with t, (y - y0) = t(v0 + v) / 2 

Substitute v with first equation’s v0+at, y - y0 = t(v0+v0+a t) / 2 =t(2v0 + a t)/2=tv0+12a t2

Keep only the displacement y on the left side and move y0 to the right side,

y = y0+tv0+12a t2

We will collect y values during the free fall, and use a parabolic curve to fit the data points to obtain 12a .

Then acceleration due to gravity will be g = a, with downward as the chosen coordinate’s positive y direction.



Steps

  1. Measure out a 60cm long paper strip and cut it to 60cm length

  2. Tie the paper strip to the loop of the 200g weight

  3. Clamp the hammer timer to the workbench with the clamp

  4. Thread the paper strip to the hammer timer between the hammer and ink patch

  5. Hold the paper strip’s far end straight up and let the 200g weight suspend close to the hammer timer

  6. Turn on the hammer timer to the 40Hz setting

  7. Let go of the paper strip and the 200g weight

  8. Hammer action leaves 1 ink mark on the paper strip for each time point.

  9. Use the caliper to measure the spacing between 2 adjacent marks

  10. Enter the measured spacing y’s into an excel or google sheet.

  11. Use a linear curve to fit the instantaneous velocity versus time data points.

  12. Use a parabola curve to fit the displacement versus time data points.


Apparatus and Procedure


Complete list of equipment


  1. Ruler

  2. Paper strip 1cm wide, 60cm long

  3. Caliper, 0.1mm precision

  1. 200g weight with loop

  2. Workbench clamp

  3. Hammering timer with ink patch


Labeled block diagram of each part of the experiment


Describe the experiment

  1. Measure out a 60cm long paper strip and cut to 60cm length

Use the 1 metre ruler to measure the length and pinch it off with fingers.


  1. Tie the paper strip to the loop of the 200g weight


  1. Clamp the hammer timer to the workbench with the clamp


  1. Thread the paper strip to the hammer timer between the hammer and the ink patch

The paper should be in between the stainless steel hammer and the ink patch


  1. Hold the paper strip’s far end straight up and let the 200g weight suspend close to the hammer timer

Keep the paper strip as verticle as possible so that the paper doesn’t rub on the hammer timer during freefall.


  1. Turn on the hammer timer to the 40Hz setting

This timing setting means that t is 1/40=0.025 sec between 2 adjacent observed displacement points.


  1. Let go of the paper strip and the 200g weight

Watch out for the falling weight.


  1. Hammer action leaves ink marks on the paper strip.


  1. Use the caliper to measure the spacing between 2 adjacent marks

Discard the initialing hammering marks that clump together. 


  1. Enter the measured spacing y’s into result table and into Excel or Google sheet.


  1. Calculate the midpoint time for each time entry tnby averaging it with the previous time entry, (tn-1+tn)/2

Calculate the average velocity for each midpoint time entry, Vav=y / 0.025s

Use a linear curve to fit the instantaneous velocity versus time data points. 


  1. Calculate t for each entry, starting with 0 sec, and accumulate 0.025 sec for each entry further in time.

The spacing y’s are also accumulated to give the actual displacement y for any time point t.

Use a parabola curve to fit the displacement versus time data points.



Results and Analysis

The recorded result y’s is shown in the following table.

Table 1.

Sample calculation for n=1, 

Yn = 0 + 0.281 = 0.281cm , t midpoint = (0 + 0.025)/2 = 0.013s,

Vav = 0.281 / 0.025 = 11.2 cm/s .

Sample calculation for n=14,

Yn = 49.112 + 7.990 = 57.102cm, t midpoint = (0.325 + 0.350)/2=0.338s,

Vav = 7.990 / 0.025 = 319.6 cm/s .


The calculated t midpoint and Vav are plotted in the following graph.

Graph 1.


The t and the calculated Yn are plotted in the following graph.

Graph 2.

Analysis


As shown in the above “Instantaneous Velocity vs Time” Graph 1, the fitting trend line has a slope of 958cm/s2. This slope is the acceleration due to gravity.


As shown in the above “Displacement vs. Time” Graph 2, the fitting parabola has a quadratic term coefficient of 481, which is 1/2a , half of acceleration by gravity.  1/2 958cm/s2 =479 481 .


This means that the measured acceleration is close to 958cm/s2 and consistent with a quadratic relationship between time and displacement when acceleration is a constant. 


Discussion

Compared to theory

My measured acceleration by gravity is 958cm/s2= 9.58m/s2 , which has a 9.8 -9.58 = 0.22m/s2 difference from the generally accepted value of earth gravity acceleration. This difference is about 2.2%.


My experiment result’s error is likely due to friction between the paper strip and hammer timer, and also air resistance. 


Uncertainty

The caliper’s precision is 0.1mm, and my measurement’s last digit, such as 6.713cm, is estimated. So the uncertainty is on the last digit 0.001cm. 



Difficulties

The friction and air resistance are the difficulties of the experiment. The experiment error is mostly attributed to friction and air resistance, not caliper precision uncertainties.

Conclusion


My experiment measured acceleration by gravity at 9.58m/s2 . It is not too far away from accepted value. 


Restatement of the objection of this experiment is to use a simple hammer timer to record gravity acceleration on a paper strip, and acceleration can be deduced by fitting the measured data points to equation curves.

The objection is achieved. My experiment was a success.




Questions

1. What is the difference between your value of g and the accepted value? What do you

consider to be the principal sources of experimental uncertainty in your

measurement?


The difference is 9.8 -9.58 = 0.22m/s2

I consider the principal source of uncertainty to be friction between the paper strip and hammer timer and air resistance on the paper strip because the paper strip flaps around in the air.


2. If the weight had been given an initial downward push instead of being released from

rest, what effect (if any) would this have on your measured value of g?


No effect on the measured value of g. Because we measure the g by the difference between successive Vav, not the Vav value itself. When all the Vav are increased equally with the initial push, the difference between successive Vav will still be the same g.


3. Prove that when the acceleration is constant, the average velocity over a time interval

is equal to the instantaneous velocity at the midpoint of the time interval.


When acceleration is a constant, the slope of the velocity plot is the same at every time point between the time interval (T1,T2). So, the velocity is a straight line, as pictured here.

The mid-point time Tm = (T2+T1)/2 . Midpoint instantaneous velocity Vm=v0+aTm .


xn = 0Tn(v0+at)dt =x0+ v0 Tn +1/2Tn2


The definition of average velocity is vav= (x2 - x1)/(T2 - T1) . 


For the numerator of the definition of average velocity, by algebra factoring

(x2-x1) = (x0+ v0 T2 +1/2a T22)-(x0+ v0 T1 +1/2a T12)=


v0(T2-T1)+1/2a (T22-T12)=v0(T2-T1)+1/2a (T2+T1)(T2-T1)


We see that (T2-T1) is a common factor of the 2 terms.


For the whole vav =(x2-x1)/(T2-T1)=


v0(T2-T1)/(T2-T1)+1/2a (T2+T1)(T2-T1)/(T2-T1)=v0+1/2a (T2+T1)=

v0+a(T2+T1)/2=v0+aTm =Vm


So, Vav=Vm .

In words, Vav=Vm means that the average velocity equals the instantaneous velocity at mid-point time.



4. Should the tangent to your displacement-time curve at the point selected to be y= 0

and t = 0 be horizontal? Explain your answer carefully.


That tangent line should be close to horizontal, but the slope of that tangent line may not be exactly zero. 

My displacement-timer curve is 0.0899 - 5.57x + 481t2

, and the tangent slope for every point of my curve is dxdt= -5.57 +481t

, and with t=0, the tangent line slope is  -5.57+ 4810 = -5.57cm/s, which is the initial velocity of the free-fall object. It is not exactly zero because my hand is not completely still when releasing the 200g weight.