Finding the Gravitational Constant: Cavendish Experiment

Finding the Gravitational Constant: Cavendish Experiment Matt Cramb    The experiment explored the story of gravity, how it was discovered and derived from observations and experimentations, and attempted to recreate those initial tests. This was done to determine whether an increase in mass will increase the force of gravity, a statement which was supported by the experimental data, despite the numerous flaws inherent in the experimental design. Finding Gravity Gravity is one of the four fundamental forces of nature, and Nave, R (2017) also explains that it is the force responsible for constructing and regulating the movement of galaxies, stars, and planets. In 1687, Isaac Newton formulated his famous Equation of Universal Gravitation based, purported by Physics Classroom (2016), on an injury in an apple orchard. Whatever the circumstances, it had far reaching impacts on the science of the time. But something crucial was missing from his equation. Newton knew from scientists before him that the force exerted by gravity grew weaker as distance between objects affected by gravity increased, or represented mathematically; Where: This was nothing new for science of the time, but Newtons major discovery was that of the universality of gravity, which indicated that all objects which possess mass also exerted gravitational forces. This discovery led to another addition to the equation, because Kurtus, R (2016) reports Newton realized that objects with less mass exerted weaker gravitational forces. Therefore, he postulated that; Where: To convert this theory into an equation, Newton only needed one more piece. A constant was needed to calculate the exact gravitational forces on objects. This constant was called the gravitational constant, or G. In the equation, G presents as follows: However, the value for G wasnt found until much later, by Lord Henry Cavendish, over a century later.       The Cavendish Experiment In Cavendishs experiment, according to Shectman, J (2003) two spheres were attached at opposite ends of a beam which is suspended from the ceiling of a custom-built shed by a thin wire. Masses are placed to the sides of the spheres, to attract them, exerting gravitational forces sufficient to rotate the beam to a measurable degree. Cavendish measured the movement of the beam using a telescope positioned far from the shed. To use this apparatus to calculate G, a formula must be created, using torque, oscillation period, torsion constant, inertia and gravitational forces. The torque on the beam can be measured by the angle of deflection of the torsion wire, using Hookes Law: Where: However, torque can also be measured by the following expression: Where: Torque can also be calculated as a vector product with this equation: Where: And because, in this experimental setup, r and F are perpendicular vectors, there are two F, and r is half the length of the beam: Combining these two formula together results in the following: From Newton, the formula for force was also known, and could be substituted in from above. The torsion constant was measured by Cavendish by disturbing the beam, then measuring the period of oscillation. This can be done using the below equation. Where: This moment of inertia can be calculated from the sum moments of the two spheres at each end of the beam. The moment of inertia for each sphere is calculated by the equation: Since each sphere had equal mass, the total I is equal to: Inserting this into the period formula and rearranging for the torsion coefficient gives: When inserted into the formula for torsion coefficient above, gives the following: With this equation, the measurements needed to be taken from the experimental apparatus are: Variable: Explanation: Units: m Rad m kg s Using the experimental setup described above, according to Kurtus, R (1997) Cavendish determined: Preliminary Trials Failed Attempts For this experiment, two previous iterations of the experiment were run. The first was to determine the validity of running such an experiment, and the second was a full-scale experiment which provided no useful data. The first experiment was done using a meter-long beam and tennis balls attached to either end. A laser beam reflected off a mirror attached to the torsion wire, giving a result of angle. However, in practice, this rig did not come to a final resting position so that the period of oscillation could be measured. Instead the torque already present in the twine torsion wire twisted the beam against a chair leg, preventing it from fully coming to a balance of forces. The second experiment had results as follows: Variable: Explanation: Units: Results: m 1.25ÃÆ'-101 Rad 9.0ÃÆ'-10-2 m 1.765 kg 1.6 s 2.25ÃÆ'-102 m3kg-1s-2 2.419ÃÆ'-102 The value for G calculated by this experiment was vastly different to Cavendishs value of . This meant the experiment was concluded to be not statistically valid, for a variety of reasons. These experiments were refined and transformed into the final experimental setup. Theoretical Data Using Newtons formula for each of the three experiments which will be conducted can determine the value for . To do this, the masses and distance must be known ahead of time. These can be found below, and copied in the results section. OBJECT MASS (kg) Mass of Sinkers Mass of Cup 1 Mass of Cup 2 Mass of Bowling Pins Using Cavendishs above listed value of G, the projected data can be calculated. MASS (kg) FORCE OF GRAVITY ( Later, these will be compared with the experimental data. Based on the above background research, the magnitude of gravity in the system will increase proportional to an increase in the mass of the large masses. Or, as increases, will proportionally increase. This hypothesis has been supported by the background research, which has guided its creation through empirical data, and researched phenomena. However, because of the precision required to obtain an accurate result, research indicates the final calculated measurement for G will be vastly different from the real value. 25.5cm support beam12cm length of fishing line2x sinkers of mass 3.28g2x plastic cups2x bowling pins of mass 1.6kg1x stopwatch1x ruler1x camera1x plastic storage box approx. 70cm x 40cm 1m2 wire mesh Safety Before the experiment was conducted, a thorough risk assessment planner was completed and approved. Measures were taken to ensure no harm came to experimenter through heavy masses falling or water causing a slipping hazard. These measures included: Constant supervision Correct and appropriate use of safety equipment, which in this experiment meant wearing a lab coat throughout Safe handling of heavy masses and water. A risk assessment matrix provided by the Department of Education (2017) was also completed. Likelihood Consequence Insignificant Minor Moderate Major Critical Almost Certain Medium Medium High Extreme Extreme Likely Low Medium High High Extreme Possible Low Medium High High High Unlikely Low Low Medium Medium High Rare Low Low Low Low Medium The likelihood of injury was unlikely, as experimenter has previous experience. The consequence was also minor, indicating injuries not requiring medical attention (i.e. bruises, minor cuts). Therefore, the total risk was low, which indicates no further control measures need be put into place. However, in due diligence the above measures were still implemented. Procedure Firstly, to limit air flow; a major disturbance in the preliminary trials, the system was constructed inside a large plastic storage container. This container was placed a distance away from walls, to reduce the effects of other gravity sources. Then, two sinkers, whose masses were known, were attached to either end of a support beam, which was hung from the top of the box by a length of fishing line. This was suspended by the wire mesh atop the box. The fishing line was chosen as twine had been used in preliminary trials as the torsion wire, and had been shown to not be effective due to the latent torque. After letting the system come to a complete rest, it was disturbed by gently pushing one end of the support beam. The period of oscillation was measured by a stopwatch. To further reduce misrepresentation of data, six measurements were taken and averaged. The system was then allowed to come to rest again, and a measurement of the rest position taken by a camera from above. This would eliminate the need to reach into the box to take measurements and thus disturb the experiment. It also provided clearer results. Then, the two cups were introduced to the system 6.25cm away from the end of the support beam, at opposing sides and ends, so the attractive forces of the masses rotated the beam. The cups were initially filled with 250g of water, then 500g, then the cups were swapped with the 1.6kg bowling pins. Each iteration of the experiment, when the system came to rest for a third time, a measurement of the final rest position was taken using the camera. This data was recorded and processed by comparing photographs of the different rest positions and calculating angle of deflection. The results were then tabulated. Images of the experimental setup. Mass OBJECT MASS (kg) Mass of Sinkers Mass of Cup 1 Mass of Cup 2 Mass of Bowling Pins Period of Oscillation TEST NUMBER PERIOD (s) 1 20 2 22 3 21 4 21 5 21 6 21 Avg. 21 Rest Position TEST NUMBER MASSES USED ANGLE OF DEFLECTION (Rad) 1 No mass used 0.00 2 Cup 1 9.65 3 Cup 2 3.31 4 Bowling Pins 1.00 OTHER Data Variable: Explanation: Units: Results: m 0.0625 m 0.255 Magnitude of Gravity Using Newtons formula for each of the three experiments will determine the value for . Firstly, the value for G for each equation must be calculated. MASS (kg) VALUE OF G ( Now the force for gravity can be calculated. MASS (kg) FORCE OF GRAVITY ( findings The experiment shows that using Cavendishs method to determine the value for G was flawed, but that the experiment could have obtained an accurate value for G. These flaws will be examined below, but a basic rundown and description of data obtained will be given here. Magnitude of Gravity As can be seen by the graph at the end of the results section, the magnitudes of gravity measured do not accurately match the theoretical data obtained. These values, and the values for G, are vastly different to that originally measured by Cavendish (found in background research), likely because of the various flaws in the experimental design, which will be discussed in the Evaluation section. However, the results far more accurately correlate to the theoretical values than those in previous experiments, and the average trendlines do indicate that the trend matches that predicted. At 250g, the first mass, the experimental data differs wildly from the theoretical. Experimental Data Theoretical Data At 500g, the second mass, it drastically spikes, much higher than either of the other points. Experimental Data Theoretical Data At 1600g, the final point, the data dips down lower than expected again. Experimental Data Theoretical Data Its unclear from the background research conducted whether Cavendishs data deviated so much, but he also had a larger rig, which as discussed below, may have helped his experiments accuracy. Period of Oscillation The average period measured was 21 seconds, which is far shorter than the fifteen minutes measured by Cavendish. This is probably mostly due to the shorter beam, the effect of which can be seen with the torsion coefficient formula derived from the background research. The squared length of the beam demonstrates an exponential relationship between the torsion coefficient, an increase in which will decrease the period, which can be seen in the following formula for period of oscillation: Recording Equipment The equipment used to measure the period of oscillation may not have changed in the two hundred years since Cavendishs original experiment, however all other recording equipment did. A camera and digital analysis was used to take measurements, which may have causes slight issues with the orientation of frames in the software, but overall was more accurate than taking the measurements by hand when compared to the preliminary tests when this was done. The lengths were taken with a tape, and so were only calculated to two decimal places. However, this will likely not impact greatly on the results of the experiment, which can be shown mathematically. Using the same formula as above, and two length measurements as given below, the difference can be theorised. cm Value for k K (2 decimal places) Length 1 (two decimal places) (given by experiment) 6.25 2.35497 2.35 Length 2 (six decimal places) 6.247832 2.35334 2.35 Limitations Recommendations There are several reasons for why the value for G determined by this experiment differed so greatly from Cavendishs value, and these expose various flaws and strengths in the original design. They will be examined each using the following method: Name Explanation of Flaw Effects Comparison to Preliminary Trials Comparison to Cavendish Experiment Recommendation/Refinement Measuring Inaccuracies Various opportunities for error arose when observing and recording data in the experiment. Most of these examples, such as misreporting the period of oscillation by a fraction, would have a m Ethical Issues in Patient Information | Case Study Ethical Issues in Patient Information | Case Study Peeking in the EMR for all the right reasons Patrick Bobst Technology has embedded itself into everyday life and is integrated into everyday human activity. Corporate scandals, violations of intellectual property rights, and violations of customer, patient, employee privacy is uncovering challenging dilemmas and ethical decision-making in every the industry around the globe. Technological advancements not only increase the impact of carelessness, foolishness, recklessness and even malevolence but also enable anyone with access to learn much more and much faster than ever before(Curtain, 2005). Ethics enables individuals with the guidance of rational approaches to make the right justifiable decision. Ethical choices distinguished from other choices involve the continual conflict of fundamental values, as well as incorporating scientific inquiry that may be influential but cannot provide answers(Curtain, 2005). Most notably, ethical choices involve placing one value above another, and because values are of the utmost importance, any decision r eached will have profound, multiple and often on anticipated impact on human concern(Curtain, 2005). Case study Jessica Parker is a nurse that has the burdening task to solely support her three small children and is in severe financial distress since her divorce. Her ex-husband, Frank Parker has evaded court ordered child support obligations for over a year and has been able to evade authorities with no known address or phone number. Jessica’s house is about to be foreclosed upon, and her automobile repossessed. Although Jessica periodically picks up extra shifts, utilizes friends instead of childcare, and despite making multiple drastic cuts to her budget, she is unable to overcome the perils of increasing debt. One day a friend that informs her that Frank Parker received stitches in her emergency department after a minor motor vehicle accident (MVA). The next day she worked Jessica looked up her ex-husband in the EMR and proceeded to gather his needed contact information. Jessica immediately passes along the phone number, living address and employment information to her attorney which in turn succeeded in the actions of court ordered child support payments being automatically garnished from his wages along with a judgment for past due child support in an amount that will stabilize her current debt. Ethical dilemma When a couple chooses the responsibilities of being a parent, it is a commitment for life whether they are living together or separately. Jessica is in a stressful environment where she holds the custody of the children and the other parent is legally obligated to provide financial support to ensure a safe and healthy environment for the children. Jessica is clearly struggling financially and the situation will continue to worsen without the court ordered child support from ex-husband. She solved the dilemma of finding her ex-husband’s whereabouts by utilizing the hospitals EMR. By utilizing the EMR in an inappropriate manner, Jessica violated multiple provisions of the American Nurses Association (ANA) code of ethics including provision 3.1, 3.2, and 3.3. These provisions stipulate the patient’s right to privacy, the duty to maintain confidentiality of all patient information, and the protection of participants in research(Nursing World website, 2011). A breach of the Health Insurance Portability and Accountability Act (HIPAA) may have been committed under the privacy rule where â€Å"patients have a right to expect privacy protections that limit the use and disclosure of their health information†(McGonigle Mastrian, 2012, p. 173). â€Å"However, the privacy rule permits unauthorized disclosures of protected health information to public health authorities for specified public health activities including†¦. child abuse or neglect†(Lee Gostin, 2009, p. 82). Possible Alternatives At the point when Jessica suspected her husband might have been in the EMR system, an alternate path might be (1) hiring a private investigator. The ex-husbands MVA is a matter of police public record and private investigators are trained and have the resources to find information in ways others might not think about; (2) contact the local child support enforcement agency with the information of the MVA; (3) contact her attorney for a medical record subpoena. Hypothesize Ethical Arguments In this scenario, Jessica showed a clear breach to hospital policy, statutory and common-law duties of confidentiality and privacy. However, Jessica’s morals were dealing with the resolution of what is right and wrong in her own situation creating the dilemma of what is morally right and not looking at the evidence that indicates that she is also morally wrong. Depending on the discipline and point of view, the term value can have different meanings. Jessica’s objective moral values may include justice, freedom and welfare, which might be her basis for decision-making. The welfarism normative ethical approach applies to Jessica situation where morality is viewed and centrally concerned with the welfare or well-being of individuals, and where advancing the best interests of individuals makes the most fundamental sense(Keller, 2009). The ethical theoretical Principlistic approach validates itself with its universally recognized moral principles of autonomy, nonmaleficence , beneficence, and justice(Bulger, 2009). Autonomy considers the right of the individual to choose for themselves, nonmaleficence asserts an obligation not to inflict harm intentionally, beneficence refers to actions performed that contribution to the welfare of others, and justice refers to the fair, equitable, and appropriate treatment in light of what is due or owed to a person(McGonigle Mastrian, 2012). â€Å"Principlism is a unified moral approach in which the addition of each principal strengthens the legitimacy of each of the other principles to the extent that each principal is specified and balanced using independent criteria and yet each principal still supports each of the other principles†(Bulger, 2009, p. 121). In Jessica’s scenario she might consider that it is generally morally right to obtain her ex-husbands contact information in the EMR because this action obeys the role moral rule what is due or owed which in turn is derived from the principal justi ce. The crux of the dilemma lies within Jessica’s responsibility of providing her family a safe and healthy environment with financial stability, her utilization of the hospitals EMR balanced with her ex-husband’s medical record confidentiality rights. Investigate, Compare, and Evaluate Alternatives to him In Jessica’s case, there is no ambiguity in our nursing code of ethics when it comes to maintaining patient privacy and confidentiality. All the alternative methods provided to pursue the coveted contact information are the only acceptable legal pathways. These alternative methods safeguard patient rights, do not violate policy and laws, do not result in bad consequences, nor do they nullify rules and regulations. Each alternative provides expected outcomes that far exceed the risk of harm that include â€Å"civil liability, job loss, disciplinary action by state licensing boards, and even criminal investigations and sanctions†(Hader Brown, 2010, p. 270). Chosen alternative Simply from a financial standpoint the alternative chosen for Jessica would be to contact the local child support services agency. Hiring a private investigator or attorney can be cost prohibitive especially with her financial difficulties. Conclusion From nursing school until retirement, nurses are taught there is no leeway when it comes to HIPAA’s integrity and confidentiality of patient information. A problem with ethics is the logic of reasoning being used in moral deliberation and moral justification(Reidl, Wagner, Rauhala, 2005). Jessica’s deliberation of moral reasoning resorted from weighting only the positive self-fulfilling gain and omitted possible alternatives in her morally perplexing situation as well as her personal reasons in moral justification. Principlists consider principles to be at the heart of moral life negotiating between the four fundamental principles and the unique nature of specific moral situations on the other(McCarthy, 2003). With the technological advancements in today’s society the ethical questions evolve around how individuals choose to use or abuse their tools. Healthcare informatics intersects healthcare, ethics and informatics and all practitioners, for the publicâ€℠¢s good, must be bound by additional ethical, moral, and legal responsibilities (Curtain, 2005). Barrie Effy (2008), conclude in their study that ethical education in information technology changed attitudes and aided students in affective learning, an important and necessary component in the overall learning process(Barrie Effy, 2008). References Barrie, L., Effy, O. (2008). Ethical issues in information technology: Does education make a difference. International Journal of Information and Communication Technology Education, 4(2), 67-83. http://dx.doi.org/10.4018/jicte.2008040106 Bulger, J. W. (2009). An approach towards applying principlism. Ethics Medicine, 25, 125-125. Curtain, L. L. (2005). Ethics in informatics. Nursing Administration Quarterly, 29, 349-352. http://dx.doi.org/10.1097/00006216-200510000-00010 Hader, A., Brown, E. (2010). Patient privacy and social media. American Association of Nurse Anesthetists, 78, 270-274. Retrieved from http://www.aana.com/newsandjournal/Documents/legbrfs_0810_p270-274.pdf Keller, S. (2009). Welfarism. Philosophy Compass, 4(1), 82-95. http://dx.doi.org/10.1111/j.1747-9991.2008.00196.x Lee, L., Gostin, L. (2009). Ethical collection, storage, and use of public health data: A proposal for a national privacy protection. The Journal of the American Medical Association, 302(1), 82-84. http://dx.doi.org/10.1001/jama.2009.958 McCarthy, J. (2003). Principlism or narrative ethics: must we choose between them? Medical Humanities, 29(2), 65-71. http://dx.doi.org/10.1136/mh.29.2.65 McGonigle, D., Mastrian, K. G. (2012). Nursing informatics and the foundation of knowledge (2nd ed.). Burlington, MA: Jones and Bartlett. Nursing World website. (2011). http://www.nursingworld.org/MainMenuCategories/EthicsStandards/CodeofEthicsforNurses/Code-of-Ethics.pdf Reidl, C., Wagner, I., Rauhala, M. (2005). Examining ethical issues of IT in healthcare. Retrieved from http://www.sfu.ca/act4hlth/pub/working/Ethical-Issues.pdf