Physics Principles And Problems Solutions

[Peppin Kishore]

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Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression).

Rubric scores from (a) 160 student solutions and (b) 159 solutions written by an instructor or taken from a textbook solution manual. This rubric was identical to the final rubric but used a maximum score of 4.

Graph of score agreement (weighted kappa) for two raters as a function of number of solutions scored for eight problems. The solutions were scored sequentially in time. The ninth data point is a rescoring of the first problem initially scored as the first data point.

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First principles thinking, which is sometimes called reasoning from first principles, is one of the most effective strategies you can employ for breaking down complicated problems and generating original solutions. It also might be the single best approach to learn how to think for yourself.

The first principles approach has been used by many great thinkers including inventor Johannes Gutenberg, military strategist John Boyd, and the ancient philosopher Aristotle, but no one embodies the philosophy of first principles thinking more effectively than entrepreneur Elon Musk.

Within a few years, SpaceX had cut the price of launching a rocket by nearly 10x while still making a profit. Musk used first principles thinking to break the situation down to the fundamentals, bypass the high prices of the aerospace industry, and create a more effective solution.3

What can you create from these individual parts? One option is to make a snowmobile by combining the handlebars and seat from the bike, the metal treads from the tank, and the motor and skis from the boat.

This is the process of first principles thinking in a nutshell. It is a cycle of breaking a situation down into the core pieces and then putting them all back together in a more effective way. Deconstruct then reconstruct.

The snowmobile example also highlights another hallmark of first principles thinking, which is the combination of ideas from seemingly unrelated fields. A tank and a bicycle appear to have nothing in common, but pieces of a tank and a bicycle can be combined to develop innovations like a snowmobile.

First principles thinking helps you to cobble together information from different disciplines to create new ideas and innovations. You start by getting to the facts. Once you have a foundation of facts, you can make a plan to improve each little piece. This process naturally leads to exploring widely for better substitutes.

First principles thinking can be easy to describe, but quite difficult to practice. One of the primary obstacles to first principles thinking is our tendency to optimize form rather than function. The story of the suitcase provides a perfect example.

What looks like innovation is often an iteration of previous forms rather than an improvement of the core function. While everyone else was focused on how to build a better bag (form), Sadow considered how to store and move things more efficiently (function).

The human tendency for imitation is a common roadblock to first principles thinking. When most people envision the future, they project the current form forward rather than projecting the function forward and abandoning the form.

This difference is one of the key distinctions between continuous improvement and first principles thinking. Continuous improvement tends to occur within the boundary set by the original vision. By comparison, first principles thinking requires you to abandon your allegiance to previous forms and put the function front and center. What are you trying to accomplish? What is the functional outcome you are looking to achieve?

Every innovation, including the most groundbreaking ones, requires a long period of iteration and improvement. The company at the beginning of this article, SpaceX, ran many simulations, made thousands of adjustments, and required multiple trials before they figured out how to build an affordable and reusable rocket.

First principles thinking does not remove the need for continuous improvement, but it does alter the direction of improvement. Without reasoning by first principles, you spend your time making small improvements to a bicycle rather than a snowmobile. First principles thinking sets you on a different trajectory.

If you want to enhance an existing process or belief, continuous improvement is a great option. If you want to learn how to think for yourself, reasoning from first principles is one of the best ways to do it.

When Musk originally looked into hiring another firm to send a rocket from Earth to Mars, he was quoted prices as high as $65 million. He also traveled to Russia to see if he could buy an intercontinental ballistic missile (ICBM), which could then be retrofitted for space flight. It was cheaper, but still in the $8 million to $20 million range.

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James Clear writes about habits, decision making, and continuous improvement. He is the author of the #1 New York Times bestseller, Atomic Habits. The book has sold over 20 million copies worldwide and has been translated into more than 60 languages.

This question was prompted by another question about a paper by Woodward (not mine). IMO Mach's principleis very problematic (?wrong) thinking. Mach was obviously influenced by Leibniz. Empty space solutions in GR would result in a Minkowski metric and would suggest no inertia.Mach's principle seems incompatible with GR. Gravitational waves could also be a problem.I had thought that papers like one by Wolfgang Rindler had more or less marginalised the Mach Principle, but I see lots of Internet discussion of it. Is it correct? Wrong? Is there evidence? (frame dragging experiments)?

In his book The Science of Mechanics (1893), Ernst Mach put forth the idea that it did not make sense to speak of the acceleration of a mass relative to absolute space. Rather, one would do better to speak of acceleration relative to the distant stars. What this implies is that the inertia of a body here is influenced by matter far distant.

Mach's principle has influenced Einstein but the final formulation of general relativity as of 1916 clearly invalidates Mach's conjecture. According to Mach's principle, motion - including accelerating and rotating one - may only be defined relatively to other objects. That would imply that there can't exist any gravitational waves.

However, general relativity predicts and experiments confirm that gravitational waves do exist: the relevant observations were awarded by the 1993 physics Nobel prize, too. The waves are vibrations of the space itself. It means that the metric tensor remembers the information about the geometry - and curvature at each point, even in the empty space, something that Mach's principle specifically wanted to prohibit.

Moreover, the perceptions and other effects of acceleration were supposed to be determined by comparisons with distant objects. This simple fact itself violates locality that has become important already in special relativity, and was simply inherited by general relativity.

If you care about history, the new cold relationship is mutual: much like general relativity rejected Mach's principle, Mach rejected general relativity - and already special relativity, in fact. ;-) If you care about sociology, there's been a poll among physicists active in relativity, and a vast majority of them would also say that Mach's principle is invalidated by general relativity.

Some people sometimes say that some effects predicted by general relativity, such as frame-dragging, are "Machian" in character. I think it is very misleading because it tries to make the listeners think that Mach's principle may be made compatible with the observations. It's very questionable what Mach's principle would predict about frame-dragging because Mach's principle has never become any viable candidate for a physical theory. But the idea that frame-dragging is Machian is more ideology and hype than a valid observation. Despite the vagueness about such very detailed effects, Mach's principle has said enough for us to be sure that it's incorrect in all of its forms.

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