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Part 1: The Theoretical Bases of the General Approach to Solving Any Physics Problem
Contents:
  1. Problem solving - Wikipedia
  2. General methods for solving physics problems
  3. B. S. Belikov-General methods for solving physics problems-Mir Publishers Moscow (1988).pdf

In some problems, computer algebra can help. Test all general results with quick-and-easy special cases. I found that during my graduate studies my productivity as a researcher went up when I started to think more about what I was going to do before actually starting to do stuff.


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I learned this lesson by wasting weeks trying to solve a nasty numerical integral which turned out to be entirely irrelevant. Had I thought more before trying to the calculation I would have realised that was the case and not wasted so much time.

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In undergraduate work I also get the impression that many students start playing around with the maths before really thinking about what the problem really means, which is what dictates the strategy a physicist should use for solving it…. That story about the integral does rather explain why you once advised me that the job of a theoretical physicist was to come up with ways to avoid having to do integrals. More on the topic, I believe a very clever physicist Gell-Man?

I think this was a wise strategy. I wonder if this is a version of the story told about von Neumann, that he never attempted problems he found difficult, only problems that others found difficult. More fully, dimensional analysis allows you to say that there is a unique functional relation between all of the dimensionless multiplicative power-law combinations of variables that you guess are involved. If there is only one such dimensionless combination then it is equal to a constant, whose value is the only thing that is missing — effectively the constant of proportionality when one of the variables in that combination is expressed in terms of the others.

Teachers must be well equipped now to understand new physics beyond Einstein and modern quantum physics with the discovery of gravitoetherton in CERN. I am a retiree with no math background. However as a little child a read about the astrologer seemingly humbly asking for a grain of whet doubled for each snare on a chess board, and took a pencil and paper and started doubling, had to switch to graph paper, and figure out how to add digest to correct occasional errors.

MegaPenny visualizes 60 time with penneis. Anyway I recently collected visualizations of the world around us and had trouble finding visualizations of the very small.


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  • You are commenting using your WordPress. You are commenting using your Google account. Next enter the values of the known variables in that equation.

    Problem solving - Wikipedia

    Have the computer repeatedly iterate successive values for the independent variable to see how the system evolves. Comments: - One advantage is that this method is fast once you have learned how write good code. For example, if you do not enter all the known values in SI units, then your computer will give you a number but it will not be dimensionally correct. For example, the equation may have more than one solution and the solution your computer returns may not be the one you are seeking.

    If you do not practice solving equations, then it becomes much harder to manipulate the relevant generic equations to generate an equation that you can put into your calculator to solve in the first place. Using a Graphing Calculator Often it useful to plot the relevant physics equation s on a graphing calculator. Many times this can be done before manipulating any of the equations first. After plotting the equations one can sometimes just look at the graph and "visually figure out" the answer.

    Example: A speeding station wagon moving at a constant speed of If the police car starts accelerating uniformly at 3. Comments: - The visual display of a graph is extremely helpful in seeing what is taking place with the variables in a problem. Seeing the graph, I can often tell if I am on the right track. If I am on the right track the structure of the graph will sometimes give me new insight into how to solve for a requested unknown. Scrutinizing Your Results Although this may look like the last step in solving a problem, it is useful to consider the following throughout your problem solving process.

    Do the signs of the quantities found make sense?

    General methods for solving physics problems

    Trouble-Shooting Actions: - Go back and examine your choice of which directions will be positive and negative when you set up the frame of reference from which you observed the action of the problem. Are each of the terms in an equation consistent with your choice of what will be positive and what will be negative? Comments: - Keeping the signs correct is one of the more difficult tasks that you will encounter in solving a problem.

    Part of the difficulty arises from the fact that there is no preferred direction which "Mother Nature" dictates as being positive or negative. It is up to you to choose which direction is positive. Depending upon the complexion of the problem, you may choose up to be positive in one problem and down in the next. This is perfectly acceptable. Experienced physicists usually choose the direction that will make the problem simplest to analyze.

    If an object's motion is always to the left, then choosing the left direction to be positive will make the equations of motion easier to analyze, rather than the normal convention of the right direction being positive. If your choice is different, then you will need to modify the generic equations to reflect your choice. For example, say you have a hot block in contact with a cold block and want to analyze the heat flow between the two.

    From the hot block's perspective, the heat flows out of the hot block, which would be a negative loss.

    Mathematical Physics : Solving Hard Physics problems

    Alternatively, the cold block would see the heat flow as a positive energy gain. Do the magnitudes of the quantities found seem reasonable? Trouble-Shooting Actions: - Compare the value of the quantity found with the range of values of that quantity in situations where you have some prior knowledge. This requires experience and is not easy to do when you are first learning a new concept. Sometimes textbooks will have a table of the values associated with different physical situations which can be useful.

    This awareness can be useful when solving future problems.

    B. S. Belikov-General methods for solving physics problems-Mir Publishers Moscow (1988).pdf

    Are the units of the quantities found correct? Comments: - If the final units do not match, then it means that either a you have made some mathematical error in manipulating the equation you are solving, or b that you have started with an incorrect equation to solve in the first place. This gives you two directions to explore: a going back through the mathematical steps of your solution to see if you can find any mistakes or b going back to the starting principles you employed to solve the problem that generated the equation you were using.

    If the equation you are using is correct and you do not make any math errors in solving the equation, then you can rest assured that the final answer has the SI units of the quantity you sought. This method is helpful on an exam when time is short. Is the quantity I found, the quantity requested in the problem? Trouble-Shooting Actions: - It useful to pause at the end of a calculation and re-read the problem to see if what you just calculated is the same as the quantity requested.

    The first thing to examine is to see if your answer represents the same type of physical quantity. If the problem calls for a speed then you should have found a quantity which is a speed. For example, there is an object's initial value, final value, average value, or change in velocity. All represent velocities but they are not the same.

    Moreover, there could be more that one object involved so you may need to make sure you have found the velocity of the correct object. How can I check my answers mathematically? Then check to see if it produces values that are identical with the original givens. There are usually many ways to solve the same problem.

    If you get the same answer using a different approach or a different equation, then there is a good chance that your answer is correct. It only means that you have solved the equations correctly. If the equation you started with is incorrect, then solving it correctly will not produce the correct answer to the quantity requested.