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Solving Physics Problems

Exploring New Thinking Paradigms

by Yipeng Gu

“Solving problems in physics is time-consuming, challenging, yet highly rewarding. It is an efficient way to master physics. Dr. Gu is an expert and has been coaching in this field for almost 20 years. This remarkable book is the crystallization of his talent and longterm effort. It provides a featured thinking paradigm and systematic analysis on plenty of models, making it distinguished from other popular books. By reading this book, you may develop problem-solving skills and also gain confidence on physics theories.” Prof. Fawei Zheng, Beijing Institute of Technology, China

• Format: Hardcover
• ISBN : 9789814877411
• Subject : General Materials Science
• Published : August 2022
• Pages : 806

USD $149.95

• Routledge (T&F)
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For Course Instructors: Inspection Copies

• Description

This book provides a complete, self-consistent, and open system for studying physics problems, which not only provides high-quality teaching materials for the field of physics education (especially for physics Olympiad training) but also points out a new direction for physics education. In this book, a form of methodology, which can comprehensively present cogitation discipline, is built up for analyzing and solving complex physics problems. The text analyzes plenty of physics problems (classical mechanics) from both theoretical and philosophical points of view to reveal the way of exerting this form. As a set of methodology reflecting the cogitation discipline, the thinking paradigm proposed in this book (called the MLQ-(ST)C paradigm) is a theoretical tool to cultivate people to acquire this ability. The paradigm successfully deconstructs the elements and the structure in physical thinking and then eliminates the obstacles of people’s underlying thinking, so that all the thinking built on it can be clear and ordered. The physics problems included in this book are much more difficult than similar books within the same theoretical domains involved, leading to better teaching and learning value.

Solving Physics Problems : Chapter has no title

Pages: 15-112

Pages: 113-316

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Pages: 451-602

Two-Body Model

Pages: 603-716

Pages: 717-774

Yipeng Gu obtained his PhD in condensed matter physics in 2014 from Jilin University, China. He teaches physics at the School of Natural Science, Changchun University of Science and Technology, China. Dr. Gu’s research interests span the philosophy of physics, theory of physics education, and the innovation and development of physics models. He is an experienced coach for Physics Olympiad and has taught basic courses of college physics and topic courses of physics competition for students who participated in the Chinese Physics Olympiad in Jilin Province, China. His students have won prizes in various levels of physics competitions, including six gold medals in the final contest of Chinese Physics Olympiad.

“Solving problems in physics is time-consuming, challenging, yet highly rewarding. It is an efficient way to master physics. Dr. Gu is an expert and has been coaching in this field for almost 20 years. This remarkable book is the crystallization of his talent and longterm effort. It provides a featured thinking paradigm and systematic analysis on plenty of models, making it distinguished from other popular books. By reading this book, you may develop problem-solving skills and also gain confidence on physics theories.” ~Prof. Fawei Zheng, Beijing Institute of Technology, China

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General Methods For Solving Physics Problems

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In this post we will see another book in the Problems and Solutions book, namely, General Methods for Solving Physics Problems by B. S. Belikov

This book attempts to create systematic use of generalised methods , general methodological principles, and very general concepts in a segment of students instruction of vital importance, the solution of physics problems. The approach is based on the application of the most general concepts of physics to the solution of any problem. I consider the theoretical aspects underlying the general approach to problem solution and methods for solving standard, non-standard, non-specific, and general problems.

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1989.

The book has three parts

Part 1: The Theoretical Bases of the General Approach to Solving Any Physics Problem

Chapter 1: The System of Fundamental Concepts of Physics

1 Some General Concepts of Physics

2 Idealization of a Physics Problem

3 Classification of Physics Problems

Chapter 2: Some General Methods for Solving Physics Problems

4 Stages in Solving a Formulated Problem

5 Method of Analysing the Physical Content of a Problem

6 General-Particular Methods. The DI Method

7 The Simplification and Complication Method. The Estimate Method

8 The Problem Statement Method

9 Another Classification of Formulated Problems

Part 2: Solution of Standard Problems

Chapter 3: The motion of a particle

10 Particle Kinematics

11 Particle Dynamics

12 Mechanical Oscillations

13 Conservation Laws

Chapter 4: The motion of a rigid body

14 Rigid Body Dynamics

15 Conservation Laws in rigid body Dynamics

Chapter 5: The Gravitational Field

16 The Basic Problem of Gravitational Theory

17 The Gravitational Field Generated by a system of particles

18 The Gravitational Field Generated by an arbitrary Mass Distribution

Chapter 6: The Electric Field

19 The Electrostatic Field in Vacuum

20 The Electrostatic Field in Insulators

21 Conductors in Electrostatic Field

22 Direct Current

Chapter 7: The Magnetic Field

23 The Magnetic Field in a Vacuum

24 The Magnetic Field in Matter

Chapter 8: The Electromagnetic Field

25 Electromagnetic Induction and Self-Induction

26 Electromagnetic Oscillations

Chapter 9: Electromagnetic Waves

27 Interference of Light

28 Diffraction of Light

Chapter 10: Thermodynamics

29 The First Law of Thermodynamics

30 The Second Law of Theormodynamics

Chapter 11: Kinetic Theory

31 The Maxwell-Boltzmann Distribution

32 The Boltzmann Distribution

Part 3: Solution of Nonstandard, Nonspecified and Arbitrary problems

Chapter 12: Non-standard and Original Problems

33 Non-standard Problems

34 Original Problems

Chapter 13: Nonspecified, Research and Arbitrary Problems

35 Nonspecified Problems

36 Research Problems

37 Arbitrary Problems

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SIMILAR ITEMS (based on metadata)

Problems & Exercises

1.2 physical quantities and units.

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

A car is traveling at a speed of 33 m/s 33 m/s size 12{"33"" m/s"} {} . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h 90 km/h size 12{"90"" km/h"} {} speed limit?

Show that 1 . 0 m/s = 3 . 6 km/h 1 . 0 m/s = 3 . 6 km/h size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {} . Hint: Show the explicit steps involved in converting 1 . 0 m/s = 3 . 6 km/h. 1 . 0 m/s = 3 . 6 km/h. size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {}

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

The speed of sound is measured to be 342 m/s 342 m/s size 12{"342"" m/s"} {} on a certain day. What is this in km/h?

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

1.3 Accuracy, Precision, and Significant Figures

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a 5.0 % 5.0 % size 12{5.0%} {} uncertainty. What is the range of possible speeds when it reads 90 km/h 90 km/h size 12{"90"" km/h"} {} ? (b) Convert this range to miles per hour. 1 km = 0.6214 mi 1 km = 0.6214 mi size 12{"1 km" "=" "0.6214 mi"} {}

An infant’s pulse rate is measured to be 130 ± 5 130 ± 5 size 12{"130" +- 5} {} beats/min. What is the percent uncertainty in this measurement?

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

A can contains 375 mL of soda. How much is left after 308 mL is removed?

State how many significant figures are proper in the results of the following calculations: (a) 106 . 7 98 . 2 / 46 . 210 1 . 01 106 . 7 98 . 2 / 46 . 210 1 . 01 size 12{ left ("106" "." 7 right ) left ("98" "." 2 right )/ left ("46" "." "210" right ) left (1 "." "01" right )} {} (b) 18 . 7 2 18 . 7 2 size 12{ left ("18" "." 7 right ) rSup { size 8{2} } } {} (c) 1 . 60 × 10 − 19 3712 1 . 60 × 10 − 19 3712 size 12{ left (1 "." "60" times "10" rSup { size 8{ - "19"} } right ) left ("3712" right )} {} .

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

(a) If your speedometer has an uncertainty of 2 . 0 km/h 2 . 0 km/h size 12{2 "." 0" km/h"} {} at a speed of 90 km/h 90 km/h size 12{"90"" km/h"} {} , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h 60 km/h size 12{"60"" km/h"} {} , what is the range of speeds you could be going?

(a) A person’s blood pressure is measured to be 120 ± 2 mm Hg 120 ± 2 mm Hg size 12{"120" +- 2" mm Hg"} {} . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg 80 mm Hg size 12{"80"" mm Hg"} {} ?

A person measures his or her heart rate by counting the number of beats in 30 s 30 s size 12{"30"" s"} {} . If 40 ± 1 40 ± 1 size 12{"40" +- 1} {} beats are counted in 30 . 0 ± 0 . 5 s 30 . 0 ± 0 . 5 s size 12{"30" "." 0 +- 0 "." 5" s"} {} , what is the heart rate and its uncertainty in beats per minute?

What is the area of a circle 3 . 102 cm 3 . 102 cm size 12{3 "." "102"" cm"} {} in diameter?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

A marathon runner completes a 42 . 188 -km 42 . 188 -km size 12{"42" "." "188""-km"} {} course in 2 h 2 h size 12{2" h"} {} , 30 min, and 12 s 12 s size 12{"12"" s"} {} . There is an uncertainty of 25 m 25 m size 12{"25"" m"} {} in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The sides of a small rectangular box are measured to be 1 . 80 ± 0 . 01 cm 1 . 80 ± 0 . 01 cm size 12{1 "." "80" +- 0 "." "01"" cm"} {} , {} 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm size 12{2 "." "05" +- 0 "." "02"" cm, and 3" "." 1 +- 0 "." "1 cm"} {} long. Calculate its volume and uncertainty in cubic centimeters.

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0 . 4539 kg 1 lbm = 0 . 4539 kg size 12{1" lbm"=0 "." "4539"`"kg"} {} . (a) If there is an uncertainty of 0 . 0001 kg 0 . 0001 kg size 12{0 "." "0001"`"kg"} {} in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

The length and width of a rectangular room are measured to be 3 . 955 ± 0 . 005 m 3 . 955 ± 0 . 005 m size 12{3 "." "955" +- 0 "." "005"" m"} {} and 3 . 050 ± 0 . 005 m 3 . 050 ± 0 . 005 m size 12{3 "." "050" +- 0 "." "005"" m"} {} . Calculate the area of the room and its uncertainty in square meters.

A car engine moves a piston with a circular cross section of 7 . 500 ± 0 . 002 cm 7 . 500 ± 0 . 002 cm size 12{7 "." "500" +- 0 "." "002"`"cm"} {} diameter a distance of 3 . 250 ± 0 . 001 cm 3 . 250 ± 0 . 001 cm size 12{3 "." "250" +- 0 "." "001"`"cm"} {} to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

1.4 Approximation

How many heartbeats are there in a lifetime?

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10 − 22  s 10 − 22  s size 12{"10" rSup { size 8{ - "22"} } " s"} {} .)

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10 − 27  kg 10 − 27  kg size 12{"10" rSup { size 8{ - "27"} } " kg"} {} and the mass of a bacterium is on the order of 10 − 15  kg. 10 − 15  kg. size 12{"10" rSup { size 8{ - "15"} } "kg"} {} )

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

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Access for free at https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: College Physics
• Publication date: Jun 21, 2012
• Location: Houston, Texas
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• Section URL: https://openstax.org/books/college-physics/pages/1-problems-exercises

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The Robots That Will Change the World Are Already Among Us

Climate change more like ecosocial crisis, openmind books, scientific anniversaries, kary mullis, the genius of a scientist, the eccentricity of a celebrity, featured author, latest book, solving problems visually.

What’s the best way to approach (and successfully solve) a mathematical problem statement? Perhaps by drawing a picture? That, at least, is the conclusion of a striking new study by researchers at the Universities of Geneva and Burgundy.

It’s not a trivial assumption. It is thought that when we face a mathematical problem that contains both mathematical information (numbers and arithmetic operations) and non-mathematical information (the context of the problem and the characteristics of the entities involved), our brains process this combination of verbal and numerical information and convert it into a mental representation in order to identify the best strategy for solving it. On the other hand, more and more studies suggest that the schematic drawings that are usually made to solve this type of problem are a reflection of these mental representations.

Game 1: Not a game, an experiment

In the study, participants were asked to solve 12 simple arithmetic problems in as few steps as possible and to draw a picture that would help them understand and solve the problem.

Here are two of these problems, and we invite you to solve them in the same way: in as few steps as possible, and with a drawing to help you understand the problem.

Problem 1 : Paul has five red marbles and also has some blue marbles. In total he has eleven marbles. Julie’s marbles are green and blue. Julie has as many blue marbles as Paul and also has two fewer green marbles than Paul has red marbles. How many marbles does Julie have?

Problem 2 : Lisa takes the train during the day, travels for 5 hours and arrives at her destination at 11am. Fred got on the train at the same time as Lisa and his trip took 2 hours less. What time did Fred arrive at his destination?

Independently of the above, many studies postulate that relying on drawings, diagrams or other types of graphical representations when processing information has numerous benefits: it improves our ability to learn and remember, it helps us to understand complex concepts, it reinforces critical and scientific thinking, and it fosters a transversal and interdisciplinary interpretation. And from a mathematical point of view, using these representations makes it easier to establish the relationships between different data, to visualise the information implicit in the statement and to identify the most direct and simplest solution strategy.

Use the drawings to answer these complex and hieroglyphic questions.

A recent study goes a step further by suggesting that the verbal information in the problem statement influences the type of diagram shown and also the strategy chosen to solve the problem. More specifically, the study has found that the type of diagram preferentially chosen depends on whether the statement is cardinal or ordinal in nature.

Thus, when the context alludes to the cardinal properties of the quantities involved—the number of elements in a set—a drawing based on groupings of entities (crosses, circles, etc.) that sometimes overlap (or intersect) is usually chosen. This in turn leads to a three-step arithmetic strategy. On the other hand, when the statement of the problem focuses on the ordinal properties of numbers—the position they occupy in a set—we usually opt for drawings based on axes, graduations or intervals, which lead to a more direct and simpler one-step solution strategy.

And this is observed even when the problems are analogous from a mathematical point of view: they have the same structure, the same numerical values and can be solved with the same strategy (as in the case of the two problems in Game 1).

But perhaps the most interesting reflection is that, knowing this, it is possible to guide and train the student to apply this second type of diagram, thereby facilitating the identification of the best way to solve it.

Game 3:  A high-flying challenge

Sara wants to travel from Madrid to Tokyo. To do so, she flies first to New York, from where she takes a plane to London and from there to Tokyo.

Paul also wants to go from Madrid to Tokyo, but in his case he flies directly from Madrid to London and then takes a flight to Tokyo.

If Sara flies for a total of 27hrs 15min and Paul for 14hrs 30min, and given that the flight from New York to London takes 4hrs 45min longer than the flight from Madrid to London, and the flight from London to Tokyo takes 12 hours, how long is the flight from Madrid to New York?

And if both Sara and Paul lose only one hour at each stopover, what will the local time be when they each arrive in Tokyo if they both depart Madrid at 2pm?

            M                                 NY    M-L + 4:45   L                    12:00 h                   T

                                                   M           L                                       12:00 h                    T 

14 hrs 30 min

The Madrid-London flight takes 2hrs 30min. New York to London is 2hrs 30min + 4hrs 45min = 7hrs 15min. And the Madrid to New York flight is 27hrs 15min – 12hrs – 7hrs 15min = 8 hours.

With this, and bearing in mind that each stopover only takes one hour:

If Sara leaves at 2pm from Madrid then: 2pm + 8hrs – 6hrs (time difference) + 1hr (at NY airport) + 7hrs 15min + 5hrs (time difference) + 1hr + 12hrs + 8hrs (time difference) = 2:15am on day 3.

In Paul’s case: 2pm + 2hrs 30min – 1hr (time difference) + 1hr + 12hrs + 8hrs (time difference) = 12:30pm on day 2.

Miguel Barral

Related publications.

• What Purpose Do the Great Mathematical Problems Serve?
• David Hilbert: The Architect of Modern Mathematics
• Magic Squares: When Art is Squared With Mathematics

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