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Physics Problem Solving Secrets: 120 Must-Know Problems Solved Step-By-Step Paperback – December 25, 2011

How much is passing physics class worth to getting your degree? Suppose you could spend one night reading and afterward be able to solve any textbook physics problem. Imagine ... spend LESS time studying yet receive BETTER grades on your homework and exams.

Well, it isn't if you have the right teaching method.

Think about it. Solving textbook problems is the most important skill you need to get through class. Everything in class centers on this. You can waste a LOT of time memorizing formulas and various problem solving "methods" without ever getting to that "Aha!" moment. Truthfully, solving textbook problems is the FIRST step in understanding physics, but most professors can't even teach that after a whole year!

Simply put, learning to solve these homework problems is the key to getting an A in class.

At last! The RIGHT way to learn physics is here.

Which of These Powerful Secrets Are You Looking For?

The most important rule for calculating the components of vectors.
How to get projectile problems right, every time.
Energy and entropy explained in a way anyone can understand.
When, where, and how to use trigonometry without losing your mind.
Step-by-step method to solve static rigid body problems.
Special relativity explained using the "twin paradox".
The single pivotal principle behind quantum mechanics.
Why quarks and electrons are the building blocks of the universe.
The relationship between electricity, magnetism, and light.

... plus lots more!

Included are 120 typical homework problems solved STEP-BY-STEP. There are no "details left to the reader" here. Each problem begins with an explanation of how and why a particular approach or equation is used, then each step is explained from beginning to end.

I love this subject. It's is my passion. And as with anything loved, I HATE to see or hear my subject butchered by the average high-school and college "systems". This subject ought to be FUN! Unfortunately, you can't see than until you can SOLVE THE PROBLEMS.

Have you ever wondered why geniuses like Einstein or Feynman ENJOYED physics? I want to help you with the first step in understanding (problem solving), so you can get a glimmer of why. That's my primary motive.

But there is another. I don't want physics to get in your way. If you just want a way through the college "system", I think that's okay. Really. Not everyone needs to be a rocket scientist. In fact, that's kind of silly when you think about it. I just want to help.

It's easy to get started right away.

Get ready to enjoy more free time and still ACE that physics class!

Print length 272 pages
Language English
Publication date December 25, 2011
Dimensions 5.25 x 0.68 x 8 inches
ISBN-10 1463798652
ISBN-13 978-1463798659
See all details

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About the author, product details.

Publisher ‏ : ‎ CreateSpace Independent Publishing Platform (December 25, 2011)
Language ‏ : ‎ English
Paperback ‏ : ‎ 272 pages
ISBN-10 ‏ : ‎ 1463798652
ISBN-13 ‏ : ‎ 978-1463798659
Item Weight ‏ : ‎ 11 ounces
Dimensions ‏ : ‎ 5.25 x 0.68 x 8 inches
#10,955 in Decision-Making & Problem Solving
#50,781 in Physics (Books)

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Physics Problem Solving Secrets: 120 Must-Know Problems Solved Step-By-Step Paperback – 25 Dec. 2011

Well, it isn't if you have the right teaching method.

Simply put, learning to solve these homework problems is the key to getting an A in class.

At last! The RIGHT way to learn physics is here.

Which of These Powerful Secrets Are You Looking For?

The most important rule for calculating the components of vectors.
How to get projectile problems right, every time.
Energy and entropy explained in a way anyone can understand.
When, where, and how to use trigonometry without losing your mind.
Step-by-step method to solve static rigid body problems.
Special relativity explained using the "twin paradox".
The single pivotal principle behind quantum mechanics.
Why quarks and electrons are the building blocks of the universe.
The relationship between electricity, magnetism, and light.

... plus lots more!

It's easy to get started right away.

Get ready to enjoy more free time and still ACE that physics class!

Print length 272 pages
Language English
Publication date 25 Dec. 2011
Dimensions 13.34 x 1.73 x 20.32 cm
ISBN-10 1463798652
ISBN-13 978-1463798659
See all details

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Customer reviews.

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Mastering Physics Problem-Solving: A Comprehensive 6-Step Guide

Introduction.

Physics problems can often be daunting, but with a systematic approach, they become manageable challenges. In this guide, we will explore a detailed six-step process designed to enhance your problem-solving skills. Whether you are a student navigating your physics coursework or a physics enthusiast delving into complex scenarios, these steps will provide a solid foundation for tackling any physics problem effectively.

1. Commence with a Clear and Comprehensive Diagram

The importance of visualization in physics cannot be overstated. To kickstart your problem-solving journey, begin by drawing a clear and comprehensive diagram. This visual representation serves as a roadmap, aiding in the understanding of the problem’s intricacies. It enables you to decipher the given information and conceptualize the scenario, providing a tangible foundation for the subsequent steps.

Consider a scenario where you are tasked with understanding the motion of objects in a gravitational field. A well-drawn diagram could depict the initial and final positions, velocities, and any forces at play. This step ensures that you have a tangible representation of the problem, helping to organize your thoughts and set the stage for a systematic solution.

2. Systematically Transfer Data to the Diagram

With the diagram in place, the next step involves systematically transferring all pertinent data and information onto it. This process serves a dual purpose – it helps you internalize the details of the problem, and it minimizes the need to revisit the question repeatedly during the solution phase. Efficiently transferring information ensures that you have a clear reference point for the specifics of the given scenario.

For instance, if dealing with a dynamics problem involving multiple forces, annotate the magnitudes, directions, and points of application directly on the diagram. This step ensures that you have a consolidated source of information, reducing the chances of overlooking critical details during the subsequent stages of problem-solving.

3. Identify Relevant Concepts

Physics problems often encompass various concepts and principles. Identifying the relevant ones is crucial for crafting a targeted solution. As you examine the given problem, consider the fundamental physics principles at play. This step requires a solid understanding of the underlying theories and laws applicable to the specific scenario.

Continuing with the example of objects in a gravitational field, you would identify concepts such as Newton’s laws of motion and the principles of gravitational acceleration. Recognizing these fundamental ideas guides the subsequent steps, providing a conceptual framework for deriving and applying the necessary equations.

4. Establish Correct Equations

Once you have a conceptual framework in place, the next step involves establishing the correct equations. At this stage, resist the temptation to substitute numerical values. Instead, focus on the relationships between the physical quantities involved. Derive or identify the equations that encapsulate the principles relevant to the given scenario.

For our gravitational field example, this step might involve recognizing the kinematic equations related to the motion of objects under constant acceleration. Establishing these equations sets the stage for a more structured and conceptual solution, laying the groundwork for the subsequent numerical analysis.

5. Integrate Numerical Values into Simplified Equations

With the equations identified, it’s time to introduce numerical values. Before doing so, ensure that the units across all quantities are consistent. If necessary, convert units to the International System of Units (SI) for uniformity. This step is crucial for maintaining precision throughout the solution process.

Consider a scenario where time is initially given in minutes, but the chosen equation requires seconds. Converting units beforehand prevents errors and ensures that the subsequent calculations are accurate. This meticulous approach contributes to the overall accuracy and reliability of the solution.

6. Present the Final Answer with Precision

The final step in this comprehensive guide involves presenting the solution with precision. State the numerical answer with the appropriate number of significant figures or decimal places, accompanied by the correct unit. This attention to detail is essential for conveying the accuracy of your solution and aligning with the standards of scientific reporting.

In our gravitational field example, if the calculated displacement is expressed as 25.678 meters, the final answer should be presented with the appropriate precision – perhaps as 25.7 meters or 2.57 x 10^1 meters, depending on the context and significant figures involved.

Mastering physics problem-solving is a journey that involves a combination of visualization, systematic data organization, conceptual understanding, and precision in numerical analysis. By following this six-step guide, you can navigate through complex physics scenarios with confidence, developing a robust problem-solving skill set that is applicable across various physics disciplines. Embrace the challenge, cultivate a disciplined approach, and watch as your proficiency in solving physics problems reaches new heights.

Back To A Level Physics Topic List

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How to Solve Any Physics Problem

Last Updated: July 21, 2023 Fact Checked

This article was co-authored by Sean Alexander, MS . Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 330,714 times.

Baffled as to where to begin with a physics problem? There is a very simply and logical flow process to solving any physics problem.

Ask yourself if your answers make sense. If the numbers look absurd (for example, you get that a rock dropped off a 50-meter cliff moves with the speed of only 0.00965 meters per second when it hits the ground), you made a mistake somewhere.
Don't forget to include the units into your answers, and always keep track of them. So, if you are solving for velocity and get your answer in seconds, that is a sign that something went wrong, because it should be in meters per second.
Plug your answers back into the original equations to make sure you get the same number on both sides.

Step 10 Put a box, circle, or underline your answer to make your work neat.

Community Q&A

Many people report that if they leave a problem for a while and come back to it later, they find they have a new perspective on it and can sometimes see an easy way to the answer that they did not notice before. Thanks Helpful 249 Not Helpful 48
Try to understand the problem first. Thanks Helpful 186 Not Helpful 51
Remember, the physics part of the problem is figuring out what you are solving for, drawing the diagram, and remembering the formulae. The rest is just use of algebra, trigonometry, and/or calculus, depending on the difficulty of your course. Thanks Helpful 115 Not Helpful 34

Physics is not easy to grasp for many people, so do not get bent out of shape over a problem. Thanks Helpful 100 Not Helpful 25
If an instructor tells you to draw a free body diagram, be sure that that is exactly what you draw. Thanks Helpful 89 Not Helpful 24

Things You'll Need

A Writing Utensil (preferably a pencil or erasable pen of sorts)
Calculator with all the functions you need for your exam
An understanding of the equations needed to solve the problems. Or a list of them will suffice if you are just trying to get through the course alive.

Expert Interview

Thanks for reading our article! If you’d like to learn more about teaching, check out our in-depth interview with Sean Alexander, MS .

↑ https://iopscience.iop.org/article/10.1088/1361-6404/aa9038
↑ https://physics.wvu.edu/files/d/ce78505d-1426-4d68-8bb2-128d8aac6b1b/expertapproachtosolvingphysicsproblems.pdf
↑ https://www.brighthubeducation.com/science-homework-help/42596-tips-to-choosing-the-correct-physics-formula/

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Ap® physics 1 secrets to problem solving, course curriculum, module 0: getting started.

How Lectures Work (Full Program)

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Problem Solving Process Document

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AP Practice: 1-D Motion #3

AP Practice: 1-D Motion #4

AP Practice: 1-D Motion #5

AP Practice: 1-D Motion #6

AP Practice: Projectile Motion #1

AP Practice: Projectile Motion #2

AP Practice: Projectile Motion #3

Kinematics MCQ

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2018 FRQ #1 (Short Answer)

2019 FRQ #2 (QQT)

2021 FRQ #2 (Experimental Design)

2022 FRQ #2 (QQT)

2023 FRQ #2 (Experimental Design)

2023 FRQ #3 (QQT)

AP Practice Problem: Forces #1

AP Practice Problem: Forces #2

AP Practice Problem: Forces #3

AP Practice Problem: Forces #4

AP Practice Problem: Forces #5

AP Practice Problem: Forces #6

AP Practice Problem: Forces #8

AP Practice Problem: Forces #9

AP Practice Problem: Forces #11

AP Practice Problem: Forces #12

AP Practice Problem: Forces #13

AP Practice Problem: Forces #14

AP Practice Problem: Forces #16

AP Practice Problem: Forces #17

AP Practice Problem: Forces #18

AP Practice Problem: Forces #19

AP Practice: Circular Motion #1

AP Practice: Circular Motion #2

AP Practice: Circular Motion #3

AP Practice: Circular Motion #4

AP Practice: Circular Motion #7

AP Practice: Circular Motion #9

Circular Motion MCQ

Module 3: Work & Energy

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Section 3 Lesson: Gravitational Potential Energy and Conservation of Energy

Section 4 Lesson: Gravitational Potential Energy (Far from Earth's Surface)

Section 5 Lesson: Spring Potential Energy

Review Lesson: Problem Solving Steps for Work-Energy

2015 FRQ #3 (QQT)

2016 FRQ #2 (Experimental Design)

2017 FRQ #4 (Short Answer)

2019 FRQ #3 (Experimental Design)

2021 FRQ #1 (Short Answer)

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AP Practice: Energy #3

AP Practice: Energy #4

AP Practice: Energy #5

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AP Practice: Energy #7

AP Practice: Energy #8

AP Practice: Energy #9

AP Practice: Energy #10

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Work & Energy MCQ

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2022 FRQ #4 (Paragraph Answer)

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AP Practice Problem: Linear Momentum #3

AP Practice Problem: Linear Momentum #4

AP Practice Problem: Linear Momentum #5

AP Practice Problem: Linear Momentum #6

AP Practice Problem: Linear Momentum #7

AP Practice Problem: Linear Momentum #8

AP Practice Problem: Linear Momentum #9

AP Practice Problem: Linear Momentum #10

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Section 2 Lesson: Pendulum

Section 3 Lesson: Horizontal Mass Spring

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Review Lesson: Simple Harmonic Motion Process

2018 FRQ #5 (Paragraph Answer)

2022 FRQ #5 (Short Answer)

2023 FRQ #1 (Short Answer)

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AP Practice: Simple Harmonic Motion #2

AP Practice: Simple Harmonic Motion #3

AP Practice: Simple Harmonic Motion #4

AP Practice: Simple Harmonic Motion #5

AP Practice: Simple Harmonic Motion #6

AP Practice: Simple Harmonic Motion #7

AP Practice: Simple Harmonic Motion #8

AP Practice: Simple Harmonic Motion #9

AP Practice: Simple Harmonic Motion #10

AP Practice: Simple Harmonic Motion #11

AP Practice: Simple Harmonic Motion #12

Simple Harmonic Motion MCQ

Module 6: Rotational Kinematics and Dynamics

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Section 1 Lesson: Rotational Kinematics

Section 2 Lesson: Torque and Rotational Statics

Section 3 Lesson: Rotational Dynamics

AP Practice Problem: Rotational Dynamics #1

AP Practice Problem: Rotational Dynamics #2

AP Practice Problem: Rotational Dynamics #3

AP Practice Problem: Rotational Dynamics #4

AP Practice Problem: Rotational Dynamics #5

AP Practice Problem: Rotational Dynamics #6

Rotational Kinematics & Dynamics MCQ

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Module 7 Note Packet

Section 1 Lesson: Rotational Kinetic Energy

Section 2 Lesson: Rolling

Section 3 Lesson: Conservation of Angular Momentum

Review Lesson: Rotation

2016 FRQ #1 (Short Answer)

2017 FRQ #3 (QQT)

2018 FRQ #3 (QQT)

2019 FRQ #1 (Short Answer)

2021 FRQ #4 (Paragraph Answer)

2021 FRQ #5 (Short Answer)

2022 FRQ #3 (Experimental Design)

2023 FRQ #4 (Paragraph Answer)

2023 FRQ #5 (Short Answer)

AP Practice: Rotation #1

AP Practice: Rotation #2

AP Practice: Rotation #3

AP Practice: Rotation #4

AP Practice: Rotation #5

AP Practice: Rotation #6

AP Practice: Rotation #7

AP Practice: Rotation #8

AP Practice: Rotation #9

AP Practice: Rotation #10

AP Practice: Rotation #11

AP Practice: Rotation #12

AP Practice: Rotation #13

AP Practice: Rotation #14

AP Practice: Rotation #15

Rotational MCQ

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Section 2: Pressure

Section 3: Bernoulli's Equation

2023 #3 (QQT)

2018 #4 (Short Answer)

AP Problem #1

AP Problem #2

AP Problem #3

AP Problem #4

AP Problem #5

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Short Answer: 2016 FRQ #1

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Short Answer: 2018 FRQ #1

Short Answer: 2019 FRQ #1

Short Answer: 2021 FRQ #1

Short Answer: 2021 FRQ #5

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The secret to becoming an excellent physicist

When most people think of a great physicist, they think of Einstein, often alongside his famous quote, “Imagination is more important than knowledge.”
Professional physicists, armchair physicists, and laypersons alike all have wild, imaginative ideas concerning how the world works, but very few ideas are worth serious scrutiny.
This isn’t because of bias, gatekeepting, close-mindedness, or dogmatism. It’s because the expertise you gain in becoming a quality physicist teaches you how to separate out the nonsense.

All across the world, young adults are working hard toward making their dreams a reality. For many students at both the undergraduate and graduate levels, that dream involves unlocking the secrets of the Universe, taking us beyond our current understanding and beyond the Standard Models of both particle physics and cosmology. For generations, aspirational students have dreamed about becoming the next Heisenberg, Bohr, Dirac, Einstein, or even Newton, believing that they might have, inside their minds, the “secret sauce,” whatever it may be, to lead the next revolution in physics.

Most of them, unfortunately, wind up doing nothing of the sort. Revolutions in physics are extraordinarily hard to initiate, and for good reason: after centuries of theoretical and experimental work by thousands upon thousands of brilliant, competent minds, the current consensus models are strong and sturdy enough that they’re extraordinarily difficult to equal in terms of success, much less surpass. While numerous ideas abound, the critical evidence that would support any of them is sorely lacking. At the frontiers of physics, we’re all still stabbing in the dark.

But while the excellent physicists doing the stabbing are doing so with the equivalent of sharp knives, others have the equivalent of nerf bats, and don’t even realize the difference. In most cases, it’s because they never learned the secret to becoming an excellent physicist. Here’s the lesson they need to learn.

When most people think about breakthroughs in physics, they think about truly revolutionary ideas. They think about Einstein and his ideas — or thought experiments — that no one had conceived of before him.

They think about Einstein’s notion of “riding a light wave,” and what it would look like to see oscillating, in-phase electric and magnetic fields appearing and disappearing with a specific amplitude, and how no such phenomena exists: the thought-experiment that led him to the principle of relativity and the constancy of the speed of light.
They think about the notion that, as objects move at speeds that take them closer to the speed of light, their kinetic energy increases dependent on your frame of reference, but in all frames of reference, a specific portion of that energy remains the same: enabling Einstein to derive the idea of a rest-mass energy and his most famous equation : E = mc² .
And they think about what Einstein himself called “his happiest thought,” or the notion that, from inside a closed room, you cannot tell whether you’re experiencing the downward pull of gravitation or the equal-and-opposite reaction from a constant thrust, or acceleration. This thought led to Einstein’s equivalence principle, which in turn eventually gave rise to Einstein’s General theory of Relativity .

It’s almost as if one person, even coming from outside the mainstream school of scientific thought, could almost single-handedly overturn the leading ideas in a modern scientific field and herald a revolution that leads us to a radical reconception of how the Universe works. Einstein himself seemed to agree with this notion, as you can find his famous quote, “Imagination is more important than knowledge,” practically anywhere you look.

But this fails to recognize the true extent of the background work that was necessary for Einstein to undertake, on his own, before any of these revolutionary thoughts could even begin to enter his head. It ignores the fact that Einstein went to school, learned physics, and even studied under one of the great mathematicians and physicists of his time: Hermann Minkowski. It ignores the fact that Einstein himself, even after leaving school, formed his own academy to study physics wherein he and his collaborators worked through the intricacies and consequences of various avenues of thought.

And it even ignores the context of Einstein’s full quote , which states ,

“I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. For knowledge is limited, whereas imagination encircles the world.”

The key that most people miss about Einstein’s quote is that a certain level of knowledge — a level that eludes most people who don’t spend the necessary time and energy in gaining it — is required, as a prerequisite, to fully understand what our modern conception of the Universe is and isn’t successful at doing. That knowledge, of course, won’t lead you to any remarkable new insights on its own; for that, imagination is required as well, but it’s imagination that’s informed by a comprehensive foundational knowledge of where we are today and how we came to know the things that we actually meaningfully know.

Imagination is more important than knowledge as far as making novel advances go, in the sense that if you have two equivalent minds with equal knowledge of physics, but one is wildly imaginative and the other only limits their thoughts to what our current understanding has already revealed to us, the imaginative one is far more likely to blaze a revolutionary path forward than the one who has restricted their imagination. Great, novel ideas very rarely emerge from taking what is known and extrapolating to the next, minimally imaginative logical step. Imagination is required, and there’s no substitute for that key ingredient.

But while imagination is desirable for coming up with revolutionary ideas, a foundational knowledge of the physical theories and ideas that have led us to our current scientific consensus is absolutely mandatory. Many students — prior to beginning their undergraduate degree, while in pursuit of their bachelor’s degree, when considering graduate schools, or while a graduate student themselves — underestimate the importance of obtaining that knowledge, overestimate their reliance on their (not fully formed) physical intuition, and fail to recognize the critical step required to become an excellent physicist.

That key step?

It’s simplicity itself: you become good at physics by solving physics problems . That’s it: that’s the secret. If you want to become competent at physics, you will solve physics problems in the area you wish to learn.

Want to learn classical mechanics? Learn how to formulate the setup for a problem, write down the equations that describe the problem, work through the steps of solving those equations to arrive at physically relevant solutions, and use those solutions to work out the expected behavior of the system you’re considering.

Want to learn electromagnetism? Same thing: learn how to identify your knowns and unknowns, how to relate them through a series of equations and boundary conditions, how to solve that system of equations, and how to extract measurable and observable quantities that reveal your predicted answer.

It’s the same story with quantum mechanics, nuclear and particle physics, astrophysics, cosmology, geophysics, or any other physical system you dare to consider. You learn physics by solving problems; only through that specific avenue of exploring what physical consequences arise under certain specific conditions can you develop the intuition necessary to bring about an understanding of the kinds of physical systems you want to consider. This is true both experimentally and theoretically, as both classes of physics necessitate their own set of expertise and their own unique set of experiences in gaining it.

If you want to learn how to be a good swimmer, get in the water and swim. If you want to learn how to paint, get out the brushes and canvas and paint. If you want to learn how to play the piano, sit down in front of a piano and start playing those keys. And if you want to learn how to do physics, break out the problem sets or the experimental apparatuses and start solving physics problems.

That’s it. That’s the big secret: if you want to become competent at physics, you have to take on physics problems and become adept with the tools and techniques needed to solve them. In the history of physics, this has been a hallmark of absolutely everyone who’s made a meaningful contribution: either experimentally or theoretically or at the intersection of both. Without sufficient experience at problem solving, you simply cannot become a competent physicist, as only through the act of solving those key problems will you develop the necessary skills to become competent at this endeavor at all.

We all have gifts and talents, but one of the rude awakenings that many physics students receive at some point along their educational journey is that no matter your gifts and talents, there is no substitute for the development of necessary skills. Problem solving is something you can be talented at, for certain, but we all need practice at solving those problems in order to gain a competence and a familiarity — and to eventually develop an intuition that doesn’t lead you astray — when it comes to any particular area of physics. If you don’t put in that specific type of work, you’ll never develop the most important aspect of becoming good at physics: understanding the quantitative relationship between different physical phenomena and effects.

A lot of students are mystified at hearing this seemingly obvious advice, thinking they’re already following it as directed by attempting the assigned homework. Although you get partial credit for that, the main advice — you become good at physics by solving physics problems — has an important corollary: you need to learn a greater amount of physics than the physics you’d encounter simply from going through your assigned homework.

You need to learn the physics in your physics textbook, for example. Most students believe, erroneously, that if you read the textbook and refer to various sections of it, as needed, while solving your homework problems, that’s sufficient. Instead, I’d recommend the following course of action instead.

Read the relevant section of the book before attending the lecture that will cover the material in the book, including taking notes and writing down the equations that appear.
When you go to your lecture, take notes on everything the instructor writes down, including anything they say that you find relevant/interesting that they don’t write down.
After your lecture — and before doing your homework — go through the relevant section of your book along with your lecture notes, and this time make sure you can step-by-step work through every problem that was solved and/or worked out in the lecture and in the relevant section of the book.
And then, only then, after you’ve done all of that, should you go and do your homework.

If that sounds like a lot of work to put in, I’d encourage you to ask yourself this question: what do you hope to get out of an education in physics? Because all you’ll ever get out is directly proportional to the work you put in. The more time you spend with the equations, setting them up correctly under a variety of physical conditions, solving the relevant system of equations to find the unknown quantities based on what you can know/measure, and then comparing those predictions with something that’s measurable, the more capable you’ll be of correctly and usefully modeling a novel, newly considered system.

There are lots of other activities, many of which are worth the time and investment of effort, that can help you improve at physics in addition to setting up and solving relevant sets of problems.

You can read books, including in-depth and popular accounts of various topics, often going back to the original sources where the idea you’re interested in was first put forth.
You can read review papers and conference proceedings, which typically offer a broader, more modern, more accessible overview of a new field than a textbook or original source can.
You can work through specialized textbooks, particularly ones that guide you through the equations relevant to the problems you’re considering.

But, once again, if you don’t work out the quantitative parts for yourself, you’re short-changing yourself on an intellectually fundamental level.

As a physicist, you’ll often receive solicitations from people who say things like, “I have an idea, I just need someone to help me with the math/details.” But unless you’re someone who’s worked through the quantitative details found in a variety of physical systems for yourself — likely correcting a vast array of misconceptions that you previously had before learning the lessons one learns by doing precisely that hard, quantitative work — you have no way of evaluating whether your idea even makes sense, much less if it has any merits.

You learn physics by solving problems, and by extension, if you haven’t solved the relevant problems, you almost certainly haven’t learned enough physics to be able to evaluate an idea in any sort of meaningful way. A huge part of learning physics involves disabusing yourself of notions that you possessed before you learned the valuable lessons one can only learn by doing that difficult, necessary, quantitative work to see which effects matter, and by how much, under a variety of circumstances. Imagination may be more important than knowledge, but a foundational level of knowledge is absolutely required for your imaginative thoughts to be relevant to the Universe at hand. You learn physics by solving problems, and that’s the secret key to achieving excellence in this particular scientific field.

4 tricks for solving any physics problem

Physics can be intimidating—all those pulleys and protons and projectile motion. If you approach it with the right mindset, however, even the hardest problems are usually easier than you think. When you come up against a tough question, don’t panic. Instead, start with these short, easy tricks to help you work through the problem.

4 tricks for solving any physics problem:

1. what is the subject.

Just about every physics question is testing specific knowledge. When you read the question ask yourself, is it exploring electricity? Torque? Parabolic motion? Each topic is associated with specific equations and approaches, so recognizing the subject will focus your effort in the right direction. Look for keywords and phrases that reveal the topic.

2. What are you trying to find?

This simple step can save a lot of time. Before starting to solve the problem, think about what the answer will look like. What are the units; is the final answer going to be in kilograms or liters? Also, consider what other physical quantities might relate to your answer. If you’re trying to find speed, it might be useful to find acceleration, then solve that for speed. Determining restrictions on the answer early also ensures you answer the specific question; a common mistake in physics is solving for the wrong thing.

3. What do you know?

Think about what details the problem mentions. Unless the question is really bad, they probably gave you exactly the information you need to solve the problem. Don’t be surprised if sometimes this information is coded in language; a problem that mentions a spring with “the mass removed from the end” is telling you something important about the quantities of force. Write down every quantity you know from the problem, then proceed to…

4. What equations can you use?

What equations include the quantities you know and also the one you’re looking for? If you have the mass of an object and a force and you’re trying to find the acceleration, start with F=ma (Newton’s second law). If you’re trying to find the electric field but you have the charge and the distance, try E=q/(4πε*r 2 ).

If you’re having trouble figuring out which equation to use, go back to our first trick. What equations are associated with the topic? Can you manipulate the quantities you have to fit in any of them?

Bonus Trick: “hack” the units

This trick doesn’t always work but it can jumpstart your brain. First, determine the units of the quantity you’re trying to find and the quantities you have. Only use base units (meters, kilograms, seconds, charge), not compound units (Force is measured in Newtons, which are just kg*m/s 2 ). Multiply and divide the quantities until the units match the units of the answer quantity. For example, if you’re trying to find Potential Energy (kg*m 2 /s 2 ) and you have the height (m), mass (kg), and gravitational acceleration (m/s 2 ), you can match the units by multiplying the three quantities (m*kg*m/s 2 =kg*m 2 /s 2 ).

Note: Unlike the other ones, this trick won’t always work. Watch out for unitless constants. For example, Kinetic energy is ½*mass*velocity 2 , not just mass*velocity 2 as the units suggest. Even though this trick isn’t perfect, however, it can still be a great place to start.

1.7 Solving Problems in Physics

Learning objectives.

By the end of this section, you will be able to:

Describe the process for developing a problem-solving strategy.
Explain how to find the numerical solution to a problem.
Summarize the process for assessing the significance of the numerical solution to a problem.

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch can be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
Identify exactly what needs to be determined in the problem (identify the unknowns) . In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

Check your units. If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these that science progresses.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

Authors: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher/website: OpenStax
Book title: University Physics Volume 1
Publication date: Sep 19, 2016
Location: Houston, Texas
Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
Section URL: https://openstax.org/books/university-physics-volume-1/pages/1-7-solving-problems-in-physics

© Jul 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Physics Wizard: 4 Secrets To Ace Problem-Solving In Exams

There’s no denying that Physics is a challenging and complicated field to study. All those theories, laws, and concepts need to be understood - not to mention the countless formulas that need to be solved and the detailed mathematical understanding and skills required! Problem-solving never goes out of the picture, too! If you are struggling with solving Physics problems, there are some tips that you can try!

Physics is a challenging course to tackle, and many students struggle when presented with a Physics problem. As difficult as it may seem, approaching it with the right mindset and practice, even the most confusing issues magically, seems more straightforward than you think! When you face a challenging or short Physics problem, don’t panic! Take a deep breath and follow these five techniques to help you solve the problem.

Understand what the topic is about

Every question in your exam is designed to test your knowledge of specific topics. Read the question carefully and understand what the question about is. Is it about heat and temperature? Forces and motion? Or perhaps about momentum? Each topic consists of specific terms, equations, and approaches, so understanding what the issue is about can help you narrow down the possible formulas to use to find the answer!

Figure out what the problem is looking for

After understanding the topic, it’s easy to get excited and quickly write down the formula used and start solving! However, this simple step can often lead to careless mistakes, especially the calculations. To avoid that, make sure to read the problem slowly and write down what you are looking for. In addition, take note of the unit of measurement used before tackling the problem!

List down familiar terms

Sometimes, you may encounter a problem that will leave you feeling lost even after days of studying for the exam. When this happens, the first thing you should do is list down which terms in the physics problem are familiar to you. Often, the question will already have the exact information that you need to identify and solve the problem.

Solve by using the correct equation/s

It is not surprising that you will likely encounter multiple calculation questions during your Physics exam. Next to understanding the problem, knowing which equation/s to use and applying them correctly is essential to get the final answer and pass your exam. So, whenever you encounter a calculation question, start by listing down the equations you know and determine which one(s) are useful in solving the problem.

For example, if you have the constant speed (v) of an object and the time (t) over which the motion occurred is given too, use the formula s = vt if you’re trying to find the displacement. But if you have the acceleration (a) and you’re trying to solve the velocity, use v = u + at.

Seek help for complicated topics

There will be times when you’ll encounter topics that are far too difficult to understand or solve on your own. In such cases, it’s wise to seek help from someone knowledgeable in the subject to guide with high-quality instruction. Enrolling in physics tuition is the most efficient way to get the help you need! The passionate and experienced tutors can help you understand the topics you need help with.

It’s common for students to struggle in Physics, especially the problem-solving part and for students transitioning to a higher level. As such, if you find yourself struggling with the course, rest assured that you are not alone! With practice and proper guidance from jc physics tuition , you’ll find yourself acing this subject in no time!

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Check Your Understanding

Answer: d = 1720 m

Answer: a = 8.10 m/s/s

Answers: d = 33.1 m and v f = 25.5 m/s

Answers: a = 11.2 m/s/s and d = 79.8 m

Answer: t = 1.29 s

Answers: a = 243 m/s/s

Answer: a = 0.712 m/s/s

Answer: d = 704 m

Answer: d = 28.6 m

Answer: v i = 7.17 m/s

Answer: v i = 5.03 m/s and hang time = 1.03 s (except for in sports commericals)

Answer: a = 1.62*10 5 m/s/s

Answer: d = 48.0 m

Answer: t = 8.69 s

Answer: a = -1.08*10^6 m/s/s

Answer: d = -57.0 m (57.0 meters deep)

Answer: v i = 47.6 m/s

Answer: a = 2.86 m/s/s and t = 30. 8 s

Answer: a = 15.8 m/s/s

Answer: v i = 94.4 mi/hr

Solutions to Above Problems

t = 32.8 s

v = 0 m/s

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s 2 )*(32.8 s) 2

Return to Problem 1

t = 5.21 s

v = 0 m/s

110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s) 2

110 m = (13.57 s 2 )*a

a = (110 m)/(13.57 s 2 )

a = 8.10 m/ s 2

Return to Problem 2

t = 2.6 s

v = 0 m/s

d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s 2 )*(2.60 s) 2

d = -33.1 m (- indicates direction)

v f = v i + a*t

v f = 0 + (-9.8 m/s 2 )*(2.60 s)

v f = -25.5 m/s (- indicates direction)

Return to Problem 3

v = 18.5 m/s

v = 46.1 m/s

t = 2.47 s

a = (46.1 m/s - 18.5 m/s)/(2.47 s)

a = 11.2 m/s 2

d = v i *t + 0.5*a*t 2

d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s 2 )*(2.47 s) 2

d = 45.7 m + 34.1 m

(Note: the d can also be calculated using the equation v f 2 = v i 2 + 2*a*d)

Return to Problem 4

v = 0 m/s

d = -1.40 m

-1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s 2 )*(t) 2

-1.40 m = 0+ (-0.835 m/s 2 )*(t) 2

(-1.40 m)/(-0.835 m/s 2 ) = t 2

1.68 s 2 = t 2

Return to Problem 5

v = 0 m/s

v = 444 m/s

a = (444 m/s - 0 m/s)/(1.83 s)

a = 243 m/s 2

d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s 2 )*(1.83 s) 2

d = 0 m + 406 m

Return to Problem 6

v = 0 m/s

v = 7.10 m/s

(7.10 m/s) 2 = (0 m/s) 2 + 2*(a)*(35.4 m)

50.4 m 2 /s 2 = (0 m/s) 2 + (70.8 m)*a

(50.4 m 2 /s 2 )/(70.8 m) = a

a = 0.712 m/s 2

Return to Problem 7

v = 0 m/s

v = 65 m/s

(65 m/s) 2 = (0 m/s) 2 + 2*(3 m/s 2 )*d

4225 m 2 /s 2 = (0 m/s) 2 + (6 m/s 2 )*d

(4225 m 2 /s 2 )/(6 m/s 2 ) = d

Return to Problem 8

v = 22.4 m/s

v = 0 m/s

d = (22.4 m/s + 0 m/s)/2 *2.55 s

d = (11.2 m/s)*2.55 s

Return to Problem 9

a = -9.8 m/s

v = 0 m/s

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(2.62 m)

0 m 2 /s 2 = v i 2 - 51.35 m 2 /s 2

51.35 m 2 /s 2 = v i 2

v i = 7.17 m/s

Return to Problem 10

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(1.29 m)

0 m 2 /s 2 = v i 2 - 25.28 m 2 /s 2

25.28 m 2 /s 2 = v i 2

v i = 5.03 m/s

To find hang time, find the time to the peak and then double it.

0 m/s = 5.03 m/s + (-9.8 m/s 2 )*t up

-5.03 m/s = (-9.8 m/s 2 )*t up

(-5.03 m/s)/(-9.8 m/s 2 ) = t up

t up = 0.513 s

hang time = 1.03 s

Return to Problem 11

v = 0 m/s

v = 521 m/s

(521 m/s) 2 = (0 m/s) 2 + 2*(a)*(0.840 m)

271441 m 2 /s 2 = (0 m/s) 2 + (1.68 m)*a

(271441 m 2 /s 2 )/(1.68 m) = a

a = 1.62*10 5 m /s 2

Return to Problem 12

(NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.)

First use: v f = v i + a*t

0 m/s = v i + (-9.8 m/s 2 )*(3.13 s)

0 m/s = v i - 30.7 m/s

v i = 30.7 m/s (30.674 m/s)

Now use: v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = (30.7 m/s) 2 + 2*(-9.8 m/s 2 )*(d)

0 m 2 /s 2 = (940 m 2 /s 2 ) + (-19.6 m/s 2 )*d

-940 m 2 /s 2 = (-19.6 m/s 2 )*d

(-940 m 2 /s 2 )/(-19.6 m/s 2 ) = d

Return to Problem 13

v = 0 m/s

d = -370 m

-370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s 2 )*(t) 2

-370 m = 0+ (-4.9 m/s 2 )*(t) 2

(-370 m)/(-4.9 m/s 2 ) = t 2

75.5 s 2 = t 2

Return to Problem 14

v = 367 m/s

v = 0 m/s

(0 m/s) 2 = (367 m/s) 2 + 2*(a)*(0.0621 m)

0 m 2 /s 2 = (134689 m 2 /s 2 ) + (0.1242 m)*a

-134689 m 2 /s 2 = (0.1242 m)*a

(-134689 m 2 /s 2 )/(0.1242 m) = a

a = -1.08*10 6 m /s 2

(The - sign indicates that the bullet slowed down.)

Return to Problem 15

t = 3.41 s

v = 0 m/s

d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s 2 )*(3.41 s) 2

d = 0 m+ 0.5*(-9.8 m/s 2 )*(11.63 s 2 )

d = -57.0 m

(NOTE: the - sign indicates direction)

Return to Problem 16

a = -3.90 m/s

v = 0 m/s

(0 m/s) 2 = v i 2 + 2*(- 3.90 m/s 2 )*(290 m)

0 m 2 /s 2 = v i 2 - 2262 m 2 /s 2

2262 m 2 /s 2 = v i 2

v i = 47.6 m /s

Return to Problem 17

v = 0 m/s

v = 88.3 m/s

( 88.3 m/s) 2 = (0 m/s) 2 + 2*(a)*(1365 m)

7797 m 2 /s 2 = (0 m 2 /s 2 ) + (2730 m)*a

7797 m 2 /s 2 = (2730 m)*a

(7797 m 2 /s 2 )/(2730 m) = a

a = 2.86 m/s 2

88.3 m/s = 0 m/s + (2.86 m/s 2 )*t

(88.3 m/s)/(2.86 m/s 2 ) = t

t = 30. 8 s

Return to Problem 18

v = 0 m/s

v = m/s

( 112 m/s) 2 = (0 m/s) 2 + 2*(a)*(398 m)

12544 m 2 /s 2 = 0 m 2 /s 2 + (796 m)*a

12544 m 2 /s 2 = (796 m)*a

(12544 m 2 /s 2 )/(796 m) = a

a = 15.8 m/s 2

Return to Problem 19

v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(91.5 m)

0 m 2 /s 2 = v i 2 - 1793 m 2 /s 2

1793 m 2 /s 2 = v i 2

v i = 42.3 m/s

Now convert from m/s to mi/hr:

v i = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

v i = 94.4 mi/hr

Return to Problem 20

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Physics problem solving secrets: 120 must-know problems solved step-by-step - softcover, ulrich, david j..

9781463798659: Physics Problem Solving Secrets: 120 Must-Know Problems Solved Step-By-Step

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Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy

Hiroshi hayasaka, takashi imoto, yuichiro matsuzaki, and shiro kawabata, phys. rev. a 110 , 022620 – published 26 august 2024.

No Citing Articles
INTRODUCTION
QUANTUM ANNEALING AND ADIABATIC GROVER…
GENERAL FRAMEWORK
ADIABATIC GROVER SEARCH WITH PENALTY…
FERROMAGNETIC p SPIN MODEL
ACKNOWLEDGMENTS

Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using what is referred to as the adiabatic condition derived from the adiabatic theorem. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most Θ ( L ) , where L is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. For concrete examples, we consider the adiabatic Grover search and the ferromagnetic p -spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap, we are able to achieve a success probability considerably higher than that of conventional QA. Moreover, in concrete examples, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA. Our findings pave the way for a better understanding of QA performance.

Received 17 November 2023
Revised 11 July 2024
Accepted 5 August 2024

DOI: https://doi.org/10.1103/PhysRevA.110.022620

Physics Subject Headings (PhySH)

Research Areas

Authors & Affiliations

1 Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568, Japan
2 NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568, Japan
* Contact author: [email protected]
† Contact author: [email protected]
‡ Contact author: [email protected], present address: [email protected]
§ Contact author: [email protected], present address: [email protected]

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Vol. 110, Iss. 2 — August 2024

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Plot of adiabatic-condition term η for the adiabatic Grover search as a function of normalized time t / T , where L is the number of qubits.

Energy spectrum and fidelity for the adiabatic Grover search as functions of t / T . Energy diagram in L = 10 (a) without penalty term and (b) with penalty term. Fidelity (c) without penalty term and (d) with penalty term. Annealing time T = 20 .

Scaling of (a) energy gap at t = T / 2 and (b) fidelity at t = T for the adiabatic Grover search. Purple (bottom) and green (top) lines correspond to cases without and with penalty term, respectively. In (a) and (b), annealing time is T = 20 . (c) The fidelity and corresponding computational cost where the system size is L = 10 . Here, we use T = 10 n ( T = 100 m ) for 1 ≤ n ≤ 20 , n ∈ N ( 1 ≤ m ≤ 60 , m ∈ N ) in the case with (without) penalty term. (d) The computational cost to obtain a fidelity higher than 0.5. We plot the cost against the number of qubits to identify the scaling behavior. In (c) and (d), purple (square) and green (circle) dots correspond to cases without and with penalty term, respectively.

Energy spectrum and fidelity as functions of t / T for the ferromagnetic p -spin model. Energy diagram in L = 40 (a) without penalty term and (b) with penalty term. Fidelity (c) without penalty term and (d) with penalty term. Annealing time T = 20 , p = 5 .

Scaling of (a) minimum of energy gap and (b) fidelity at t = T for the ferromagnetic p -spin model. Purple (bottom) and green (top) lines correspond to cases without and with penalty term, respectively. In (a) and (b), we set T = 20 and p = 5 . (c) The fidelity and corresponding computational cost where the system size is L = 16 . Here, we use T = 10 n ( T = 100 m ) for 1 ≤ n ≤ 20 , n ∈ N ( 1 ≤ m ≤ 20 , m ∈ N ) in the case with (without) penalty term. (d) The computational cost to obtain a fidelity higher than 0.5. We plot the cost against the number of qubits to identify the scaling behavior. In (c) and (d), purple (square) and green (circle) dots correspond to cases without and with penalty term, respectively.

Fidelity (a) without penalty term and (b) with penalty term as functions of t / T . Annealing time T = 20 .

Scaling of fidelity at t = T . Purple (bottom) and green (top) lines denote the cases without and with penalty term, respectively. Annealing time T = 20 .

Fidelity for the adiabatic Grover search with penalty term as functions of T . The system size is L = 10 .

Maximum of transition matrix for the ferromagnetic p -spin model. Purple (middle), green (top), and blue (bottom) lines denote cases without and with penalty term and with nonstoquastic term, respectively. Annealing time T = 20 .

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At the Democratic Convention, a Historic Nomination

What story did the democrats tell about kamala harris and will it be enough to win.

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

[BACKGROUND CHATTER]

I’m standing in a sea of people coming out of this vast convention. And people are holding signs, smiling. There’s confetti everywhere. There are balloons, white, red, and blue. And there’s a lot of excitement.

From “The New York Times,” I’m Sabrina Tavernise. And this is “The Daily” from inside the Democratic National Convention Hall, where Kamala Harris has just accepted her party’s nomination, becoming the first woman of color in US history to do so.

Today, the story this convention told about Harris and whether that story could be enough to win.

It’s Friday, August 23.

[SERENE MUSIC]

The work and prayers of centuries have brought us to this day. What shall our our legacy be? What will our children say? Let me in my heart, when my days are through, America, America, I gave my best to you.

On night one of the Democratic National Convention, the evening was really defined by this very emotional, quite bittersweet goodbye from President Biden.

And there’s nothing we cannot do when we do it together.

God bless you all. And may God protect our troops.

It was the closing of one chapter so that another could begin. It was Kamala Harris’s moment.

[UPBEAT JAZZ MUSIC]

So right now, it’s 7:40. We are on the floor at the Democratic National Convention. It is a crazy party atmosphere, which is like a massive understatement.

Day two kicked off with delegates gathering on the convention floor, casting their votes in a kind of symbolic way to make Harris the party’s nominee.

This giant festival of lights, people in cowboy hats, people with blinking bracelets, people with Christmas lights wrapped around their hats, heads, shoulders, people wearing donkey hats. I mean, it’s very, very, very celebratory in here.

We need to see that we’re moving on. We are turning a chapter in America.

How do you feel right now?

Awesome, excitement, energized. Ready to win this election.

I love it. I love it. People are just excited, electrified, and they’re just loving it, and they’re happy.

This has been the most electrifying event I’ve ever attended in my life. It’s my first convention. But what a convention to come for, right? To make history right now, as we charge forward to November 5, to elect the first female Black president. I’m excited.

So with Harris now the nominee, a new campaign slogan appeared everywhere. And that was, “A new way forward.” But in a campaign that’s just four weeks old, it was really an open question what “a new way forward” actually meant.

We’re not going back!

We’re not going back! We’re not going back!

And then over the course of the week, as speaker after speaker took the stage, we started to get an answer. The story of forward would be told through the story of Kamala Harris herself. And the question hanging over the week was really whether that story could appeal to a broad majority of Americans, voters outside of the convention hall who will ultimately decide the election.

[UPBEAT MUSIC]

Astead, welcome to the show.

Thank you for having me.

Again. The second time in a week. And I’m very excited for it.

So Astead, we had on the show on Monday to answer a question for us, that I think a lot of people have, which is, who is Kamala Harris? And you ended that conversation by saying that the Democratic Party also recognizes this reality, that for a lot of people, she is still this unknown quantity.

And that the party had a big task here at the convention this week, which was to find a way to finally tell her story. It does seem like they’ve tried to do that. Let’s walk through the case that they’re making for her. And what you’ve seen here in your reporting for your show, “The Run-Up.”

Yeah, I mean, I think that the Democrats have definitely laid out a case for her as a candidate, but also a story for her as a person. They have leaned into the different parts of her biography to really follow through on what, I think, is the best version of her campaign, which is a little bit for everybody. There is a story there about more moderate legislation, but pieces of progressive history. There’s different parts of her bio that speak to Black communities, immigrant communities.

Of course, the historic nature of her gender and the roles like that. And I really think it has followed through on what I expected for this week, which is that she seems to function politically as a mirror of some sort, where the party wants to position her as someone who basically, no matter what you’re looking for in terms of a vessel to beat Donald Trump, you can find it in this candidate.

Let’s dig into that more. Where did the convention start, that story?

Hello, Democrats!

Yeah, I think it really starts in her personal biography.

And I’m here tonight to tell you all about the Kamala Harris that I know.

They have told a story that she often tells about her being a first generation American.

Her mother moved here from India at 19.

And being a daughter of an immigrant mother who really raised two daughters in the Bay Area from working class roots. And that’s been a real thing that they’ve tried to own.

Kamala was not born into privilege. She had to work for what she’s got.

When she was young, she worked at McDonald’s.

They talk about her working at McDonald’s in college.

And she greeted every person without thousand watt smile and said, how can I help you?

I think it’s overall about trying to present this as someone who pulled himself up by bootstraps. It represents the American dream. And I think for Democrats, it really returns them back to the place they want to be. Democrats like thinking of themselves as a party who appeals to the diversity of America, both in racial ways, in gender ways, but also in class ways.

In Kamala Harris, we have a chance to elect a president who is for the middle class because she is from the middle class.

And I think they used other parts of her identity, specifically thinking about being the first Black woman to accept a major party’s nomination.

We know folks are going to do everything they can to distort her truth.

And I think Michelle Obama’s speech, specifically, spoke to the power and anxiety that sometimes that identity can bring.

My husband and I sadly know a little something about this.

For years, Donald Trump did everything in his power to try to make people fear us. See, his limited, narrow view of the world made him feel threatened by the existence of two hard-working, highly educated, successful people who happen to be Black.

And I would also say that it was an implicit response to what Republicans and others have been trying to say, talking about Kamala Harris as a DEI hire, someone who was only in their position because of their identity. But the way that Michelle Obama framed it was that those identities have power.

I want to know. I want to know. Who’s going to tell him, who’s going to tell him that the job he’s currently seeking might just be one of those Black jobs?

Just because someone the first to be in a position, does not mean that is the only reason in the position. But it also doesn’t make those identities meaningless. The fact that she is a Black woman should be seen as a strength, not as a weakness.

Is there a risk to that, though? I mean, by openly talking about race, is there a risk that goes too far and begins to alienate voters outside the convention out in the world who they need to win in November.

I mean, there’s always a risk. But I don’t really think so. Democrats have had increasing trouble with Black voters. There’s been a downturn in Black vote share all the way dating back to 2012.

In Biden’s now suspended candidacy, that was one of the things driving his polling weaknesses was kind of tepid reception from Black voters. A pitch to them is something that is a upside of the Kamala Harris campaign. And the hope that they could consolidate that community is where any Democratic nominee needs to be as a baseline.

We both got our start as young lawyers, helping children who were abused and neglected.

One thing I noticed that came up a lot during the speeches was her background as a prosecutor. How did the party present that part of her biography?

As a prosecutor, Kamala stood up for children who had been victims of sexual abuse.

She put rapists, child molesters, and murderers behind bars.

They talk about it in the way that I think fuels what they want to say is the reason she can take on Trump, that this is someone who has stood up to bullies before, who’s not going to be intimidated easily —

And Kamala is as tough as it comes.

— who’s tough, and who doesn’t shirk away from a challenge.

And she knows the best way to deal with a coward is to take him head on, because we all know cowards are weak. And Kamala Harris can smell weakness.

I think all of that adds up to say, you can trust this person to go up against Donald Trump. You can trust this person to go up against the Republican Party, because she’s not someone who is scared.

She never runs from a fight.

A woman, a fierce woman for the people.

But then, of course, we heard about another side of Kamala Harris, a more personal side.

Yeah, and I think this is the part of Kamala Harris where I think was kind of most missing in the presidential run. Frankly, it’s the part that she keeps most private. She is a warm family member and friend.

Hello to my big, beautiful blended family up there.

And I think what the speech from her husband did was really show and lay that out.

I got married, became a dad to Cole and Ella. Unfortunately, went through a divorce, but eventually started worrying about how I would make it all work. And that’s when something unexpected happened, I ended up with Kamala Harris’s phone number.

He talks about the kind of awkwardness of their first interaction.

I got Kamala’s voicemail, and I just started rambling. “Hey, it’s Doug.”

And I think you have a real kind of sense of their genuine connection to one another.

By the way, Kamala saved that voicemail. And she makes me listen to it on every anniversary.

Like, yes, this is someone who is tough, who is taking on corporations and cartels and all of that stuff by day. But this is someone who also makes a point to cook Sunday dinner for family every week.

And she makes a mean brisket for Passover.

And makes sure to really go close to his kids and is very close with her family.

That’s Kamala. She’s always been there for our children. And I know she’ll always be there for yours, too.

Going back to the last time the Democratic Party nominated a woman, Hillary Clinton, she had presented herself in a very different way. She kind of ran away from that stuff. She was saying, I don’t bake cookies, that’s not what I do. I’m kind of out there with the men, fighting.

And this convention and this candidate, Harris, is very different. She’s a newer generation. And she can do her career and bake cookies. Those things are not in conflict. This is a different type of woman leader.

This week we talked to Senator Elizabeth Warren on “The Run-Up,” and one of the things that she mentioned was she feels that there’s been a big change from 2016, even 2020 to now. Not just the amount of women in public office, but she said they don’t have to choose between sides of themselves. And I think that’s what diversity means.

Of course, Kamala Harris can be a tough politician and also bake cookies. Hillary Clinton did that, too. It was just that she was told that was not the way that she had to present herself. What Kamala Harris is benefiting from is there’s a greater space and ability to choose multiple things at once. And so particularly if others are going to talk more directly about gender or race or other things, that kind of frees her from having the burden of doing that herself.

And in fact, Hillary Clinton, herself, did speak, of course, on day one. She talked about that glass ceiling in the history that has led to now, including her own experience in 2016.

Yeah, I thought the Hillary Clinton speech was really powerful. I think a lot of the speakers put this moment in historical context, both politically and personally.

My mother, Dorothy, was born right here in Chicago before women had the right to vote. That changed 104 years ago yesterday. And since that day, every generation has carried the torch forward. In 1972, a fearless Black congresswoman named Shirley Chisholm —

— she ran for president. In 1984, I brought my daughter to see Geraldine Ferraro, the first woman nominated for vice president. And then there was 2016, when it was the honor of my life to accept our party’s nomination for president.

The last time I was here in my hometown was to memorialize my mother, the woman who showed me the power of my own voice. My mother volunteered at the local school.

I’m the proud granddaughter of a housekeeper, Sarah Daisy, who raised her three children in a one-bedroom apartment. It was her dream to work in government, to help people.

My grandmother, the woman who helped raise me as a child, a little old white lady born in a tiny town called Peru, Kansas.

I want to talk now about somebody who’s not with us tonight. Tessie Prevost Williams was born in New Orleans not long after the Supreme Court ruled that segregated public schools were unconstitutional. That was in 1954, same year I was born. Parents pulled their kids out of the school.

There was a way that I think the candidacy and the person was placed in a long legacy, both about gender identity and racial identity that kind of teed up this Thursday as a culminating moment, both politically and I think, in a broader historical context.

Together, we put a lot of cracks in the highest, hardest glass ceiling. And you know what? On the other side of that glass ceiling is Kamala Harris raising her hand and taking the oath of office as our 47th president of the United States!

I wish my mother and Kamala’s mother could see us. They would say, keep going. Shirley and Jerry would say, keep going!

I think you can do a lot to set up a candidate to be in a good position. All of this stuff adds up to some part of the puzzle, but the biggest piece is the candidate themself. At the end of the day, they have to close the deal. And I think this moment is her chance to tell her own story in a way that sometimes she has not decided to. And that’s still what this whole convention success and failure will ride on.

We’re going to watch tonight. We’re going to watch with our colleague, Reid Epstein. And you are going to have a great episode of “The Run-Up” on Friday. We will all be tuning in.

Thank you. I appreciate you doing this, Sabrina.

Really thanks a lot, Astead.

Are you a delegate?

Sorry, we caught you mid French fry eating. What’s your feeling about Kamala and what her story has been? Are you getting to know her this week? Are there things you’ve learned about her this week?

Yeah, I’m learning more and more as we go along. The more and more I learn about her, the more I’m impressed with her. I mean, she worked at McDonald’s when she was going to college to try to pay her way through.

Her very small beginnings. Not a trust fund baby type of thing. I relate to that. Like, I was on food stamps this year. So it’s like if she can do it with that background, it gives everybody hope.

Hillary was my girl. When Hillary ran, I championed her as well. But I didn’t feel this way as I feel about Harris. I’m like, do I want to run for office? If she can do it, I can. She looks just like me, right? She represents, she works at McDonald’s. She paid for every. It’s relatable. And that’s what everybody needs.

We’re going to break that glass ceiling. I’m getting teary, teary in my eyes. And it just means so much to be inclusive.

[WHIMSICAL MUSIC]

What does it mean to you that Kamala Harris is a woman? What does it mean to you that she’s a Black woman?

To have a Black woman become the president of the United States, and for her to turn the world upside down in 30 days, to know that I’m in the midst of this miraculous history is phenomenal.

One delegate who really stood out to us was Beverly Hatcher, a 76-year-old Black woman from Texas.

I was raised by a wonderful Baptist mama. I just lost her. But I am who I am because of my mother. We were always pushed to do whatever we wanted to do. I’ll never forget. I wanted to be a majorette. I taught myself, because we had no money for, what is it called, lessons

And a majorette is like the baton twirler, right?

Yes. And when I did finally try out in my 11th grade, I won right off. And my classmates, who were predominantly white, as years have gone by, have told me at class reunions and stuff, Beverly, the sleepy town of Wellington woke up.

Oh, my god, we got a Black girl getting ready to be the head majorette. But it happened because I had the drive and the will. My mother and my family stood behind me, and didn’t miss a parade, or a football game, or a basketball game.

And you see that in Harris?

Beverly, what would your mom say if she saw this?

My sisters have been telling me every day how proud my mom is. And I’m just happy. I’m happy to make her happy. Yeah.

We women, who have had mothers like Kamala, like Michelle, I remember Hillary’s mother, we women value their strength and their wisdom. And we’re just glad that they gave us a legacy to pass it on.

Thank you very much.

We’ll be right back.

Reid, hello.

OK. Kamala Harris just wrapped up her acceptance speech. Before we talk about what she said and the case she presented, tell us how her campaign was thinking about the stakes of this moment.

Sabrina, this evening was one of two opportunities, along with the debate next month, for her to speak to tens of millions of people at once. And so for that, the stakes were really high.

Her goal was to present herself as a serious person and a serious candidate, who was not the candidate who flamed out in 2019 or the unsteady vice president from the beginning of her term. She had to show that she had the gravitas to be the commander in chief, the political aptitude to reach out to the middle, and also to progressives in her party all at the same time.

A very tall order. Tell us how she went about doing that.

Good evening, everyone. Good evening.

Well, she started talking around 9:30 Chicago time to a packed United Center with 14,000 or 15,000 people, many, many wearing all white, the color of the suffragettes, a color that makes a statement just by wearing it. And when Harris took the stage —

— they erupted in a cheer that forced her for a couple of minutes to wait before she could start talking.

Thank you. OK, let’s get to business. Let’s get to business. All right.

And what did she finally say once she started talking?

She told the story of her life.

The path that led me here in recent weeks was, no doubt, unexpected. But I’m no stranger to unlikely journeys.

My mother, our mother, Shyamala Harris, had one of her own. And I miss her every day, and especially right now.

She talked about the influence of her mother, who raised her and her sister.

And she also taught us, “And never do anything half-assed.” And that is a direct quote. [LAUGHS]

She spoke about her family’s humble beginnings in Oakland.

Before she could finally afford to buy a home, she rented a small apartment in the East Bay.

Then she started talking about her career as a prosecutor.

In the courtroom, I stood proudly before a judge and I said five words.

She brought back one of the lines that she used in her 2020 campaign about how when she stood up in a courtroom, she began with the same words.

Kamala Harris for the people.

And she said she would bring that same philosophy to the White House, that she was not working for specific individuals, but for the people at large.

And so on behalf of the people —

Eventually she did a bigger wind up to formally accepting the nomination.

— on behalf of every American, regardless of party, race, gender, or the language your grandmother speaks —

And listed the people on whose behalf she did so.

— on behalf of everyone whose story could only be written in the greatest nation on Earth —

It was really a kind of a feat of speech writing to build up to this big emotional moment.

— I accept your nomination to be president of the United States of America.

And what did you make of that, how she was doing that?

It was building up this speech to be a serious political document and present her as a serious figure in this moment. And so she still has to prove to people that she is capable of being the commander in chief and running the country.

And how does she try to prove that she’s capable of being a commander in chief?

What she did was try to draw the distinction between herself and Donald Trump.

In many ways, Donald Trump is an unserious man. But the consequences, but the consequences of putting Donald Trump back in the White House are extremely serious.

And she warns that Trump would not have guardrails on him if he were elected to a second term.

Just imagine Donald Trump with no guardrails.

And how he would use the immense powers of the presidency of the United States not to improve your life, not to strengthen our national security, but to serve the only client he has ever had, himself.

The speech was very clear-eyed about the stakes of the election.

They know Trump won’t hold autocrats accountable because he wants to be an autocrat himself.

There was a whole section in the middle of the speech where she ticked through, one by one, a whole series of warnings about things that Trump would do to the country if he were back in the White House.

Get this, he plans to create a national anti-abortion coordinator and force states to report on women’s miscarriages and abortions.

Simply put, they are out of their minds.

What else stuck out to you?

It was remarkable, the section of the speech where she talked about Gaza.

President Biden and I are working around the clock, because now is the time to get a hostage deal and a ceasefire deal done.

She did not veer too far to the left.

I will always stand up for Israel’s right to defend itself.

She managed to say things that would be appealing to both sides.

President Biden and I are working to end this war, such that Israel is secure, the hostages are released, the suffering in Gaza ends, and the Palestinian people can realize their right to dignity, security, freedom, and self-determination.

It was a remarkable moment to hear the arena erupt at the end of that section, to hear her support for both the Israelis and the Palestinians reveal that kind of enthusiasm, after the party has been really ripped apart for months about how to handle the situation.

Fellow Americans, I love our country with all my heart.

She ended this speech with a paean to patriotism.

We are the heirs to the greatest democracy in the history of the world.

She dove headlong into the American exceptionalism argument that is native to Republicans and to older generations of politicians, like Joe Biden.

It is now our turn to do what generations before us have done. Guided by optimism and faith to fight for this country we love. To fight —

But is not something you always hear from younger Democrats, who are a little less comfortable with some of the flag waving.

Let’s vote for it. And together, let us write the next great chapter in the most extraordinary story ever told. Thank you. God bless you and may God bless the United States of America. Thank you all.

She seemed to really be taking aim at this criticism of her, which is that she’s this radical California liberal and she can’t be trusted with the keys to the country.

I mean, that was one of the tasks that she had tonight, was to make the argument, particularly to voters in the middle, the suburban voters that used to vote for Republicans, but have been repelled by Trump and driven to Democrats in the last several years, that they can vote for her without worrying that she’s some kind of Bernie Sanders acolyte.

And some of that is based on the way she ran her last presidential campaign. Some of it, frankly, is because she’s a Black woman from California. And that the voters who will determine this election are voters in less diverse states, for the most part.

So Reid stepping back here, it feels worth remembering just where we were at the end of the Republican National Convention that was just over a month ago. Things couldn’t have felt more different. The GOP was on top of the world, while the Democrats were in disarray over Biden’s refusal to leave the race.

And now here we are. And it feels like things couldn’t be better for the Democrats. At least that’s the feeling I’m having coming out of this convention.

I mean, the whole race has turned upside down from where it was when we left Milwaukee. And Democrats are upbeat. They are confident. It is a party that is remarkably united behind their candidate.

But you have to remember, this election will be very close. It is, indeed, a game of inches in the key battleground states. And what she was trying to do was to present herself as someone who can be trusted as commander in chief to win over the tiny slices of the electorate that will determine the winner in places like Wisconsin, and Michigan, and Pennsylvania, Georgia, and Arizona.

And those are the states that will determine the election. And they have made a calculated decision that those voters needed to see her as a commander in chief, something they had not seen from her before. And we will see in the coming days and weeks whether she’s accomplished that in a way that brings enough of those people on board for her to win a term as president.

Reid, thank you.

Thank you, Sabrina. [WHIMSICAL MUSIC]

Here’s what else you should know today. On Thursday, the Supreme Court allowed Arizona Republicans, for now, to impose tougher voting requirements, including a new rule that people registering to vote there before the coming election must show proof of citizenship.

As a result, Arizonans newly registering to vote for this year’s presidential election must provide copies of one of several documents, such as a birth certificate or a passport, in order to prove that they are US citizens. Democrats have denounced the new rule as an attempt to prevent legal immigrants from voting.

And US Health officials have approved the latest slate of annual COVID vaccines, clearing the way for Americans six months and older to receive updated shots in the coming days. The approvals come amid a prolonged surge of COVID infections, which have risen all summer.

Remember to catch a new episode of “The Interview” right here tomorrow. This week, Lulu Garcia-Navarro talks with Jenna Ortega, the star of the Netflix series “Wednesday,” and the new “Bettlejuice” sequel, about her head-spinning success over the past few years.

One day I just I woke up in somebody else’s shoes. I felt like I had entered somebody else’s life. And I didn’t know how to get back to mine.

Today’s episode was produced by Lynsea Garrison, Rob Szypko, Jessica Cheung, Asthaa Chaturvedi, and Shannon Lin. It was edited by Rachel Quester, contains original music by Rowan Niemisto, Dan Powell, Diane Wong, and Marion Lozano, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

[THEME MUSIC]

That’s it for “The Daily.” I’m Sabrina Tavernise. See you on Monday.

Apple Podcasts
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Hosted by Sabrina Tavernise

Featuring Astead W. Herndon and Reid J. Epstein

Produced by Lynsea Garrison Rob Szypko Jessica Cheung Asthaa Chaturvedi and Shannon Lin

Edited by Rachel Quester

Original music by Rowan Niemisto Marion Lozano Dan Powell and Diane Wong

Engineered by Chris Wood

Listen and follow ‘The Daily’ Apple Podcasts | Spotify | Amazon Music | YouTube | iHeartRadio

Last night, at the Democratic National Convention, Vice President Kamala Harris accepted her party’s nomination, becoming the first woman of color in U.S. history to do so.

Astead W. Herndon and Reid J. Epstein, who cover politics for The Times, discuss the story this convention told about Ms. Harris — and whether that story could be enough to win the presidential election.

On today’s episode

Astead W. Herndon , a national politics reporter and the host of the politics podcast “ The Run-Up ” for The New York Times.

Reid J. Epstein , who covers politics for The New York Times.

Kamala Harris and her husband, Doug, stand in front of a photo of the American flag, smiling and embracing.

Background reading

Kamala Harris promised to chart a “new way forward” as she accepted the nomination.

“The Run-Up”: It’s her party now. What’s different?

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

Astead W. Herndon is a national politics reporter and the host of the politics podcast “The Run-Up.” More about Astead W. Herndon

Reid J. Epstein covers campaigns and elections from Washington. Before joining The Times in 2019, he worked at The Wall Street Journal, Politico, Newsday and The Milwaukee Journal Sentinel. More about Reid J. Epstein

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Physics Problem Solving Secrets: 120 Must-Know Problems Solved Step-By-Step Paperback – December 25, 2011

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Mastering Physics Problem-Solving: A Comprehensive 6-Step Guide

1. Commence with a Clear and Comprehensive Diagram

2. Systematically Transfer Data to the Diagram

3. Identify Relevant Concepts

4. Establish Correct Equations

5. Integrate Numerical Values into Simplified Equations

6. Present the Final Answer with Precision

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Module 1: Kinematics (1-D and 2-D Motion)

Module 2: Forces and Dynamics

Module 3: Work & Energy

Module 4: Linear Momentum

Module 5: Simple Harmonic Motion

Module 6: Rotational Kinematics and Dynamics

Module 7: Rotational Energy and Angular Momentum

Module 8: Fluids

Module 9: Exam Review and Test Strategies

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The secret to becoming an excellent physicist

4 tricks for solving any physics problem

4 tricks for solving any physics problem:

2. What are you trying to find?

3. What do you know?

4. What equations can you use?

Bonus Trick: “hack” the units

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