physics problem solving secrets pdf

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1.8: Solving Problems in Physics

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Learning Objectives

• 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 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 science that progresses.

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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 328,063 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.

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.

You Might Also Like

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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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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Problem Solving Performance in Physics Among Secondary School Students in Dire Dawa Ethiopia

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Abstract

The main aim of this study was to assess problem solving performance in physics of grade 9th students. A test of reasoning was administered to a sample of 578 students. The results show differential performance of the students. Question based performance with background variable as school sector shows that performance of private school students was significantly better than students of public schools. Similarly female private school students performed well than male private school students.

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The Crackdown on Student Protesters

Columbia university is at the center of a growing showdown over the war in gaza and the limits of free speech..

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.

[TRAIN SCREECHING]

Well, you can hear the helicopter circling. This is Asthaa Chaturvedi. I’m a producer with “The Daily.” Just walked out of the 116 Street Station. It’s the main station for Columbia’s Morningside Heights campus. And it’s day seven of the Gaza solidarity encampment, where a hundred students were arrested last Thursday.

So on one side of Broadway, you see camera crews. You see NYPD officers all lined up. There’s barricades, steel barricades, caution tape. This is normally a completely open campus. And I’m able to — all members of the public, you’re able to walk through.

[NON-ENGLISH SPEECH]

Looks like international media is here.

Have your IDs out. Have your IDs out.

Students lining up to swipe in to get access to the University. ID required for entry.

Swipe your ID, please.

Hi, how are you, officer? We’re journalists with “The New York Times.”

You’re not going to get in, all right? I’m sorry.

Hi. Can I help please?

Yeah, it’s total lockdown here at Columbia.

Please have your IDs out ready to swipe.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.” Today, the story of how Columbia University has become the epicenter of a growing showdown between student protesters, college administrators, and Congress over the war in Gaza and the limits of free speech. I spoke with my colleague, Nick Fandos.

[UPBEAT MUSIC]

It’s Thursday, April 25.

Nick, if we rewind the clock a few months, we end up at a moment where students at several of the country’s best known universities are protesting Israel’s response to the October 7 attacks, its approach to a war in Gaza. At times, those protests are happening peacefully, at times with rhetoric that is inflammatory. And the result is that the leaders of those universities land before Congress. But the president of Columbia University, which is the subject we’re going to be talking about today, is not one of the leaders who shows up for that testimony.

That’s right. So the House Education Committee has been watching all these protests on campus. And the Republican Chairwoman decides, I’m going to open an investigation, look at how these administrations are handling it, because it doesn’t look good from where I sit. And the House last winter invites the leaders of several of these elite schools, Harvard, Penn, MIT, and Columbia, to come and testify in Washington on Capitol Hill before Congress.

Now, the President of Columbia has what turns out to be a very well-timed, pre-planned trip to go overseas and speak at an international climate conference. So Minouche Shafik isn’t going to be there. So instead, the presidents of Harvard, and Penn, and MIT show up. And it turned out to be a disaster for these universities.

They were asked very pointed questions about the kind of speech taking place on their campuses, and they gave really convoluted academic answers back that just baffled the committee. But there was one question that really embodied the kind of disconnect between the Committee — And it wasn’t just Republicans, Republicans and Democrats on the Committee — and these college presidents. And that’s when they were asked a hypothetical.

Does calling for the genocide of Jews violate Penn’s rules or code of conduct? Yes or no?

If the speech turns into conduct, it can be harassment.

And two of the presidents, Claudine Gay of Harvard and Elizabeth Magill of the University of Pennsylvania, they’re unwilling to say in this really kind of intense back and forth that this speech would constitute a violation of their rules.

It can be, depending on the context.

What’s the context?

Targeted at an individual. Is it pervasive?

It’s targeted at Jewish students, Jewish individuals. Do you understand your testimony is dehumanizing them?

And it sets off a firestorm.

It does not depend on the context. The answer is yes. And this is why you should resign. These are unacceptable answers across the board.

Members of Congress start calling for their resignations. Alumni are really, really ticked off. Trustees of the University start to wonder, I don’t know that these leaders really have got this under control. And eventually, both of them lose their jobs in a really high profile way.

Right. And as you’ve hinted at, for somewhat peculiar scheduling reasons, Columbia’s President escapes this disaster of a hearing in what has to be regarded as the best timing in the history of the American Academy.

Yeah, exactly. And Columbia is watching all this play out. And I think their first response was relief that she was not in that chair, but also a recognition that, sooner or later, their turn was going to come back around and they were going to have to sit before Congress.

Why were they so certain that they would probably end up before Congress and that this wasn’t a case of completely dodging a bullet?

Well, they remain under investigation by the committee. But also, as the winter wears on, all the same intense protests just continue unabated. So in many ways, Columbia’s like these other campuses. But in some ways, it’s even more intense. This is a university that has both one of the largest Jewish student populations of any of its peers. But it also has a large Arab and Muslim student population, a big Middle Eastern studies program. It has a dual degree program in Tel Aviv.

And it’s a university on top of all that that has a real history of activism dating back to the 1960s. So when students are recruited or choose to come to Columbia, they’re actively opting into a campus that prides itself on being an activist community. It’s in the middle of New York City. It’s a global place. They consider the city and the world, really, like a classroom to Columbia.

In other words, if any campus was going to be a hotbed of protest and debate over this conflict, it was going to be Columbia University.

Exactly. And when this spring rolls around, the stars finally align. And the same congressional committee issues another invitation to Minouche Shafik, Columbia’s President, to come and testify. And this time, she has no excuse to say no.

But presumably, she is well aware of exactly what testifying before this committee entails and is highly prepared.

Columbia knew this moment was coming. They spent months preparing for this hearing. They brought in outside consultants, crisis communicators, experts on anti-Semitism. The weekend before the hearing, she actually travels down to Washington to hole up in a war room, where she starts preparing her testimony with mock questioners and testy exchanges to prep her for this. And she’s very clear on what she wants to try to do.

Where her counterparts had gone before the committee a few months before and looked aloof, she wanted to project humility and competence, to say, I know that there’s an issue on my campus right now with some of these protests veering off into anti-Semitic incidents. But I’m getting that under control. I’m taking steps in good faith to make sure that we restore order to this campus, while allowing people to express themselves freely as well.

So then the day of her actual testimony arrives. And just walk us through how it goes.

The Committee on Education and Workforce will come to order. I note that —

So Wednesday morning rolls around. And President Shafik sits at the witness stand with two of her trustees and the head of Columbia’s new anti-Semitism task force.

Columbia stands guilty of gross negligence at best and at worst has become a platform for those supporting terrorism and violence against the Jewish people.

And right off the bat, they’re put through a pretty humbling litany of some of the worst hits of what’s been happening on campus.

For example, just four days after the harrowing October 7 attack, a former Columbia undergraduate beat an Israeli student with a stick.

The Republican Chairwoman of the Committee, Virginia Foxx, starts reminding her that there was a student who was actually hit with a stick on campus. There was another gathering more recently glorifying Hamas and other terrorist organizations, and the kind of chants that have become an everyday chorus on campus, which many Jewish students see as threatening. But when the questioning starts, President Shafik is ready. One of the first ones she gets is the one that tripped up her colleagues.

Does calling for the genocide of Jews violate Columbia’s code of conduct, Mr. Greenwald?

And she answers unequivocally.

Dr. Shafik?

Yes, it does.

And, Professor —

That would be a violation of Columbia’s rules. They would be punished.

As President of Columbia, what is it like when you hear chants like, by any means necessary or Intifada Revolution?

I find those chants incredibly distressing. And I wish profoundly that people would not use them on our campus.

And in some of the most interesting exchanges of the hearing, President Shafik actually opens Columbia’s disciplinary books.

We have already suspended 15 students from Columbia. We have six on disciplinary probation. These are more disciplinary actions that have been taken probably in the last decade at Columbia. And —

She talks about the number of students that have been suspended, but also the number of faculty that she’s had removed from the classroom that are being investigated for comments that either violate some of Columbia’s rules or make students uncomfortable. One case in particular really underscores this.

And that’s of a Middle Eastern studies professor named Joseph Massad. He wrote an essay not long after Hamas invaded Israel and killed 1,200 people, according to the Israeli government, where he described that attack with adjectives like awesome. Now, he said they’ve been misinterpreted, but a lot of people have taken offense to those comments.

Ms. Stefanik, you’re recognized for five minutes.

Thank you, Chairwoman. I want to follow up on my colleague, Rep Walberg’s question regarding Professor Joseph Massad. So let me be clear, President —

And so Representative Elise Stefanik, the same Republican who had tripped up Claudine Gay of Harvard and others in the last hearing, really starts digging in to President Shafik about these things at Columbia.

He is still Chair on the website. So has he been terminated as Chair?

Congresswoman, I —

And Shafik’s answers are maybe a little surprising.

— before getting back to you. I can confirm —

I know you confirmed that he was under investigation.

Yes, I can confirm that. But I —

Did you confirm he was still the Chair?

He says that Columbia is taking his case seriously. In fact, he’s under investigation right now.

Well, let me ask you this.

I need to check.

Will you make the commitment to remove him as Chair?

And when Stefanik presses her to commit to removing him from a campus leadership position —

I think that would be — I think — I would — yes. Let me come back with yes. But I think I — I just want to confirm his current status before I write —

We’ll take that as a yes, that you will confirm that he will no longer be chair.

Shafik seems to pause and think and then agree to it on the spot, almost like she is making administrative decisions with or in front of Congress.

Now, we did some reporting after the fact. And it turns out the Professor didn’t even realize he was under investigation. So he’s learning about this from the hearing too. So what this all adds up to, I think, is a performance so in line with what the lawmakers themselves wanted to hear, that at certain points, these Republicans didn’t quite know what to do with it. They were like the dog that caught the car.

Columbia beats Harvard and UPenn.

One of them, a Republican from Florida, I think at one point even marvelled, well, you beat Harvard and Penn.

Y’all all have done something that they weren’t able to do. You’ve been able to condemn anti-Semitism without using the phrase, it depends on the context. But the —

So Columbia’s president has passed this test before this committee.

Yeah, this big moment that tripped up her predecessors and cost them their jobs, it seems like she has cleared that hurdle and dispatched with the Congressional committee that could have been one of the biggest threats to her presidency.

Without objection, there being no further business, the committee stands adjourned. [BANGS GAVEL]

But back on campus, some of the students and faculty who had been watching the hearing came away with a very different set of conclusions. They saw a president who was so eager to please Republicans in Congress that she was willing to sell out some of the University’s students and faculty and trample on cherished ideas like academic freedom and freedom of expression that have been a bedrock of American higher education for a really long time.

And there was no clearer embodiment of that than what had happened that morning just as President Shafik was going to testify before Congress. A group of students before dawn set up tents in the middle of Columbia’s campus and declared themselves a pro-Palestinian encampment in open defiance of the very rules that Dr. Shafik had put in place to try and get these protests under control.

So these students in real-time are beginning to test some of the things that Columbia’s president has just said before Congress.

Exactly. And so instead of going to celebrate her successful appearance before Congress, Shafik walks out of the hearing room and gets in a black SUV to go right back to that war room, where she’s immediately confronted with a major dilemma. It basically boils down to this, she had just gone before Congress and told them, I’m going to get tough on these protests. And here they were. So either she gets tough and risks inflaming tension on campus or she holds back and does nothing and her words before Congress immediately look hollow.

And what does she decide?

So for the next 24 hours, she tries to negotiate off ramps. She consults with her Deans and the New York Police Department. And it all builds towards an incredibly consequential decision. And that is, for the first time in decades, to call the New York City Police Department onto campus in riot gear and break this thing up, suspend the students involved, and then arrest them.

To essentially eliminate this encampment.

Eliminate the encampment and send a message, this is not going to be tolerated. But in trying to quell the unrest, Shafik actually feeds it. She ends up leaving student protesters and the faculty who support them feeling betrayed and pushes a campus that was already on edge into a full blown crisis.

[SLOW TEMPO MUSIC]

After the break, what all of this has looked like to a student on Columbia’s campus. We’ll be right back.

[PHONE RINGS]

Is this Isabella?

Yes, this is she.

Hi, Isabella. It’s Michael Barbaro from “The Daily.”

Hi. Nice to meet you.

Earlier this week, we called Isabella Ramírez, the Editor in Chief of Columbia’s undergraduate newspaper, “The Columbia Daily Spectator,” which has been closely tracking both the protests and the University’s response to them since October 7.

So, I mean, in your mind, how do we get to this point? I wonder if you can just briefly describe the key moments that bring us to where we are right now.

Sure. Since October 7, there has certainly been constant escalation in terms of tension on campus. And there have been a variety of moves that I believe have distanced the student body, the faculty, from the University and its administration, specifically the suspension of Columbia’s chapters of Students for Justice in Palestine and Jewish Voice for Peace. And that became a huge moment in what was characterized as suppression of pro-Palestinian activism on campus, effectively rendering those groups, quote, unquote, unauthorized.

What was the college’s explanation for that?

They had cited in that suspension a policy which states that a demonstration must be approved within a certain window, and that there must be an advance notice, and that there’s a process for getting an authorized demonstration. But the primary point was this policy that they were referring to, which we later reported, was changed before the suspension.

So it felt a little ad hoc to people?

Yes, it certainly came as a surprise, especially at “Spectator.” We’re nerds of the University in the sense that we are familiar with faculty and University governance. But even to us, we had no idea where this policy was coming from. And this suspension was really the first time that it entered most students’ sphere.

Columbia’s campus is so known for its activism. And so in my time of being a reporter, of being an editor, I’ve overseen several protests. And I’ve never seen Columbia penalize a group for, quote, unquote, not authorizing a protest. So that was certainly, in our minds, unprecedented.

And I believe part of the justification there was, well, this is a different time. And I think that is a reasonable thing to say. But I think a lot of students, they felt it was particularly one-sided, that it was targeting a specific type of speech or a specific type of viewpoint. Although, the University, of course, in its explicit policies, did not outline, and was actually very explicit about not targeting specific viewpoints —

So just to be super clear, it felt to students — and it sounds like, journalistically, it felt to you — that the University was coming down in a uniquely one-sided way against students who were supporting Palestinian rights and may have expressed some frustrations with Israel in that moment.

Yes. Certainly —

Isabella says that this was just the beginning of a really tense period between student protesters and the University. After those two student groups were suspended, campus protests continued. Students made a variety of demands. They asked that the University divest from businesses that profit from Israel’s military operations in Gaza. But instead of making any progress, the protests are met with further crackdown by the University.

And so as Isabella and her colleagues at the college newspaper see it, there’s this overall chilling effect that occurs. Some students become fearful that if they participate in any demonstrations, they’re going to face disciplinary action. So fast forward now to April, when these student protesters learned that President Shafik is headed to Washington for her congressional testimony. It’s at this moment that they set out to build their encampment.

I think there was obviously a lot of intention in timing those two things. I think it’s inherently a critique on a political pressure and this congressional pressure that we saw build up against, of course, Claudine Gay at Harvard and Magill at UPenn. So I think a lot of students and faculty have been frustrated at this idea that there are not only powers at the University that are dictating what’s happening, but there are perhaps external powers that are also guiding the way here in terms of what the University feels like it must do or has to do.

And I think that timing was super crucial. Having the encampment happen on the Wednesday morning of the hearing was an incredible, in some senses, interesting strategy to direct eyes to different places.

All eyes were going to be on Shafik in DC. But now a lot of eyes are on New York. The encampment is set up in the middle of the night slash morning, prior to the hearing. And so what effectively happens is they caught Shafik when she wasn’t on campus, when a lot of senior administration had their resources dedicated to supporting Shafik in DC.

And you have all of those people not necessarily out of commission, but with their focus elsewhere. So the encampment is met with very little resistance at the beginning. There were public safety officers floating around and watching. But at the very beginning hours, I think there was a sense of, we did it.

[CHANTING]: Disclose! Divest! We will not stop! We will not rest. Disclose! Divest! We will not stop!

It would be quite surprising to anybody and an administrator to now suddenly see dozens of tents on this lawn in a way that I think very purposely puts an imagery of, we’re here to stay. As the morning evolved and congressional hearings continued —

Minouche Shafik, open your eyes! Use of force, genocide!

Then we started seeing University delegates that were coming to the encampment saying, you may face disciplinary action for continuing to be here. I think that started around almost — like 9:00 or 10:00 AM, they started handing out these code of conduct violation notices.

Hell no! Hell no! Hell no!

Then there started to be more public safety action and presence. So they started barricading the entrances. The day progressed, there was more threat of discipline. The students became informed that if they continue to stay, they will face potential academic sanctions, potential suspension.

The more they try to silence us, the louder we will be! The more they —

I think a lot of people were like, OK, you’re threatening us with suspension. But so what?

This is about these systems that Minouche Shafik, that the Board of Trustees, that Columbia University is complicit in.

What are you going to do to try to get us out of here? And that was, obviously, promptly answered.

This is the New York State Police Department.

We will not stop!

You are attempting participate in an unauthorized encampment. You will be arrested and charged with trespassing.

My phone blew up, obviously, from the reporters, from the editors, of saying, oh my god, the NYPD is on our campus. And as soon as I saw that, I came out. And I saw a huge crowd of students and affiliates on campus watching the lawns. And as I circled around that crowd, I saw the last end of the New York Police Department pulling away protesters and clearing out the last of the encampment.

[CHANTING]: We love you! We will get justice for you! We see you! We love you! We will get justice for you! We see you! We love you! We will get justice for you! We see you! We love you! We will get justice for you!

It was something truly unimaginable, over 100 students slash other individuals are arrested from our campus, forcefully removed. And although they were suspended, there was a feeling of traumatic event that has just happened to these students, but also this sense of like, OK, the worst of the worst that could have happened to us just happened.

And for those students who maybe couldn’t go back to — into campus, now all of their peers, who were supporters or are in solidarity, are — in some sense, it’s further emboldened. They’re now not just sitting on the lawns for a pro-Palestinian cause, but also for the students, who have endured quite a lot.

So the crackdown, sought by the president and enforced by the NYPD, ends up, you’re saying, becoming a galvanizing force for a broader group of Columbia students than were originally drawn to the idea of ever showing up on the center of campus and protesting?

Yeah, I can certainly speak to the fact that I’ve seen my own peers, friends, or even acquaintances, who weren’t necessarily previously very involved in activism and organizing efforts, suddenly finding themselves involved.

Can I — I just have a question for you, which is all journalism, student journalism or not student journalism, is a first draft of history. And I wonder if we think of this as a historic moment for Columbia, how you imagine it’s going to be remembered.

Yeah, there is no doubt in my mind that this will be a historic moment for Colombia.

I think that this will be remembered as a moment in which the fractures were laid bare. Really, we got to see some of the disunity of the community in ways that I have never really seen it before. And what we’ll be looking to is, where do we go from here? How does Colombia repair? How do we heal from all of this? so That is the big question in terms of what will happen.

Nick, Isabella Ramírez just walked us through what this has all looked like from the perspective of a Columbia student. And from what she could tell, the crackdown ordered by President Shafik did not quell much of anything. It seemed, instead, to really intensify everything on campus. I’m curious what this has looked like for Shafik.

It’s not just the students who are upset. You have faculty, including professors, who are not necessarily sympathetic to the protesters’ view of the war, who are really outraged about what Shafik has done here. They feel that she’s crossed a boundary that hasn’t been crossed on Columbia’s campus in a really long time.

And so you start to hear things by the end of last week like censure, no confidence votes, questions from her own professors about whether or not she can stay in power. So this creates a whole new front for her. And on top of it all, as this is going on, the encampment itself starts to reform tent-by-tent —

— almost in the same place that it was. And Shafik decides that the most important thing she could do is to try and take the temperature down, which means letting the encampment stand. Or in other words, leaning in the other direction. This time, we’re going to let the protesters have their say for a little while longer.

The problem with that is that, over the weekend, a series of images start to emerge from on campus and just off of it of some really troubling anti-Semitic episodes. In one case, a guy holds up a poster in the middle of campus and points it towards a group of Jewish students who are counter protesting. And it says, I’m paraphrasing here, Hamas’ next targets.

I saw an image of that. What it seemed to evoke was the message that Hamas should murder those Jewish students. That’s the way the Jewish students interpreted it.

It’s a pretty straightforward and jarring statement. At the same time, just outside of Columbia’s closed gates —

Stop killing children!

— protestors are showing up from across New York City. It’s hard to tell who’s affiliated with Columbia, who’s not.

Go back to Poland! Go back to Poland!

There’s a video that goes viral of one of them shouting at Jewish students, go back to Poland, go back to Europe.

In other words, a clear message, you’re not welcome here.

Right. In fact, go back to the places where the Holocaust was committed.

Exactly. And this is not representative of the vast majority of the protesters in the encampment, who mostly had been peaceful. They would later hold a Seder, actually, with some of the pro-Palestinian Jewish protesters in their ranks. But those videos are reaching members of Congress, the very same Republicans that Shafik had testified in front of just a few days before. And now they’re looking and saying, you have lost control of your campus, you’ve turned back on your word to us, and you need to resign.

They call for her outright resignation over this.

That’s right. Republicans in New York and across the country began to call for her to step down from her position as president of Columbia.

So Shafik’s dilemma here is pretty extraordinary. She has set up this dynamic where pleasing these members of Congress would probably mean calling in the NYPD all over again to sweep out this encampment, which would mean further alienating and inflaming students and faculty, who are still very upset over the first crackdown. And now both ends of this spectrum, lawmakers in Washington, folks on the Columbia campus, are saying she can’t lead the University over this situation before she’s even made any fateful decision about what to do with this second encampment. Not a good situation.

No. She’s besieged on all sides. For a while, the only thing that she can come up with to offer is for classes to go hybrid for the remainder of the semester.

So students who aren’t feeling safe in this protest environment don’t necessarily have to go to class.

Right. And I think if we zoom out for a second, it’s worth bearing in mind that she tried to choose a different path here than her counterparts at Harvard or Penn. And after all of this, she’s kind of ended up in the exact same thicket, with people calling for her job with the White House, the Mayor of New York City, and others. These are Democrats. Maybe not calling on her to resign quite yet, but saying, I don’t know what’s going on your campus. This does not look good.

That reality, that taking a different tack that was supposed to be full of learnings and lessons from the stumbles of her peers, the fact that didn’t really work suggests that there’s something really intractable going on here. And I wonder how you’re thinking about this intractable situation that’s now arrived on these college campuses.

Well, I don’t think it’s just limited to college campuses. We have seen intense feelings about this conflict play out in Hollywood. We’ve seen them in our politics in all kinds of interesting ways.

In our media.

We’ve seen it in the media. But college campuses, at least in their most idealized form, are something special. They’re a place where students get to go for four years to think in big ways about moral questions, and political questions, and ideas that help shape the world they’re going to spend the rest of their lives in.

And so when you have a question that feels as urgent as this war does for a lot of people, I think it reverberates in an incredibly intense way on those campuses. And there’s something like — I don’t know if it’s quite a contradiction of terms, but there’s a collision of different values at stake. So universities thrive on the ability of students to follow their minds and their voices where they go, to maybe even experiment a little bit and find those things.

But there are also communities that rely on people being able to trust each other and being able to carry out their classes and their academic endeavors as a collective so they can learn from one another. So in this case, that’s all getting scrambled. Students who feel strongly about the Palestinian cause feel like the point is disruption, that something so big, and immediate, and urgent is happening that they need to get in the faces of their professors, and their administrators, and their fellow students.

Right. And set up an encampment in the middle of campus, no matter what the rules say.

Right. And from the administration’s perspective, they say, well, yeah, you can say that and you can think that. And that’s an important process. But maybe there’s some bad apples in your ranks. Or though you may have good intentions, you’re saying things that you don’t realize the implications of. And they’re making this environment unsafe for others. Or they’re grinding our classes to a halt and we’re not able to function as a University.

So the only way we’re going to be able to move forward is if you will respect our rules and we’ll respect your point of view. The problem is that’s just not happening. Something is not connecting with those two points of view. And as if that’s not hard enough, you then have Congress and the political system with its own agenda coming in and putting its thumb on a scale of an already very difficult situation.

Right. And at this very moment, what we know is that the forces that you just outlined have created a dilemma, an uncertainty of how to proceed, not just for President Shafik and the students and faculty at Columbia, but for a growing number of colleges and universities across the country. And by that, I mean, this thing that seemed to start at Columbia is literally spreading.

Absolutely. We’re talking on a Wednesday afternoon. And these encampments have now started cropping up at universities from coast-to-coast, at Harvard and Yale, but also at University of California, at the University of Texas, at smaller campuses in between. And at each of these institutions, there’s presidents and deans, just like President Shafik at Columbia, who are facing a really difficult set of choices. Do they call in the police? The University of Texas in Austin this afternoon, we saw protesters physically clashing with police.

Do they hold back, like at Harvard, where there were dramatic videos of students literally running into Harvard yard with tents. They were popping up in real-time. And so Columbia, really, I think, at the end of the day, may have kicked off some of this. But they are now in league with a whole bunch of other universities that are struggling with the same set of questions. And it’s a set of questions that they’ve had since this war broke out.

And now these schools only have a week or two left of classes. But we don’t know when these standoffs are going to end. We don’t know if students are going to leave campus for the summer. We don’t know if they’re going to come back in the fall and start protesting right away, or if this year is going to turn out to have been an aberration that was a response to a really awful, bloody war, or if we’re at the beginning of a bigger shift on college campuses that will long outlast this war in the Middle East.

Well, Nick, thank you very much. Thanks for having me, Michael.

We’ll be right back.

Here’s what else you need to know today. The United Nations is calling for an independent investigation into two mass graves found after Israeli forces withdrew from hospitals in Gaza. Officials in Gaza said that some of the bodies found in the graves were Palestinians who had been handcuffed or shot in the head and accused Israel of killing and burying them. In response, Israel said that its soldiers had exhumed bodies in one of the graves as part of an effort to locate Israeli hostages.

And on Wednesday, Hamas released a video of Hersh Goldberg-Polin, an Israeli-American dual citizen, whom Hamas has held hostage since October 7. It was the first time that he has been shown alive since his captivity began. His kidnapping was the subject of a “Daily” episode in October that featured his mother, Rachel. In response to Hamas’s video, Rachel issued a video of her own, in which she spoke directly to her son.

And, Hersh, if you can hear this, we heard your voice today for the first time in 201 days. And if you can hear us, I am telling you, we are telling you, we love you. Stay strong. Survive.

Today’s episode was produced by Sydney Harper, Asthaa Chaturvedi, Olivia Natt, Nina Feldman, and Summer Thomad, with help from Michael Simon Johnson. It was edited by Devon Taylor and Lisa Chow, contains research help by Susan Lee, original music by Marion Lozano and Dan Powell, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

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Hosted by Michael Barbaro

Featuring Nicholas Fandos

Produced by Sydney Harper ,  Asthaa Chaturvedi ,  Olivia Natt ,  Nina Feldman and Summer Thomad

With Michael Simon Johnson

Edited by Devon Taylor and Lisa Chow

Original music by Marion Lozano and Dan Powell

Engineered by Chris Wood

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Columbia University has become the epicenter of a growing showdown between student protesters, college administrators and Congress over the war in Gaza and the limits of free speech.

Nicholas Fandos, who covers New York politics and government for The Times, walks us through the intense week at the university. And Isabella Ramírez, the editor in chief of Columbia’s undergraduate newspaper, explains what it has all looked like to a student on campus.

On today’s episode

Nicholas Fandos , who covers New York politics and government for The New York Times

Isabella Ramírez , editor in chief of The Columbia Daily Spectator

Background reading

Inside the week that shook Columbia University .

The protests at the university continued after more than 100 arrests.

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

Research help by Susan Lee .

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, Mike 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, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, 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, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Nicholas Fandos is a Times reporter covering New York politics and government. More about Nicholas Fandos

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