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Discover Frequently Asked Physics Questions and Their Answers
A solid disk, spinning counter-clockwise, has a mass of #4 kg# and a radius of #3/4 m#. If a point on the edge of the disk is moving at #5/9 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?
A container with a volume of #48 L# contains a gas with a temperature of #210^o K#. If the temperature of the gas changes to #810 ^o K# without any change in pressure, what must the container's new volume be?
Is it possible to have a non-whole number harmonic in sound?
A container with a volume of #21 L# contains a gas with a temperature of #150^o K#. If the temperature of the gas changes to #120 ^o K# without any change in pressure, what must the container's new volume be?
Does specific heat change with molality?
Help with this cal question?
What are some examples that show heat transfer?
What is the mathematical symbol used for the period of a wave.?
A sound wave traveling at 343 m/s is emitted by the foghorn of a tugboat. An echo is heard 2.60 s later. How far away is the reflecting object?
If #9/4 L# of a gas at room temperature exerts a pressure of #15 kPa# on its container, what pressure will the gas exert if the container's volume changes to #5/3 L#?
Are quasars galaxies or fast moving stars?
What is the the difference between a quasar and a galaxy?
Why do perihelion and aphelion occur?
What is the composition of a quasar compared to a star or nebula?
A certain quasar recedes from Earth at 0.55 c. A jet of material ejected from the quasar toward the Earth moves at 0.13 c relative to the quasar. How do you find the speed of the ejected material relative to Earth?
How far can we measure stellar parallax?
What theory describes the formation of the moon?
How far is the sun from the earth?
What is a solar system?
How far is Pluto from the sun in light minutes? How is this calculated?
A space-based telescope can achieve a diffraction-limited angular resolution of 0.14 for red light (wavelength 650 nm). What would the resolution of the instrument be in the ultraviolet, at 150nm ?
What is interstellar medium? Where is it found?
How is the speed of light measured?
At what point in a star's life are they classified as AGB?
How does the sun atmosphere differ from its interior?
How does the Sun's mass affect its evolution?
From hottest to coolest, what is the order of the spectral types of stars?
What causes gamma ray bursts?
What is the size of Saturn?
Is empty space a pure vacuum?
Number Line
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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.
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4.6 Problem-Solving Strategies
Learning objectives.
By the end of this section, you will be able to:
Understand and apply a problem-solving procedure to solve problems using Newton's laws of motion.
Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams. The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newton’s laws of motion are emphasized. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop.
Problem-Solving Strategy for Newton’s Laws of Motion
Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation . Such a sketch is shown in Figure 4.20 (a). Then, as in Figure 4.20 (b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists).
Step 2. Identify what needs to be determined and what is known or can be inferred from the problem as stated. That is, make a list of knowns and unknowns. Then carefully determine the system of interest . This decision is a crucial step, since Newton’s second law involves only external forces. Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newton’s second law. (See Figure 4.20 (c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). As illustrated earlier in this chapter, the system of interest depends on what question we need to answer. This choice becomes easier with practice, eventually developing into an almost unconscious process. Skill in clearly defining systems will be beneficial in later chapters as well. A diagram showing the system of interest and all of the external forces is called a free-body diagram . Only forces are shown on free-body diagrams, not acceleration or velocity. We have drawn several of these in worked examples. Figure 4.20 (c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.
Step 3. Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem . This is done in Figure 4.20 (d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.
Applying Newton’s Second Law
Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction. If the acceleration is zero in a particular direction, then the net force is zero in that direction. Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: F net = ma F net = ma .
For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions:
You will need this information in order to determine unknown forces acting in a system.
Step 4. As always, check the solution to see whether it is reasonable . In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.
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Using Python to Solve Computational Physics Problems
Introduction
Laplace equation is a simple second-order partial differential equation. It is also a simplest example of elliptic partial differential equation. This equation is very important in science, especially in physics, because it describes behaviour of electric and gravitation potential, and also heat conduction. In thermodynamics (heat conduction), we call Laplace equation as steady-state heat equation or heat conduction equation.
In this article, we will solve the Laplace equation using numerical approach rather than analytical/calculus approach. When we say numerical approach, we refer to discretization. Discretization is a process to "transform" the continuous form of differential equation into a discrete form of differential equation; it also means that with discretization, we can transform the calculus problem into matrix algebra problem, which is favored by programming.
Here, we want to solve a simple heat conduction problem using finite difference method. We will use Python Programming Language, Numpy (numerical library for Python), and Matplotlib (library for plotting and visualizing data using Python) as the tools. We'll also see that we can write less code and do more with Python.
In computational physics, we "always" use programming to solve the problem, because computer program can calculate large and complex calculation "quickly". Computational physics can be represented as this diagram.
There are so many programming languages that are used today to solve many numerical problems, Matlab for example. But here, we will use Python, the "easy to learn" programming language, and of course, it's free. It also has powerful numerical, scientific, and data visualization library such as Numpy, Scipy, and Matplotlib. Python also provides parallel execution and we can run it in computer clusters.
Back to Laplace equation, we will solve a simple 2-D heat conduction problem using Python in the next section. Here, I assume the readers have basic knowledge of finite difference method, so I do not write the details behind finite difference method, details of discretization error, stability, consistency, convergence, and fastest/optimum iterating algorithm. We will skip many steps of computational formula here.
Instead of solving the problem with the numerical-analytical validation, we only demonstrate how to solve the problem using Python, Numpy, and Matplotlib, and of course, with a little bit of simplistic sense of computational physics, so the source code here makes sense to general readers who don't specialize in computational physics.
Preparation
To produce the result below, I use this environment:
OS : Linux Ubuntu 14.04 LTS
Python : Python 2.7
Numpy : Numpy 1.10.4
Matplotlib : Matplotlib 1.5.1
If you are running Ubuntu, you can use pip to install Numpy and Matplotib, or you can run this command in your terminal.
and use this command to install Matplotlib:
Note that Python is already installed in Ubuntu 14.04. To try Python, just type Python in your Terminal and press Enter.
You can also use Python, Numpy and Matplotlib in Windows OS, but I prefer to use Ubuntu instead.
Using the Code
This is the Laplace equation in 2-D cartesian coordinates (for heat equation):
Where T is temperature, x is x-dimension, and y is y-dimension. x and y are functions of position in Cartesian coordinates. If you are interested to see the analytical solution of the equation above, you can look it up here .
Here, we only need to solve 2-D form of the Laplace equation. The problem to solve is shown below:
What we will do is find the steady state temperature inside the 2-D plat (which also means the solution of Laplace equation) above with the given boundary conditions (temperature of the edge of the plat). Next, we will discretize the region of the plat, and divide it into meshgrid, and then we discretize the Laplace equation above with finite difference method. This is the discretized region of the plat.
We set Δ x = Δ y = 1 cm , and then make the grid as shown below:
Note that the green nodes are the nodes that we want to know the temperature there (the solution), and the white nodes are the boundary conditions (known temperature). Here is the discrete form of Laplace Equation above.
In our case, the final discrete equation is shown below.
Now, we are ready to solve the equation above. To solve this, we use "guess value" of interior grid (green nodes), here we set it to 30 degree Celsius (or we can set it 35 or other value), because we don't know the value inside the grid (of course, those are the values that we want to know). Then, we will iterate the equation until the difference between value before iteration and the value until iteration is "small enough", we call it convergence. In the process of iterating, the temperature value in the interior grid will adjust itself, it's "selfcorrecting", so when we set a guess value closer to its actual solution, the faster we get the "actual" solution.
We are ready for the source code. In order to use Numpy library, we need to import Numpy in our source code, and we also need to import Matplolib.Pyplot module to plot our solution. So the first step is to import necessary modules.
and then, we set the initial variables into our Python source code:
What we will do next is to set the "plot window" and meshgrid . Here is the code:
np.meshgrid() creates the mesh grid for us (we use this to plot the solution), the first parameter is for the x-dimension, and the second parameter is for the y-dimension. We use np.arange() to arrange a 1-D array with element value that starts from some value to some value, in our case, it's from 0 to lenX and from 0 to lenY . Then we set the region: we define 2-D array, define the size and fill the array with guess value, then we set the boundary condition, look at the syntax of filling the array element for boundary condition above here.
Then we are ready to apply our final equation into Python code below. We iterate the equation using for loop.
You should be aware of the indentation of the code above, Python does not use bracket but it uses white space or indentation. Well, the main logic is finished. Next, we write code to plot the solution, using Matplotlib.
That's all, This is the complete code .
It's pretty short, huh ? Okay, you can copy-paste and save the source code, name it findif.py . To execute the Python source code, open your Terminal, and go to the directory where you locate the source code, type:
and press Enter . Then the plot window will appear.
You can try to change the boundary condition's value, for example, you change the value of right edge temperature to 30 degree Celcius ( Tright = 30 ), then the result will look like this:
Points of Interest
Python is an "easy to learn" and dynamically typed programming language, and it provides (open source) powerful library for computational physics or other scientific discipline. Since Python is an interpreted language, it's slow as compared to compiled languages like C or C++, but again, it's easy to learn. We can also write less code and do more with Python, so we don't struggle to program, and we can focus on what we want to solve.
In computational physics, with Numpy and also Scipy (numeric and scientific library for Python), we can solve many complex problems because it provides matrix solver (eigenvalue and eigenvector solver), linear algebra operation, as well as signal processing, Fourier transform, statistics, optimization, etc.
In addition to its use in computational physics, Python is also used in machine learning, even Google's TensorFlow uses Python.
21 st March, 2016: Initial version
This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)
Comments and Discussions
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17-Feb-23 7:59
17-Feb-23 7:59
The article appears to be nicely written. However, I observe that the following code could be re-written to make it more efficient, I think.
iteration inrange(0, maxIter): for i inrange(1, lenX-1, delta): for j inrange(1, lenY-1, delta): T[i, j] = 0.25 * (T[i+1][j] + T[i-1][j] + T[i][j+1] + T[i][j-1])
Great article. Runs great, however, I wanted to modify it to a rectangular grid and got an error. My only change to your code was:
lenY = 20
which gives the error: " , 25) instead of (25, 20)."
Any help would be appreciated. thanks.
·
10-Jun-20 10:04
10-Jun-20 10:04
Hi there! How are you Garbel? Would you please able to help me solve couple questions using Python 3? Thank You
·
18-Jan-20 10:16
18-Jan-20 10:16
The goal of this is to produce a small program to solve a physical problem with numerical data. An electron of charge −e and mass me is moving at a speed ~v(t = 0) = v~ex in the plane Oxy between the two plates of a capacitor. The field is given by E~ = E~ey. The only force is Lorentz F~ = qE~ . Plot the trajectory of this electron. Plot the trajectory of this electron; use matplotlib.pyplot to plot and scipy.integrate.ode to solve the problem.
·
14-Jan-20 21:29
14-Jan-20 21:29
That's a simple approach, here relaxation is used with a simple multigrid, code in javascript: [ ]
It can be done with FFT, too, here Poisson is solved that way (C++): [ ]
And better, here Poisson is solved with full multigrid, on a non-uniform grid (1D, but can be generalized to 2D or 3D): [ ]
·
13-Jan-20 2:21
13-Jan-20 2:21
Really well explained simple examples but not stupid simple.
·
12-Jan-20 7:49
12-Jan-20 7:49
Hi guys I have the gift for computer programming, I make my first steps at php as I noticed it can be very beneficial, please help develop this field
Much love :>
Keeps the thigns together.
·
23-Jul-19 0:15
23-Jul-19 0:15
Hello Gabrel,
I'd like to say thank you for sharer that code. It was extremely helpful. Two things I'd like to ask:
have you ever done the same for Poisson's equation, and if so, would you be willing to share it or share any tips on how to adapt the Laplace code? Say, instead of temperature we had voltage, and within the 'box' there was a certain charge density.
Secondly, for your i and j in range loop, is there a way of doing this so that my step size can be a float? As I get an error if I set my box size to 1m x 1m, and set my step size to say 0.05m.
Many thanks!
·
25-Mar-17 23:16
25-Mar-17 23:16
Nice!! more examples?
·
26-Aug-16 5:23
26-Aug-16 5:23
first of all
I would like to thank you for sharing your code and well explained solution ... I appreciate your work
my only question is what iterative method did you use in this code cause I couldn't figure it out
did you used Jacobi for instance ?
thank you again
·
26-Aug-16 20:15
26-Aug-16 20:15
Hi, thank you Rechter.. It's "Gauss-Seidell method".. When the code completed the calculation (let's say) for T(1,9), in the next move in T(2,9), it will use the calculated value of T(1,9) without waiting for the next iteration.
·
Last Visit: 31-Dec-99 18:00 Last Update: 28-Jun-24 11:05
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WOOT (Worldwide Online Olympiad Training)
Over 7 months, WOOT students train with former medalists and collaborate with peers from around the world to solve Olympiad-level problems. Together, they build the creativity and confidence to successfully compete in key competitions in the following subjects.
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The supportive community of very bright students in WOOT motivated me to study even more Olympiad-level math, while providing the structure I needed. I found myself collaborating with past USAMO winners and IMO medalists, working (and solving!) problems that I'd barely been able to understand before I took the class.
I've been taking AoPS classes ever since elementary school and they've really helped me develop strong problem-solving skills and keen intuition. Thanks to what I learned in calculus class, I was able to win a bronze medal the first time I took the USAPhO—even without any prior AP-level physics courses.
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The training I received in math from AoPS was absolutely crucial to helping me develop problem-solving skills in physics. At the Olympiad level, most problems can't be solved with only one concept-cracking them usually requires putting multiple concepts together, and the WOOT program really helped me develop this essential skill.
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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 329,465 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.
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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 .
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Fueled by problem-solving
Undergraduate research helped feed physics and eecs major thomas bergamaschi’s post-mit interest in tackling challenges..
“Every time I try to solve a problem — whether it be physics or computer science — I always try to find an elegant solution,” says MIT senior Thomas Bergamaschi, who spent four years learning how to solve problems while an Undergraduate Research Opportunities Program ( UROP ) student in the Engineering Quantum Systems (EQUS) laboratory at MIT.
“Of course,” he adds, “there are many times where a problem doesn’t have an elegant solution, or finding an elegant solution is much harder than a normal solution, but it is something I always try to do, as it helps me understand at most something. Another compelling reason is that these solutions are usually the simplest to teach other people, which is always appealing to me.”
Now, as the physics and electrical engineering and computer science (EECS) major ponders post-graduation life, he believes he’s ready to tackle challenges in his career as a software engineer at Five Rings, where he had an internship. “There are a lot of hard and interesting problems to be solved there,” he says. “Challenges are something that fuels me.”
STEM family
Born in Brazil, Bergamaschi lived in the United States until he was 6, when his family moved back to a small town in rural Sao Paulo called Vinhedo. His Brazilian father is a software engineer, and his mother, who is from England, studied biology in college and now teaches English. He followed in the footsteps of his older brother, Thiago, who was the first in the family to be drawn to physics. And when his brother entered physics competitions in high school, Thomas did too.
He had high school teachers who encouraged him to study physics beyond the usual curriculum. “One teacher accompanied me on many bus and plane rides to physics competitions and classes,” he recalls. “She was a huge motivator for me to continue studying physics and helped find me new books and problems throughout high school.”
The younger Bergamaschi went on to win silver medals at the International Physics Olympiad and at the International Young Physicists’ Tournament , and more than a dozen other medals in national and regional Brazilian science competitions in physics, math, and astronomy.
Thiago Bergamaschi ’21 joined MIT as a physics and EECS major in 2017, and his brother wasn’t far behind him, entering MIT in 2019.
Bergamaschi ended up spending nearly all four years at MIT as a UROP student in the Engineering Quantum Systems (EQUS) laboratory, under the supervision of PhD student Tim Menke and Professor William Oliver . That’s when he was introduced to quantum computing — his supervisors were constructing a device that had a phenomenon where many qubits could interact simultaneously.
“This type of interaction is very useful for quantum computers, as it gives us a possible way that we can map problems we are interested in onto a quantum computer,” he says. “My project was to try to answer the question of how we can actually measure things, and prove that the constructed device actually had this coupling term we were interested in.”
He proposed and analyzed methods to experimentally detect many-body quantum systems. “These systems are extremely important and interesting as they have many cool applications, and in particular can be used to map computationally hard problems — such as route optimization, Boolean satisfiability, and more — to quantum computers in an easy way.”
This project was supposed to be a warmup project for his UROP. “However, we soon noticed that the problem of accurately measuring these effects was a pretty tricky problem. I ended up working on this problem for around six months — my summer, the fall semester, and the beginning of IAP [Independent Activities Period] — trying to figure out how we can measure these effects.”
He presented his research at the 2021 and 2022 American Physical Society March meetings, and published “Distinguishing multi-spin interactions from lower-order effects” in Physical Review Applied .
“The experience of presenting my work in a conference and publishing a paper is a huge highlight from my time at MIT and gave me a taste of scientific communication and research, which was invaluable for me,” Bergamaschi says. “Being able to do research with the help of Tim Menke and Professor Oliver was inspiring, and is one of the largest highlights from my time at MIT.”
He also worked with William Isaac Jay, a postdoc at the MIT Center for Theoretical Physics , on lattice quantum field theory. He studies quantum theories at the microscopic level, where strong nuclear interactions are relevant. “This is particularly appealing as we can simulate these theories on a computer — albeit usually a huge supercomputer — and try to make predictions about phenomena involving atoms at a minuscule scale. I UROP’d in this lab over both my junior and senior year, and my project involved implementing techniques from one of these computer simulations, how can we go back to the real world and obtain something that an experiment would measure.”
Brazil blues
Bergamaschi missed Brazil but found community playing soccer with intramural teams Ousadia and Alegria Futebol Clube, and eating churrasco with his friends at Oliveira’s Brazilian-style steakhouse in Somerville, Massachusetts. He also loved going to college with his brother, who graduated in 2021 and is now pursuing his PhD in physics at the University of California at Berkeley.
“One of my favorite memories of MIT is from my sophomore spring, when I managed to take two classes with him just before he graduated,” he recalls. “It was a lot of fun discussing physics problem sets and projects with him.”
What also keeps him in touch with his homeland is working with Brazilian high school students competing in physics tournaments. He is part of an academic committee that creates and grades the physics problems taken by the top 100 Brazilian high school students. Those with top scores go on to the International Physics Olympiad . He says he sees this as a way to pay forward what his high school teacher did for him: to encourage others to study physics.
“These olympiads were one of the main reasons for my interest in physics and me coming to MIT, and I hope that other Brazilian students can have these same opportunities as I had,” he says. “These students are all incredibly talented. A large amount of them end up coming to MIT after they graduate high school, so it’s a very gratifying and incredible experience for me to be able to participate and help in their physics education.”
Post-graduation thoughts
What will he miss most at MIT? “Late-night problem set sessions immediately before a deadline, trying to find a free food event across campus, and getting banana lounge bananas and coffee.”
And what were his biggest lessons? He says that MIT taught him how to work with other people, “handle imposter syndrome,” and most importantly, unravel complicated challenges.
“I think one of my major motivators is my desire to learn new things, whether it be physics or computer science. So, I am a big fan of very difficult problems or projects which require continual work but have large payoffs at the end. I think there are many instances during my time at MIT in which I worked all night for a project, just to get up and hop back on because of the excitement of obtaining a result or solution.”
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Version 2 of The Calculator Pad consists of a collection of relatively short problem sets that address a collection of discrete topics for each unit. Students can choose to do a set of problems on the topic of interest conduct a keyword search for specific problems. And teachers with Task Tracker subscriptions can assign the problem sets, modify the problems sets, create problems and problem sets of their own, and view student progress on any problem set that have been assigned. Learn more About Version 2 .
Just snap a picture. And yes, Phy understands your hand-writing. 5. Click it. Try Phy. A free to use AI Physics tutor. Solve, grade, and explain problems. Just speak to Phy or upload a screenshot of your working.
AI Physics Solver
Upload your problem and get expert-level tutoring in seconds. Scan-and-solve physics, math, and chemistry. Generate polished analyses and summaries. Create sleek looking data visualizations. Ask anything to your data, and get answers. Perform modeling and predictive forecasting.
Physics Solver: Solve Your Physics Problems & Homework with AI
Our physics problem solver is powered by industry-leading AI models and is frequently updated. As such, it ensures approximately 98% precision in answering physics questions. However, as with any AI homework assistant, it's best to review the generated solutions before submitting your assignment. 5.
Step-by-Step Calculator
Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. ... define the variables, and plan a strategy for solving the problem. en. Related Symbolab blog posts. Practice Makes Perfect. Learning math takes practice, lots of practice. Just like running ...
PhyWiz
Key features: Solve any physics question quickly. Over 100 equations at your fingertips. Practice with more than 300 free physics questions. Ask PhyWiz a question and get an answer instantly. The supported topics in this version are: Alternating Currents, Blackbody Radiation, Capacitance, Circular Motion, Diffraction Grating, Double-Slit ...
1.8: Solving Problems in Physics
Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life. . Figure 1.8.1 1.8. 1: Problem-solving skills are essential to your success in physics. (credit: "scui3asteveo"/Flickr) As you are probably well aware, a certain amount of creativity and insight is required to solve problems.
PhysicsWOOT Online Physics Course
All the training I received in math from AoPS was absolutely crucial to helping me gain problem-solving skills in physics. At the Olympiad level, most problems can't be solved with only one concept—cracking them usually requires putting multiple concepts together, and the WOOT program really helped me develop this essential skill.
The Calculator Pad: Physics Problem-Solving
Version 2 of our Calculator Pad was introduced in August of 2022. It includes six times as many problems and several additional topics (including Chemistry topics). Problem sets have been broken down into more than 400 smaller, single-topic problem sets. Problems utilize a random number generator to provide numerical information that is unique ...
1.7 Solving Problems in Physics
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.
Mastering Physics Problem-Solving: A Comprehensive 6-Step Guide
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 ...
Mathway
Free math problem solver answers your physics homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. Start 7-day free trial on the app. Download free on Amazon. Download free in Windows Store. Take a photo of your math problem on the app. get Go. Physics. Basic Math. Pre-Algebra ...
The Calculator Pad: Physics Problem-Solving
Most are enrolled in a physics course; some are studying physics as part of a home-school program. ... Far from a spectator sport, physics problem-solving requires that a student become involved in the process - doing the reading, preparation, thinking, strategy-plotting, algebra, and calculator work. Simply listening to the audio files will do ...
4.6 Problem-Solving Strategies
These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop. Problem-Solving Strategy for Newton's Laws of Motion. Step 1.
1.4: Solving Physics Problems
How To Solve Any Physics Problem: Learn five simple steps in five minutes! In this episode we cover the most effective problem-solving method I've encountered and call upon some fuzzy friends to help us remember the steps. ... the California State University Affordable Learning Solutions Program, and Merlot. We also acknowledge previous ...
Using Python to Solve Computational Physics Problems
In computational physics, we "always" use programming to solve the problem, because computer program can calculate large and complex calculation "quickly". Computational physics can be represented as this diagram. There are so many programming languages that are used today to solve many numerical problems, Matlab for example.
WOOT
The training I received in math from AoPS was absolutely crucial to helping me develop problem-solving skills in physics. At the Olympiad level, most problems can't be solved with only one concept-cracking them usually requires putting multiple concepts together, and the WOOT program really helped me develop this essential skill.
PDF An Expert's Approach to Solving Physics Problems
An example problem, its solution, and annotations on the process of solving the problem. The solutions to the problems from past exams will help you see what a good solution looks like. But seeing the solution alone may not illustrate the general method that could be used to solve other problems.
How to Solve Any Physics Problem: 10 Steps (with Pictures)
Calm down. It is just a problem, not the end of the world! 2. Read through the problem once. If it is a long problem, read and understand it in parts till you get even a slight understanding of what is going on. 3. Draw a diagram. It cannot be emphasized enough how much easier a problem will be once it is drawn out.
Students' Attitudes and Approaches towards Physics Problem Solving
Solving program and will serve as a framework for action or creativity. In this context, the re sults of the surveys identified the . ... While trying to solve physics problems, students often ...
1.8: Solving Problems in Physics
Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life. . Figure 1.8.1 1.8. 1: Problem-solving skills are essential to your success in physics. (credit: "scui3asteveo"/Flickr) As you are probably well aware, a certain amount of creativity and insight is required to solve problems.
Kinematic Equations: Sample Problems and Solutions
A useful problem-solving strategy was presented for use with these equations and two examples were given that illustrated the use of the strategy. Then, the application of the kinematic equations and the problem-solving strategy to free-fall motion was discussed and illustrated. In this part of Lesson 6, several sample problems will be presented.
Fueled by problem-solving » MIT Physics
Undergraduate research helped feed physics and EECS major Thomas Bergamaschi's post-MIT interest in tackling challenges. "Every time I try to solve a problem — whether it be physics or computer science — I always try to find an elegant solution," says MIT senior Thomas Bergamaschi, who spent four years learning how to solve problems while an Undergraduate Research Opportunities ...
The Calculator Pad: Physics Problem-Solving
Version 2 of The Calculator Pad consists of a collection of relatively short problem sets that address a collection of discrete topics for each unit. Students. can choose to do a set of problems on the topic of interest conduct a keyword search for specific problems. And teachers with Task Tracker subscriptions can assign the problem sets ...
IMAGES
VIDEO
COMMENTS
Just snap a picture. And yes, Phy understands your hand-writing. 5. Click it. Try Phy. A free to use AI Physics tutor. Solve, grade, and explain problems. Just speak to Phy or upload a screenshot of your working.
Upload your problem and get expert-level tutoring in seconds. Scan-and-solve physics, math, and chemistry. Generate polished analyses and summaries. Create sleek looking data visualizations. Ask anything to your data, and get answers. Perform modeling and predictive forecasting.
Our physics problem solver is powered by industry-leading AI models and is frequently updated. As such, it ensures approximately 98% precision in answering physics questions. However, as with any AI homework assistant, it's best to review the generated solutions before submitting your assignment. 5.
Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. ... define the variables, and plan a strategy for solving the problem. en. Related Symbolab blog posts. Practice Makes Perfect. Learning math takes practice, lots of practice. Just like running ...
Key features: Solve any physics question quickly. Over 100 equations at your fingertips. Practice with more than 300 free physics questions. Ask PhyWiz a question and get an answer instantly. The supported topics in this version are: Alternating Currents, Blackbody Radiation, Capacitance, Circular Motion, Diffraction Grating, Double-Slit ...
Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life. . Figure 1.8.1 1.8. 1: Problem-solving skills are essential to your success in physics. (credit: "scui3asteveo"/Flickr) As you are probably well aware, a certain amount of creativity and insight is required to solve problems.
All the training I received in math from AoPS was absolutely crucial to helping me gain problem-solving skills in physics. At the Olympiad level, most problems can't be solved with only one concept—cracking them usually requires putting multiple concepts together, and the WOOT program really helped me develop this essential skill.
Version 2 of our Calculator Pad was introduced in August of 2022. It includes six times as many problems and several additional topics (including Chemistry topics). Problem sets have been broken down into more than 400 smaller, single-topic problem sets. Problems utilize a random number generator to provide numerical information that is unique ...
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.
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 ...
Free math problem solver answers your physics homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. Start 7-day free trial on the app. Download free on Amazon. Download free in Windows Store. Take a photo of your math problem on the app. get Go. Physics. Basic Math. Pre-Algebra ...
Most are enrolled in a physics course; some are studying physics as part of a home-school program. ... Far from a spectator sport, physics problem-solving requires that a student become involved in the process - doing the reading, preparation, thinking, strategy-plotting, algebra, and calculator work. Simply listening to the audio files will do ...
These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop. Problem-Solving Strategy for Newton's Laws of Motion. Step 1.
How To Solve Any Physics Problem: Learn five simple steps in five minutes! In this episode we cover the most effective problem-solving method I've encountered and call upon some fuzzy friends to help us remember the steps. ... the California State University Affordable Learning Solutions Program, and Merlot. We also acknowledge previous ...
In computational physics, we "always" use programming to solve the problem, because computer program can calculate large and complex calculation "quickly". Computational physics can be represented as this diagram. There are so many programming languages that are used today to solve many numerical problems, Matlab for example.
The training I received in math from AoPS was absolutely crucial to helping me develop problem-solving skills in physics. At the Olympiad level, most problems can't be solved with only one concept-cracking them usually requires putting multiple concepts together, and the WOOT program really helped me develop this essential skill.
An example problem, its solution, and annotations on the process of solving the problem. The solutions to the problems from past exams will help you see what a good solution looks like. But seeing the solution alone may not illustrate the general method that could be used to solve other problems.
Calm down. It is just a problem, not the end of the world! 2. Read through the problem once. If it is a long problem, read and understand it in parts till you get even a slight understanding of what is going on. 3. Draw a diagram. It cannot be emphasized enough how much easier a problem will be once it is drawn out.
Solving program and will serve as a framework for action or creativity. In this context, the re sults of the surveys identified the . ... While trying to solve physics problems, students often ...
Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life. . Figure 1.8.1 1.8. 1: Problem-solving skills are essential to your success in physics. (credit: "scui3asteveo"/Flickr) As you are probably well aware, a certain amount of creativity and insight is required to solve problems.
A useful problem-solving strategy was presented for use with these equations and two examples were given that illustrated the use of the strategy. Then, the application of the kinematic equations and the problem-solving strategy to free-fall motion was discussed and illustrated. In this part of Lesson 6, several sample problems will be presented.
Undergraduate research helped feed physics and EECS major Thomas Bergamaschi's post-MIT interest in tackling challenges. "Every time I try to solve a problem — whether it be physics or computer science — I always try to find an elegant solution," says MIT senior Thomas Bergamaschi, who spent four years learning how to solve problems while an Undergraduate Research Opportunities ...
Version 2 of The Calculator Pad consists of a collection of relatively short problem sets that address a collection of discrete topics for each unit. Students. can choose to do a set of problems on the topic of interest conduct a keyword search for specific problems. And teachers with Task Tracker subscriptions can assign the problem sets ...