how to solve a physics problem

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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 329,724 times.

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

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

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

Community Q&A

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

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

Things You'll Need

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

Expert Interview

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

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

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1.7 Solving Problems in Physics

Learning objectives.

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

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

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

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

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

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

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

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

Significance

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

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

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Example Physics Problems and Solutions

Learning how to solve physics problems is a big part of learning physics. Here’s a collection of example physics problems and solutions to help you tackle problems sets and understand concepts and how to work with formulas:

Physics Homework Tips Physics homework can be challenging! Get tips to help make the task a little easier.

Unit Conversion Examples

There are now too many unit conversion examples to list in this space. This Unit Conversion Examples page is a more comprehensive list of worked example problems.

Newton’s Equations of Motion Example Problems

Equations of Motion – Constant Acceleration Example This equations of motion example problem consist of a sliding block under constant acceleration. It uses the equations of motion to calculate the position and velocity of a given time and the time and position of a given velocity.

Equations of Motion Example Problem – Constant Acceleration This example problem uses the equations of motion for constant acceleration to find the position, velocity, and acceleration of a breaking vehicle.

Equations of Motion Example Problem – Interception

This example problem uses the equations of motion for constant acceleration to calculate the time needed for one vehicle to intercept another vehicle moving at a constant velocity.

Vertical Motion Example Problem – Coin Toss Here’s an example applying the equations of motion under constant acceleration to determine the maximum height, velocity and time of flight for a coin flipped into a well. This problem could be modified to solve any object tossed vertically or dropped off a tall building or any height. This type of problem is a common equation of motion homework problem.

Projectile Motion Example Problem This example problem shows how to find different variables associated with parabolic projectile motion.

Accelerometer and Inertia Example Problem Accelerometers are devices to measure or detect acceleration by measuring the changes that occur as a system experiences an acceleration. This example problem uses one of the simplest forms of an accelerometer, a weight hanging from a stiff rod or wire. As the system accelerates, the hanging weight is deflected from its rest position. This example derives the relationship between that angle, the acceleration and the acceleration due to gravity. It then calculates the acceleration due to gravity of an unknown planet.

Weight In An Elevator Have you ever wondered why you feel slightly heavier in an elevator when it begins to move up? Or why you feel lighter when the elevator begins to move down? This example problem explains how to find your weight in an accelerating elevator and how to find the acceleration of an elevator using your weight on a scale.

Equilibrium Example Problem This example problem shows how to determine the different forces in a system at equilibrium. The system is a block suspended from a rope attached to two other ropes.

Equilibrium Example Problem – Balance This example problem highlights the basics of finding the forces acting on a system in mechanical equilibrium.

Force of Gravity Example This physics problem and solution shows how to apply Newton’s equation to calculate the gravitational force between the Earth and the Moon.

Coupled Systems Example Problems

Coupled systems are two or more separate systems connected together. The best way to solve these types of problems is to treat each system separately and then find common variables between them. Atwood Machine The Atwood Machine is a coupled system of two weights sharing a connecting string over a pulley. This example problem shows how to find the acceleration of an Atwood system and the tension in the connecting string. Coupled Blocks – Inertia Example This example problem is similar to the Atwood machine except one block is resting on a frictionless surface perpendicular to the other block. This block is hanging over the edge and pulling down on the coupled string. The problem shows how to calculate the acceleration of the blocks and the tension in the connecting string.

Friction Example Problems

These example physics problems explain how to calculate the different coefficients of friction.

Friction Example Problem – Block Resting on a Surface Friction Example Problem – Coefficient of Static Friction Friction Example Problem – Coefficient of Kinetic Friction Friction and Inertia Example Problem

Momentum and Collisions Example Problems

These example problems show how to calculate the momentum of moving masses.

Momentum and Impulse Example Finds the momentum before and after a force acts on a body and determine the impulse of the force.

Elastic Collision Example Shows how to find the velocities of two masses after an elastic collision.

It Can Be Shown – Elastic Collision Math Steps Shows the math to find the equations expressing the final velocities of two masses in terms of their initial velocities.

Simple Pendulum Example Problems

These example problems show how to use the period of a pendulum to find related information.

Find the Period of a Simple Pendulum Find the period if you know the length of a pendulum and the acceleration due to gravity.

Find the Length of a Simple Pendulum Find the length of the pendulum when the period and acceleration due to gravity is known.

Find the Acceleration due to Gravity Using A Pendulum Find ‘g’ on different planets by timing the period of a known pendulum length.

Harmonic Motion and Waves Example Problems

These example problems all involve simple harmonic motion and wave mechanics.

Energy and Wavelength Example This example shows how to determine the energy of a photon of a known wavelength.

Hooke’s Law Example Problem An example problem involving the restoring force of a spring.

Wavelength and Frequency Calculations See how to calculate wavelength if you know frequency and vice versa, for light, sound, or other waves.

Heat and Energy Example Problems

Heat of Fusion Example Problem Two example problems using the heat of fusion to calculate the energy required for a phase change.

Specific Heat Example Problem This is actually 3 similar example problems using the specific heat equation to calculate heat, specific heat, and temperature of a system.

Heat of Vaporization Example Problems Two example problems using or finding the heat of vaporization.

Ice to Steam Example Problem Classic problem melting cold ice to make hot steam. This problem brings all three of the previous example problems into one problem to calculate heat changes over phase changes.

Charge and Coulomb Force Example Problems

Setup diagram of Coulomb's Law Example Problem.

Electrical charges generate a coulomb force between themselves proportional to the magnitude of the charges and inversely proportional to the distance between them. Coulomb’s Law Example This example problem shows how to use Coulomb’s Law equation to find the charges necessary to produce a known repulsive force over a set distance. Coulomb Force Example This Coulomb force example shows how to find the number of electrons transferred between two bodies to generate a set amount of force over a short distance.

4 tricks for solving any physics problem

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

4 tricks for solving any physics problem:

1. what is the subject.

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

2. What are you trying to find?

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

3. What do you know?

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

4. What equations can you use?

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

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

Bonus Trick: “hack” the units

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

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

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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-x+3\gt 2x+1
line\:(1,\:2),\:(3,\:1)
prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x)
\frac{d}{dx}(\frac{3x+9}{2-x})
(\sin^2(\theta))'
\lim _{x\to 0}(x\ln (x))
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How To Solve Physics Problems

Proper problem-solving techniques not only help guide you through the difficulties of a problem but also enable you to communicate your solution effectively to others. When working out solutions to problems in this course, please bear the following points in mind.

. Near the diagram, draw up a table of the givens, being sure to respect the precision and units given in the problem statement.

. Outline the final (rounded) answer written . An answer of 1.0 x 10 s should often be converted to 120 days or 3.8 months to make the answer more meaningful or useful. In subsequent calculations, use unrounded values and round at the end.

Object weighs 94.0 lb and object weighs 29.0 lb. Between object and the plane the coefficient of static friction is 0.56 and coefficient of kinetic friction is 0.25. ( ) Find the acceleration of the system if is initially at rest. ( ) Find the acceleration if is moving up the plane. ( ) What is the acceleration if is moving down the plane? The plane is inclined by 42.0°.

From the force diagram for , we get the equation

, we get the pair of equations

, for the object to remain at rest. Let us calculate assuming the objects remain at rest to determine whether this is less than the given value. Substituting < , the objects remain at rest.

(b) If is initially moving up the plane, then the sense of the frictional force is opposite to that indicated in the diagram. We can solve for either case by writing the third equation as

the plane, and the lower sign to motion the plane. Solving for the acceleration gives

= 32.2 ft s-2 gives

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The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6 . The four kinematic equations are:

In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in v i ) indicates that the velocity value is the initial velocity value and a subscript of f (as in v f ) indicates that the velocity value is the final velocity value.

Problem-Solving Strategy

Construct an informative diagram of the physical situation.
Identify and list the given information in variable form.
Identify and list the unknown information in variable form.
Identify and list the equation that will be used to determine unknown information from known information.
Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information.
Check your answer to insure that it is reasonable and mathematically correct.

The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below.

Example Problem A

Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s 2 , then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.)

The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the v f value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity ( v i ) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration ( a ) of the car is given as - 8.00 m/s 2 . (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below.

Diagram:	Given:	Find:
	v = +30.0 m/s v = 0 m/s a = - 8.00 m/s	d = ??

The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are v f , v i , a , and d . Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables.

Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below.

(0 m/s) 2 = (30.0 m/s) 2 + 2 • (-8.00 m/s 2 ) • d

0 m 2 /s 2 = 900 m 2 /s 2 + (-16.0 m/s 2 ) • d

(16.0 m/s 2 ) • d = 900 m 2 /s 2 - 0 m 2 /s 2

(16.0 m/s 2 )*d = 900 m 2 /s 2

d = (900 m 2 /s 2 )/ (16.0 m/s 2 )

The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.)

The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is!

Example Problem B

Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s 2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period.

Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the v i value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration ( a ) of the car is 6.00 m/s 2 . And the time ( t ) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below.

Diagram:	Given:	Find:
	v = 0 m/s t = 4.10 s a = 6.00 m/s	d = ??

The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, v i , a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables.

d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s 2 ) • (4.10 s) 2

d = (0 m) + ½ • (6.00 m/s 2 ) • (16.81 s 2 )

d = 0 m + 50.43 m

The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.)

The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is!

The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6 , we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions.

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Problem-Solving Basics for One-Dimensional Kinematics

Learning objectives.

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

Apply problem-solving steps and strategies to solve problems of one-dimensional kinematics.
Apply strategies to determine whether or not the result of a problem is reasonable, and if not, determine the cause.

Close-up photo of a hand writing in a notebook. On top of the notebook is a graphing calculator.

Figure 1. Problem-solving skills are essential to your success in Physics. (credit: scui3asteveo, Flickr)

Problem-solving skills are obviously essential to success in a quantitative course in physics. More importantly, 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 and professional life.

Problem-Solving Steps

While there is no simple step-by-step method that works for every problem, the following general procedures facilitate problem solving and make it more meaningful. A certain amount of creativity and insight is required as well.

Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You will also need to decide which direction is positive and note that on your sketch. Once 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. A sketch can also be very useful at this point. Formally identifying the knowns is of particular importance in applying physics to real-world situations. Remember, “stopped” means velocity is zero, and we often can take initial time and position as zero.

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.

Find an equation or set of equations that can help you solve the problem . Your list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all of the other variables are known, so you can easily solve for the unknown. If the equation contains more than one unknown, then an additional equation is 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.

Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units . This step produces the numerical answer; it also provides a check on units that can help you find errors. If the units of the answer are incorrect, then an error has been made. However, be warned that correct units do not guarantee that the numerical part of the answer is also correct.

Check the answer to see if it is reasonable: Does it make sense? This final step is extremely important—the goal of physics is to accurately describe nature. To see if the answer is reasonable, check both its magnitude and its sign, in addition to its units. Your judgment will improve as you solve more and more physics problems, and it will become possible for you to make finer and finer judgments regarding whether nature is adequately described 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 mechanically solve a problem.

When solving problems, we often perform these steps in different order, and we also tend to do several steps simultaneously. There is no rigid procedure that will work every time. Creativity and insight grow with experience, and 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 progressing to the more difficult. Once 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.

Unreasonable Results

Physics must describe nature accurately. Some problems have results that are unreasonable because one premise is unreasonable or because certain premises are inconsistent with one another. The physical principle applied correctly then produces an unreasonable result. For example, if a person starting a foot race accelerates at 0.40 m/s 2 for 100 s, his final speed will be 40 m/s (about 150 km/h)—clearly unreasonable because the time of 100 s is an unreasonable premise. The physics is correct in a sense, but there is more to describing nature than just manipulating equations correctly. Checking the result of a problem to see if it is reasonable does more than help uncover errors in problem solving—it also builds intuition in judging whether nature is being accurately described.

Use the following strategies to determine whether an answer is reasonable and, if it is not, to determine what is the cause.

Solve the problem using strategies as outlined and in the format followed in the worked examples in the text . In the example given in the preceding paragraph, you would identify the givens as the acceleration and time and use the equation below to find the unknown final velocity. That is,

Check to see if the answer is reasonable . Is it too large or too small, or does it have the wrong sign, improper units, …? In this case, you may need to convert meters per second into a more familiar unit, such as miles per hour.

This velocity is about four times greater than a person can run—so it is too large.

If the answer is unreasonable, look for what specifically could cause the identified difficulty . In the example of the runner, there are only two assumptions that are suspect. The acceleration could be too great or the time too long. First look at the acceleration and think about what the number means. If someone accelerates at 0.40 m/s 2 , their velocity is increasing by 0.4 m/s each second. Does this seem reasonable? If so, the time must be too long. It is not possible for someone to accelerate at a constant rate of 0.40 m/s 2 for 100 s (almost two minutes).

Section Summary

The six basic problem solving steps for physics are:

Step 1 . Examine the situation to determine which physical principles are involved.
Step 2 . Make a list of what is given or can be inferred from the problem as stated (identify the knowns).
Step 3 . Identify exactly what needs to be determined in the problem (identify the unknowns).
Step 4 . Find an equation or set of equations that can help you solve the problem.
Step 5 . Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units.
Step 6 . Check the answer to see if it is reasonable: Does it make sense?

Conceptual Questions

1. What information do you need in order to choose which equation or equations to use to solve a problem? Explain. 2. What is the last thing you should do when solving a problem? Explain.

College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:aNsXe6tc@2/Problem-Solving-Basics-for-One . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected].

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No GPS, no problem: Researchers are making quantum sensing tools more compact and accurate to replace GPS

by Bernice Chan, University of Southern California

Fundamental physics—let alone quantum physics—might sound complicated to many, but it can actually be applied to solve everyday problems.

Imagine navigating to an unfamiliar place. Most people would suggest using GPS, but what if you were stuck in an underground tunnel where radio signals from satellites were not able to penetrate? That's where quantum sensing tools come in.

USC Viterbi Information Sciences Institute researchers Jonathan Habif and Justin Brown, both from ISI's new Laboratory for Quantum-Limited Information, are working at making sensing instruments like atomic accelerometers smaller and more accurate so they can be used to navigate when GPS is down.

Tackling the size conundrum

Atoms are excellent at making accurate measurements because they are all the same. Atomic measurements made in one laboratory would be indistinguishable from those made in another laboratory, as the atoms behave in precisely the same way.

One example of how this physics concept can be applied is making a highly accurate navigation system with these atoms.

"As an atomic physicist, I work with atoms in a gas and talk to the atoms with lasers," Brown said. "As atoms have mass, they can be used to measure accelerations, helping us build atom-based sensors like atomic accelerometers."

Habif added, "The accelerometers let you know how fast and far you're moving in a given direction. They can be coupled with gyroscopes, which tell you whether you've changed directions and how far you've turned, to make a complete measurement. These navigation instruments are useful when you don't have access to GPS."

One of the challenges they're facing is how they can engineer this in a thoughtful way.

For example, they have to think very carefully about how they can miniaturize atomic accelerometers. These accelerometers have historically operated in big laboratory scale systems, where equipment is heavy and consumes a lot of power. To make the accelerometers suitable for public use, Habif and Brown are investigating how to retain their high precision in a much more compact, power-efficient and attractive medium.

Brown said, "We want to take this out in the field and make it smaller at the same time, but the techniques and supplies that we're drawing from are not very conducive to doing so just yet. I'm thinking about how to talk to the atoms in a different way so that we can get the capabilities to apply it to problems outside the laboratory."

Applications in defense and adapting to the real world

Not only do quantum sensing devices work in areas that don't have access to GPS, they can also be part of an exciting new avenue: national security applications.

"Modern conflicts are becoming increasingly electronic and less kinetic, as nations vie for information superiority. The radio signal from GPS satellites is easy to disrupt and jam because it is far away. Thus, in any modern conflict, both sides will attempt to deny each other access to these radio signals ," Brown said.

"More traditional navigation instruments like inertial systems are un-jammable, as they work by adding up accelerations and rotations to measure our change in position. So they can replace GPS in times of conflict. However, all the errors made also get added up, so we are interested in using an atom-based measurement to ensure it is more accurate."

Atomic accelerometers are one example of these inertial systems. These systems are present in sensors on aircraft and ships, guiding their movement through airspaces and waters. However, existing mechanical-based sensors can wear out easily due to friction, leading to them being swapped out every year and costing a lot of money. They are also hard to build because they're small and delicate.

The US Department of Defense (DoD) is looking for upgrades in their inertial systems so that these difficulties can be overcome. The quantum approach based on atoms pursued by Brown and other groups could provide acceleration measurements with no moving parts.

"For example, if submarines want to be stealthy and quiet in defense scenarios, keeping track of what it's doing and how it's moved through inertial systems is pretty much the only game in town. I'm developing ideas on improving these systems for the DoD, so that they can be downsized and more cost-efficient," noted Brown.

Simplifying the tools

Brown maintains that quantum sensing will be important on many fronts.

"Preparing for technical surprise means preparing for when GPS fails—the question isn't if GPS fails," said Brown. "It's very easy to stop GPS from working, so inertial sensors will always be useful. But it's still vital for us to solve the size issue, because a lot of these sensors still end up at about the size of a washing machine. I could simplify the tool itself, but I still need to make a good measurement."

Achieving this fine balance between simplicity and accuracy is the researchers' main goal, and they hope that their efforts will translate to real-world prototypes someday.

Provided by University of Southern California

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Stumped five ways to hone your problem-solving skills.

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Respect the worth of other people's insights

Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?

1. Understand the root cause of the problem

“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .

Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.

“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”

He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.

Best High-Yield Savings Accounts Of 2024

Best 5% interest savings accounts of 2024, 2. unfocus the mind.

“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .

To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”

To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”

Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”

3. Be comfortable making judgment calls

“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”

Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”

Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.

4. Be prepared to fail and learn

“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .

Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.

Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”

5. Unleash the power of empathy

Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .

Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”

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Why US schools need to shake up the way they teach physics

Assistant Professor of Education, Michigan State University

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Clausell Mathis receives funding from U.S. Department of Education as a Co-PI on the Education Innovation and Research Grant program. .

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America has a physics problem.

Research shows that access to physics education varies based on race, gender, sexuality and disability . Physics courses are usually standard offerings in suburban high schools, but at urban and rural schools that isn’t the case .

Even in places where physics is taught, the lessons rarely highlight how physics can be applied to students’ everyday lives.

This approach can hamper students’ desire to learn . In my work as a physics education researcher , I’ve encountered lessons centered on the rote memorization of formulas. This method fails to encourage critical thinking, constraining students’ ability to creatively solve problems.

Teachers sometimes believe that if a student can’t grasp a physics concept, it’s the student’s problem. Instructors oftentimes don’t try to present the materials in a way that could help students engage more deeply with the lessons. This adds to the challenges poorer, nonwhite students already face, which include being held to lower standards and having fewer classroom resources .

Imagine if, instead, students could see how physics influences their daily lives in sports, extreme weather or baking and cooking. How might these real-world connections spark curiosity and foster a deeper understanding of physics?

Making physics relevant

Not adequately teaching physics has consequences.

As the economy becomes more tech-centered , understanding physics is critical. Yet the number of Americans with a solid grasp of physics is dwindling .

If there’s a shortage of candidates for jobs requiring a basic understanding of physics, it could hurt the ability of the U.S. to compete in the global economy, or it could compel companies to outsource certain jobs to countries with a better-educated workforce.

Many students have a vague notion that they would like to pursue STEM careers; they realize that these jobs usually pay well and can be interesting and fulfilling. But they aren’t even aware that learning physics can better prepare you for a role as an aerospace engineer, software developer or environmental scientist, to name just a few.

Understanding that relationship alone could boost their desire to learn the material.

But there’s another way to boost motivation, which I’ve spent years studying and developing , called “culturally relevant physics education.”

Physics is usually taught in ways that don’t connect with a diverse student body, leading to lower performance and engagement, especially among poor and nonwhite students. This can cause these populations to see little value in learning physics .

A traditional high school physics class teaches abstract equations and focuses on topics such as projectile motion and electrical circuits. The teacher might explain Newton’s laws of motion using examples exclusively from European history, such as the firing of cannonballs .

I wouldn’t fault students in, say, Raymond, Mississippi, for wondering why in the world they’re learning about the trajectory of 18th-century weaponry.

Physics in racing, texting and farming

By shifting to teaching physics in culturally responsive ways, I believe it’s possible to reverse this trend and cultivate a new generation of physics enthusiasts and professionals. There are plenty of ways to do this.

I’ve worked with teachers in California to explore how the physics of wave motion affects earthquake dynamics and how buildings are constructed. Other lessons include understanding how text messages are transmitted through wave motion and how the physics of firearms can be taught using the concepts of the conservation of momentum and impulse .

In these ways, teachers can tap into students’ cultures and interests to make physics more relatable and engaging. There is no one-size-fits-all approach: While the physics of earthquakes might resonate better in one region’s school district, the physics of hurricanes might work better in another.

The rural South, in particular, has an acute need for more opportunities to learn physics.

Data from the National Center for Education Statistics indicates that students in these areas have less access to advanced science courses , including physics, than their urban and suburban counterparts. And a 2021 report by the American Institute of Physics notes that fewer high schools in the rural South offer Advanced Placement physics courses, which could be due, in part, to the significant shortage of qualified physics teachers in these communities.

Man with beard takes a break from harvesting soybeans on a farm in Tennessee. A green soybean harvester idles in the background.

Targeted interventions could help meet this need.

I’ve already collaborated with teachers in the Southeast to develop activities using NASCAR – a hugely popular sport in the region – so students can learn about engine types, acceleration and thermal energy. I’m also one of the principal investigators in a collaboration between Michigan State University and two HBCUs, Alabama A&M University and Winston-Salem State University , to implement culturally responsive physics education in the rural South .

Given the region’s rich agricultural history , the science of raising plants and crops can be another avenue for physics instruction. Teachers could detail how light energy is converted into chemical energy; explain how fruits and vegetables have unique colors due to the ways they absorb and reflect wavelengths of light; and relate how physics concepts such as fluid dynamics can be used to improve irrigation techniques.

By learning these real-world applications, students from agricultural areas could become empowered to contribute to their communities.

This project is not just about filling a gap in physics instruction; it’s also about unlocking the potential of students in the rural South. And we hope they’ll eventually feel confident enough about their physics backgrounds to one day pursue careers in STEM.

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Electrostatic Problems with Solutions and Explanations. Gravity Problems with Solutions and Explanations. Projectile Problems with Solutions and Explanations. Velocity and Speed: Problems. Uniform Acceleration Motion: Problems. Free Physics SAT and AP Practice Tests Questions.
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How did you get better at solving physics problems? : r/AskPhysics
In my experience, becoming really good at solving physics problems follows this path: You need to really understand the concepts at an intuitive level, and you need to learn about many different situations where those concepts are applied. This step requires a good teacher, or for you to find great videos/explanations online.
Problem-Solving Basics for One-Dimensional Kinematics
The six basic problem solving steps for physics are: Step 1. Examine the situation to determine which physical principles are involved. Step 2. Make a list of what is given or can be inferred from the problem as stated (identify the knowns). Step 3.
How To Solve Physics Problems
Buy the Book. How to solve physics problems is a practical guide to using your pre-university physics knowledge to create solutions for unfamiliar situations. Combining hand-written answers with commentary, it illustrates the problem-solving processes involved, as well as highlighting the importance of good diagrams and clear, logical working.
No GPS, no problem: Researchers are making quantum sensing tools more
Fundamental physics—let alone quantum physics—might sound complicated to many, but it can actually be applied to solve everyday problems. Imagine navigating to an unfamiliar place. Most people ...
Stumped? Five Ways To Hone Your Problem-Solving Skills
Respect the worth of other people's insights. getty. Problems continuously arise in organizational life, making problem-solving an essential skill for leaders.
Full article: The engineering students' use of multiple representations
Problem-solving is one of the competencies that students must develop and highlight in the 21 st-century learning paradigm because it is one of the key aims of learning physics. Students can shape their problem-solving abilities or attitudes by applying their experience and information in everyday circumstances.
Why US schools need to shake up the way they teach physics
This method fails to encourage critical thinking, constraining students' ability to creatively solve problems. Teachers sometimes believe that if a student can't grasp a physics concept, it ...
Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear
View PDF Abstract: We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov-Muskhelishvili representation of the solution in terms of holomorphic potentials, we train a complex-valued ...