what is problem solving in physics

. 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

Dynamics: Force and Newton’s Laws of Motion

Problem-solving strategies, learning objective.

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 1(a). Then, as in Figure 1(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).

Figure 1. (a) A sketch of Tarzan hanging from a vine. (b) Arrows are used to represent all forces. T is the tension in the vine above Tarzan, F T is the force he exerts on the vine, and w is his weight. All other forces, such as the nudge of a breeze, are assumed negligible. (c) Suppose we are given the ape man’s mass and asked to find the tension in the vine. We then define the system of interest as shown and draw a free-body diagram. F T is no longer shown, because it is not a force acting on the system of interest; rather, F T  acts on the outside world. (d) Showing only the arrows, the head-to-tail method of addition is used. It is apparent that T = –w , if Tarzan is stationary.

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 1(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 1(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 1(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

F net x  = ma ,

F net y = 0.

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.

Section Summary

To solve problems involving Newton’s laws of motion, follow the procedure described:

• Draw a sketch of the problem.
• Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in directions that are not horizontal or vertical, resolve the vectors into horizontal and vertical components and draw them on the free-body diagram.
• Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, the x-direction) then  F net x  = 0 . If the object does accelerate in that direction,  F net x  = ma .
• Check your answer. Is the answer reasonable? Are the units correct?

Problems & Exercises

1. A 5.00 × 10 5 -kg rocket is accelerating straight up. Its engines produce 1.250 × 10 7  of thrust, and air resistance is 4.50 × 10 6 N. What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

2. The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is 1.80 m/s 2 , what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. For this situation, draw a free-body diagram and write the net force equation.

3. Calculate the force a 70.0-kg high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

4. When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

5. A freight train consists of two 8.00 × 10 4   engines and 45 cars with average masses of 5.50 × 10 4 kg . (a) What force must each engine exert backward on the track to accelerate the train at a rate of 5.00 × 10 -2  if the force of friction is 7.50 × 10 5 , assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

6. Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor. (a) An 1800-kg tractor exerts a force of 1.75 × 10 5  backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.150 m/s 2 , what is the mass of the airplane? (b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane. (c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.

7. A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of 0.550 m/s 2 ? The mass of the boat plus trailer is 700 kg. (b) What is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

8. (a) Find the magnitudes of the forces F 1 and F 2  that add to give the total force F tot  shown in Figure 4. This may be done either graphically or by using trigonometry. (b) Show graphically that the same total force is obtained independent of the order of addition of   F 1 and F 2 . (c) Find the direction and magnitude of some other pair of vectors that add to give F tot . Draw these to scale on the same drawing used in part (b) or a similar picture.

9. Two children pull a third child on a snow saucer sled exerting forces  F 1 and F 2 as shown from above in Figure 4 . Find the acceleration of the 49.00-kg sled and child system. Note that the direction of the frictional force is unspecified; it will be in the opposite direction of the sum of  F 1 and F 2 .

10. Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in Figure 6 to pull it out. (a) What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle is 2.00°? In this part, explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to 7.00° and you still apply the force found in part (a) to its center?

11. What force is exerted on the tooth in Figure 7 if the tension in the wire is 25.0 N? Note that the force applied to the tooth is smaller than the tension in the wire, but this is necessitated by practical considerations of how force can be applied in the mouth. Explicitly show how you follow steps in the Problem-Solving Strategy for Newton’s laws of motion.

Figure 7. Braces are used to apply forces to teeth to realign them. Shown in this figure are the tensions applied by the wire to the protruding tooth. The total force applied to the tooth by the wire, F app , points straight toward the back of the mouth.

12. Figure 9 shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the rope. (b) Find the tension in the rope above Superhero. (c) Find the tension in the rope between Superhero and Trusty Sidekick. Indicate on your free-body diagram the system of interest used to solve each part.

Figure 9. Superhero and Trusty Sidekick hang motionless on a rope as they try to figure out what to do next. Will the tension be the same everywhere in the rope?

13. A nurse pushes a cart by exerting a force on the handle at a downward angle 35.0º below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N. (a) Draw a free-body diagram for the system of interest. (b) What force must the nurse exert to move at a constant velocity?

14. Construct Your Own Problem Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.

15. Construct Your Own Problem Consider two people pushing a toboggan with four children on it up a snow-covered slope. Construct a problem in which you calculate the acceleration of the toboggan and its load. Include a free-body diagram of the appropriate system of interest as the basis for your analysis. Show vector forces and their components and explain the choice of coordinates. Among the things to be considered are the forces exerted by those pushing, the angle of the slope, and the masses of the toboggan and children.

16. Unreasonable Results (a) Repeat Exercise 7, but assume an acceleration of 1.20 m/s 2  is produced. (b) What is unreasonable about the result? (c) Which premise is unreasonable, and why is it unreasonable?

17. Unreasonable Results (a) What is the initial acceleration of a rocket that has a mass of 1.50 × 10 6  at takeoff, the engines of which produce a thrust of 2.00 × 10 6 ? Do not neglect gravity. (b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.) (c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)

Selected Solutions to Problems & Exercises

1. Using the free-body diagram:

• [latex]{F}_{\text{net}}=T-f-mg=\text{ma}\\[/latex] ,

[latex]a=\frac{T-f-\text{mg}}{m}=\frac{1\text{.}\text{250}\times {\text{10}}^{7}\text{N}-4.50\times {\text{10}}^{\text{6}}N-\left(5.00\times {\text{10}}^{5}\text{kg}\right)\left(9.{\text{80 m/s}}^{2}\right)}{5.00\times {\text{10}}^{5}\text{kg}}=\text{6.20}{\text{m/s}}^{2}\\[/latex]

3. Use Newton’s laws of motion.

[latex]F=\left(\text{70.0 kg}\right)\left[\left(\text{39}\text{.}{\text{2 m/s}}^{2}\right)+\left(9\text{.}{\text{80 m/s}}^{2}\right)\right]\\[/latex] [latex]=3.\text{43}\times {\text{10}}^{3}\text{N}\\[/latex].  The force exerted by the high-jumper is actually down on the ground, but F is up from the ground and makes him jump.

• This result is reasonable, since it is quite possible for a person to exert a force of the magnitude of 10 3 N.

5. (a) 4.41 × 10 5 N (b) 1.50 × 10 5 N

7. (a) 910 N (b) 1.11 × 10 3

9. (a) a = 0.139 m/s, θ = 12.4º

11. Use Newton’s laws since we are looking for forces.

• Draw a free-body diagram:

• The tension is given as T = 25.0 N. Find F app . Using Newton’s laws gives:[latex]\sigma{F}_{y}=0\\[/latex], so that applied force is due to the y -components of the two tensions: F app = 2 T  sin  θ  = 2(25.0 N) sin(15º) = 12.9 N The x -components of the tension cancel. [latex]\sum{F}_{x}=0\\[/latex].
• This seems reasonable, since the applied tensions should be greater than the force applied to the tooth.
• College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics . License : CC BY: Attribution . License Terms : Located at License

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Physics is a branch of science that studies the properties of matter, energy, and many more. Physics is considered to be the most fundamental of all the sciences, and is also the oldest.

• 2 History of Physics
• 3.1 Isaac Newton
• 3.2 Albert Einstein
• 4 Classical Mechanics
• 5 Statistical Mechanics
• 6 Acoustics
• 8 Thermodynamics
• 9 Electromagnetism
• 10 See also

Physics before the 19th century is called Classical Physics . Physics after the 19th century is know as Modern Physics .

Classical Physics can be split even further into its own branches:

• Classical Mechanics
• Statistical Mechanics
• Thermodynamics
• Electromagnetism

Modern Physics is also a group of different subjects in physics:

• Quantum Mechanics
• Nuclear Physics
• Condensed Matter Physics
• Particle Physics
• Astrophysics

History of Physics

The history of physics is long and exciting. Physics started with the first scientist, Thales of Miletus, who was the first to try to systematically explain the world using theories and hypotheses instead of using gods and magic. Archimedes also made a big breakthrough in physics when he devised the concept of buoyancy . This discovery was in the third century BC and not much innovation was made thereafter for many centuries.

However, Galileo Galilei, an Italian scientist, first advocated for the systematic study of physics. He was the one who tried to preach his scientific thoughts about how the Earth orbited the Sun, opposing the ideas of the Catholic establishment, and became the first patron of physics.

This was then further developed by Sir Isaac Newton , an English scientist, who devised the modern study of physics by discovering many laws. Since then, physics has never looked back!

Notable Figures

Isaac newton.

Isaac Newton was born on January 4, 1643, in Lincolnshire, England. Newton was born very shortly after the death of his father. He did very well at his local school and later attended Trinity College.

What is now considered Newton's most famous achievement is the formal statement of three basic, almost trivial laws of motion:

• If the net force on any amount of matter is Zero , then the object's velocity will not change if viewing from a constant reference point.

Albert Einstein

Relativity is a branch of modern science that has two parts: special relativity and general relativity. Both were formed by Albert Einstein.

Mechanics is the study of movement. Kinematics , mechanical forces , work , power , energy , and matter are all part of mechanics.

The rules of physics are almost fully summarized by the three famous laws of motion formulated by Isaac Newton :

• A body continues to be in its state of uniform rectilinear motion until it is disturbed by an external force. This property is known as inertia.
• The rate of change of momentum of a body with respect to time is directly proportional to the force acting on it.
• Every action has an equal and opposite reaction.

Mass is one of the two most basic intrinsic properties of a body. It is a measure of its inertia . Momentum is defined as the product of the mass and velocity of a body. Force is something that changes or tends to change the momentum of a body, (informally, a "push or pull").

Among the various properties of matter are elasticity, surface tension, and viscosity. The most important one is gravity . Gravity is indeed considered one of the most mysterious things not only in physics but in science as a whole.

Newton's laws can also be used to study the behavior of continuous substances. This has, for example, led to the development of fluid mechanics , which, despite being almost entirely summarized by the Navier-Stokes equations or its variants, has many open questions about, for example, whether fluids continue to be well-behaved after arbitrary amounts of time.

Statistical Mechanics is mechanics that use statistics to draw conclusions.

Acoustics is the study of sound . Sound waves are mechanical waves - they travel by actual vibrations in some material medium. Acoustics concerns itself with mechanical waves in general. Phenomena such as forced vibrations , resonance , damped vibrations and the Doppler effect come under this branch of physics.

Optics is the study of vision and light. Light waves are electromagnetic waves - they consist of mutually perpendicular electric fields and magnetic fields , and can travel through a vacuum. Optics is the study of electromagnetic waves in general. So it covers all waves in the electromagnetic spectrum given below:

• Ultraviolet rays
• Visible light
• Infrared Rays
• Radio waves

One of the most controversial questions in optics is whether light is a wave or a ray. Accordingly, there are two branches of optics, but only ray optics belongs to classical physics. Wave optics are a topic of modern physics. In ray, optics covers topics such as reflection and refraction and the dispersion of white light into its constituent colors.

Thermodynamics is the study of heat transfer. Anything in physics related to heat is classified as thermodynamics. There are three laws of thermodynamics:

• The First Law of Thermodynamics is a form of conservation of energy: The change in internal energy of a system is equal to the sum of the energy transferred to the system by heat and the work done on the system.
• The Second Law of Thermodynamics states that the efficiency of heat engines must always be < 1.
• The Third Law of Thermodynamics states that the temperature of a system cannot reach absolute zero (0 K); as the system approaches absolute zero, entropy approaches a constant.

Electromagnetism is the combined study of electricity and magnetism , and the most important addition to classical physics after Isaac Newton 's work. The concept of electromagnetism has wide applications in everyday devices such as modern computers, televisions, linear particle accelerators, and more. Electromagnetism operates on the fact that when electricity is run through a conductor, it produces a magnetic field

• Physics books
• Physics competitions
• Physics scholarships
• Physics summer programs
• Electricity

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PHYSICS PROBLEM SOLVING STRATEGY Dr. Mark Hollabaugh Normandale Community College

http://www.nr.cc.mn.us/physics/Faculty/HOLLABGH/probsolv.htm

    Two factors can help make you a better physics problem solver.  First of all, you must know and understand the principles of physics.  Secondly, you must have a strategy for applying these principles to new situations in which physics can be helpful.  We call these situations problems.  Many students say, “I understand the material, I just can’t do the problems.”  If this is true of you as a physics student, then maybe you need to develop your problem-solving skills.  Having a strategy to organize those skills can help you.

    Physics problem solving can be learned just like you learned to drive a car, play a musical instrument, or ride a bike.  What can aid you more than anything is to have a general approach to follow with each problem you encounter.  You may use different tools or tactics with differing areas of physics, but the overall strategy remains the same.  Most likely, you have already acquired some problem-solving skills and habits from previous courses in physics, chemistry, or mathematics.  Like other areas of learning and life, some of these habits may be beneficial and some may actually hinder your progress in learning how to solve physics problems.

    So, in learning this new approach, be willing to try new ideas and to discard old habits that may in fact be hindering your understanding.  As you mature as a physics problem solver, you will find that the approach will become second nature to you.  You will begin automatically to do those things that will lead you to construct an effective solution to the problem.

    As with so many other learning activities, it is useful to break a problem solving strategy into major and minor steps.  The strategy we would like you to learn has five major steps:  Focus the Problem , Physics Description , Plan a Solution , Execute the Plan , and Evaluate the Solution .  Let’s take a detailed look at each of these steps and then do an sample problem following the strategy.  At this stage of our discussion, do not worry if there are physics terms or concepts that you do not understand.  You will learn these concepts as they are needed.  Then, refer back to this discussion.

FOCUS the PROBLEM      Usually when you read the statement of a physics problem, you must visualize the objects involved and their context.  You need to draw a picture and indicate any given information.

(1) First, construct a mental image of the problem situation. (2)Next draw a rough, although literal, picture showing the important objects, their motion, and their interactions.  An interaction, for example, may consist of one object being connected to another by a rope. (3) Label all known information.  At this point, do not worry about assigning algebraic symbols to specific quantities.

    Sometimes the question being asked in the problem is not obvious.  “Is the rope safe?” is not something you can directly answer.  Ask yourself, what specifically is being asked?  How does this translate into some calculable quantity?

    There are many ways to solve a physics problem.  One part of learning how to solve a problem is to know what approach to use.  You will need to outline the concepts and principles you think will be useful in solving the problem.

If simple motions are involved, use the kinematics definition of velocity and acceleration. If forces are involved and objects interact due to these forces, use Newton's Laws of Motion. Forces that act over a time interval and cause objects to change their velocities suggests using the Conservation of Momentum. Frequently in situations involving thermal physics or electromagnetism, the principle of Conservation of Energy is useful. You may need to specify time intervals over which the application of each principle will be the most useful. It is important to identify any constraints present in this situation, such as “the car doesn’t leave the road”. Specify any approximations or simplifications you think will make the problem solution easier, but will not affect the result significantly.  Frequently we ignore frictional forces due to air resistance.

    Your approach probably will be very consistent throughout a particular section of the textbook.  The challenge for you will be to apply the approach in a variety of situations.

DESCRIBE the PHYSICS      A “physics description” of a problem translates  the given information and a very literal picture into an idealized diagram and defines variables that can be manipulated to calculate desired quantities.  In a sense, you are translating the literal situation into an idealized situation where you can then apply the laws the physics.  The biggest shortcoming of beginning physics problem solvers is attempting to apply the laws of physics, that is write down equations, before undertaking this qualitative analysis of the problem.  If you can resist the temptation to look for equations too early in your problem solution, you will become a much more effective problem solver.

To construct your physics description, you must do the following:

• Translate your picture into a diagram(s) which gives only the essential information for a mathematical solution.  In an idealized diagram, people, cars, and other objects may become square blocks or points.
• Define a symbol for every important physics variable on your diagram.
• Usually you need to draw a coordinate system showing the + and - directions.
• If you are using kinematics concepts, draw a motion diagram specifying the objects’ velocity and acceleration at definite positions and times.
• If interactions are important, draw idealized, free body, and force diagrams.
• When using conservation principles, draw "before", "transfer" (i.e., during), and "after" diagrams to show how the system changes. To the side of your diagram(s), give the value for each physics variable you have labeled on the diagram(s) or specify that it is unknown.

    Then, using the question, your physics description and the approach you have stated, you will need to identify a target variable.  That is, you must decide what unknown quantity is it that you must calculate from your list of variables.  Ask yourself if the calculated quantity answers the question.  In complex problems there may be more than one target variable or some intermediate variables you will calculate.

     Now, knowing the target variable(s), and your approach, you can assemble your toolbox of mathematical expressions using the principles and constraints from your approach to relate the physics variables from your diagrams.  This is the first time you really begin to look for quantitative relationships among the variables.

 PLAN the SOLUTION     Before you actually begin to calculate an answer, take time to make a plan.  Usually when the laws of physics are expressed in an equation, the equation is a general, universal statement.  You must construct specific algebraic equations that will enable you to calculate the target variable.

• Determine how the equations in your toolbox can be combined to find your target variable. Begin with an equation containing the target variable.
• Identify any unknowns in that equation.
• Find equations from your toolbox containing these unknowns.
• Continue this process until your equations contain no new unknowns.
• Number each equation for easy reference.
• Do not solve equations numerically at this time.

    Frequently expert problem solvers will start with the target variable and work backwards to determine a path to the answer.  Sometimes the units will help you find the correct path.  For example, if you are looking for a velocity, you know your final answer must be in m/s.

    You have a solution if your plan has as many independent equations as there are unknowns.  If not, determine other equations or check the plan to see if it is likely that a variable will cancel from your equations.

    If you have the same number of equations and unknowns, indicate the order in which to solve the equations algebraically for the target variable. Typically, you begin your construction of the plan at the end and work backwards to the first step,  That is, you write down the equation containing the target variable first.

EXECUTE the PLAN     Now you are ready to execute the plan.

• Do the algebra in the order given by your outline.
• When you are done you should have a single equation with your target variable isolated on one side and only known quantities on the other side.
• Substitute the values (numbers with units) into this final equation.
• Make sure units are consistent so that they will cancel properly.

    Finally, calculate the numerical result for the target variable(s).  Make sure your final answer is clear to the person who will evaluate your solution.

    It is extremely important to solve the problem algebraically before inserting any numerical values.  Some unknown quantities may cancel out and you won’t need to actually know their numerical value.  In some complex problems it can be useful to calculate intermediate numerical results as a check on the reasonableness of your solution.

EVALUATE the SOLUTION      Finally, you are ready to evaluate your answer.  Here, you must use your common sense about how the real world works as well as those aspects of the physical world you have learned in your physics class.

• Do vector quantities have both magnitude and direction?
• Can someone else follow your solution?
• Is the result reasonable and within your experience?  Remember, for example, that cars don’t travel down the highway at 300 mi/hr.  If you put a cooler object into hot water, the water cools down and the object rises in temperature.
• Do the units make sense?  Velocity is not measured, for example, in kg/s.
• Have you answered the question?

    Whenever possible, it is a good idea to read through the solution carefully, especially if it is being evaluated by your instructor.  If your evaluation suggests to you that your answer is incorrect or unreasonable, make a statement to that effect and explain your reasoning.  

Further Reading:

Patricia Heller, Ronald Keith, and Scott Anderson (1992), Teaching Problem Solving Through Cooperative Grouping.  Part 1:  Group Versus Individual Problem Solving, American Journal of Physics , Vol. 60, No. 7, pp. 627-636.

Patricia Heller and Mark Hollabaugh (1992), Teaching Problem Solving Through Cooperative Grouping.  Part 2:  Designing Problems and Structuring Groups,  American Journal of Physics , Vol. 60, No. 7, pp. 637-644.  

Physics Problems with Solutions

Projectile problems with solutions and explanations, problems with detailed solutions.

An object is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal. a) What is the maximum height reached by the object? b) What is the total flight time (between launch and touching the ground) of the object? c) What is the horizontal range (maximum x above ground) of the object? d) What is the magnitude of the velocity of the object just before it hits the ground? Solution to Problem 1

A ball kicked from ground level at an initial velocity of 60 m/s and an angle θ with ground reaches a horizontal distance of 200 meters. a) What is the size of angle θ? b) What is time of flight of the ball? Solution to Problem 5

A ball of 600 grams is kicked at an angle of 35° with the ground with an initial velocity V 0 . a) What is the initial velocity V 0 of the ball if its kinetic energy is 22 Joules when its height is maximum? b) What is the maximum height reached by the ball Solution to Problem 6

A projectile starting from ground hits a target on the ground located at a distance of 1000 meters after 40 seconds. a) What is the size of the angle θ? b) At what initial velocity was the projectile launched? Solution to Problem 7

The trajectory of a projectile launched from ground is given by the equation y = -0.025 x 2 + 0.5 x, where x and y are the coordinate of the projectile on a rectangular system of axes. a) Find the initial velocity and the angle at which the projectile is launched. Solution to Problem 8

Two balls A and B of masses 100 grams and 300 grams respectively are pushed horizontally from a table of height 3 meters. Ball has is pushed so that its initial velocity is 10 m/s and ball B is pushed so that its initial velocity is 15 m/s. a) Find the time it takes each ball to hit the ground. b) What is the difference in the distance between the points of impact of the two balls on the ground? Solution to Problem 9

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Problem Solving Ai generator. Problem solving is a crucial skill in both personal and professional settings. Whether it’s addressing a personal challenge or drafting a business problem solving proposal , the ability to identify a problem and develop a solution is essential. Writing a problem solving essay helps articulate the issue clearly and systematically outline potential solutions. Effective problem and solution involves critical thinking, creativity, and a structured approach to overcome obstacles and achieve goals. What is Problem Solving? Problem solving is the process of identifying a challenge, analyzing its components, and finding an effective solution. It involves critical thinking, creativity, and the application of various techniques and tools. Examples of Problem Solving Analytical Thinking : Breaking down complex problems into manageable parts. Creativity : Developing innovative solutions to problems. Critical Thinking : Evaluating information and arguments to make a reasoned decision. Decision-Making : Choosing the best course of action from various alternatives. Research : Gathering relevant information to understand and solve a problem. Communication : Clearly conveying ideas and solutions to others. Collaboration : Working effectively with others to solve problems. Time Management : Prioritizing tasks to efficiently address problems. Adaptability : Adjusting strategies as new information or challenges arise. Attention to Detail : Ensuring all aspects of a problem are considered. Logical Reasoning : Using logic to identify solutions and predict outcomes. Empathy : Understanding others’ perspectives to create more effective solutions. Negotiation : Finding mutually acceptable solutions through discussion. Conflict Resolution : Addressing and resolving disagreements. Patience : Remaining calm and persistent when solving complex problems. Organization : Structuring tasks and information systematically. Leadership : Guiding and motivating a team to solve problems. Decision Analysis : Evaluating the potential impact of different solutions. Project Management : Planning and executing solutions effectively. Technical Skills : Using specialized knowledge to solve technical problems. Customer Service : Resolving customer issues effectively and efficiently. Risk Management : Identifying and mitigating potential problems. Innovation : Implementing new ideas to solve existing problems. Strategic Planning : Developing long-term solutions and plans. Resourcefulness : Finding quick and clever ways to overcome difficulties. Stress Management : Handling pressure while solving problems. Observation : Noticing subtle details that could be key to solving a problem. Data Analysis : Interpreting data to inform problem-solving decisions. Flexibility : Being open to new approaches and changing plans when necessary. Self-Assessment : Reflecting on your own problem-solving process to improve future performance. Problem-Solving Examples for Students 1. math word problems. Problem: Jane has 3 apples, and she buys 4 more apples from the store. How many apples does she have now? Understand the problem: Jane starts with 3 apples and buys 4 more. Break it down: 3 apples (initial) + 4 apples (additional). Solve: 3 + 4 = 7. Answer: Jane has 7 apples. 2. Group Project Coordination Problem: A group of students needs to complete a science project, but they are having trouble coordinating their schedules. Understand the problem: The main issue is scheduling conflicts. Break it down: Identify each member’s available times. Research: Use tools like Doodle or Google Calendar to find common free times. Brainstorm solutions: Propose meeting during lunch breaks or weekends. Evaluate: Choose the most convenient and feasible option for everyone. Develop an action plan: Set a recurring meeting time and delegate tasks. Implement: Start meeting and working on the project according to the plan. Monitor and review: Adjust schedules if conflicts arise and keep track of progress. 3. Essay Writing Problem: A student struggles to start writing an essay on a given topic. Understand the problem: The difficulty is starting the essay. Break it down: Identify the essay topic, main points, and required structure. Research: Gather information and resources related to the topic. Brainstorm solutions: Create an outline, jot down ideas, and decide on the thesis statement. Evaluate: Choose the most compelling points and organize them logically. Develop an action plan: Write a draft based on the outline, then revise and edit. Implement: Begin writing the introduction, followed by the body paragraphs and conclusion. Monitor and review: Proofread the essay and make necessary corrections. 4. Time Management Problem: A student has trouble managing time between homework, extracurricular activities, and leisure. Understand the problem: The issue is balancing multiple responsibilities. Break it down: Identify all tasks and time commitments. Research: Look for time management techniques and tools. Brainstorm solutions: Use planners, to-do lists, or apps like Trello or Todoist. Evaluate: Choose the most effective tool and technique. Develop an action plan: Create a weekly schedule, prioritizing tasks by importance and deadlines. Implement: Follow the schedule and adjust as necessary. Monitor and review: Reflect on the effectiveness of the schedule and make improvements. 5. Conflict Resolution Problem: Two students have a disagreement over a shared locker space. Understand the problem: The conflict is about sharing limited space. Break it down: Identify each student’s concerns and needs. Research: Look into conflict resolution strategies. Brainstorm solutions: Propose solutions like dividing the locker into specific sections or creating a rotation schedule. Evaluate: Choose the fairest and most practical solution. Develop an action plan: Agree on the solution and set guidelines. Implement: Follow the agreed plan and make adjustments if needed. Monitor and review: Ensure both students are satisfied with the arrangement and resolve any further issues. Problem-Solving Examples in Real-life Example 1: workplace conflict. Situation : Two team members have a disagreement that affects their productivity. Identify the Problem : Understand the root cause of the conflict. Analyze : Talk to both parties separately to get their perspectives. Generate Solutions : Consider solutions like mediation, reassignment of tasks, or team-building exercises. Evaluate : Assess which solution is likely to resolve the conflict without affecting team morale. Implement : Arrange a mediation session. Review : Follow up to ensure the conflict is resolved and monitor team dynamics. Example 2: Personal Finance Management Situation : Struggling to manage monthly expenses and savings. Identify the Problem : Determine specific areas where overspending occurs. Analyze : Review bank statements and categorize expenses. Generate Solutions : Create a budget, reduce unnecessary expenses, and set savings goals. Evaluate : Choose a budgeting method that fits your lifestyle. Implement : Start tracking expenses and adjust spending habits. Review : Regularly review your budget and savings to ensure you are on track. How to Improve Your Problem-Solving Skills? Understand the Problem: Before attempting to solve any problem, it’s crucial to fully understand it. Read through the problem statement carefully and make sure you grasp every detail. Break It Down : Divide the problem into smaller, more manageable parts. This approach, known as decomposition, makes it easier to tackle complex issues by focusing on individual components one at a time. Research and Gather Information : Collect all relevant information and data that might help in solving the problem. Look for similar problems and their solutions. Brainstorm Possible Solutions : Generate as many potential solutions as possible. Don’t worry about evaluating them at this stage; the goal is to think creatively and come up with a wide range of ideas. Evaluate and Select the Best Solution : Assess the feasibility, pros, and cons of each potential solution. Consider factors such as resources, time, and potential risks. Choose the solution that best addresses the problem and is most practical. Develop an Action Plan : Create a detailed plan for implementing your chosen solution. Outline the steps you need to take, assign tasks if working in a team, and set deadlines to ensure timely progress. Implement the Solution : Put your plan into action. Stay focused and be prepared to adapt if necessary. Keep track of your progress and make adjustments as needed. Monitor and Review : After implementing the solution, monitor the results to ensure the problem is resolved. Evaluate the outcome and review the process to learn from any mistakes or successes. Problem-solving in workplace Enhancing Efficiency : Quick and effective problem resolution can streamline processes and reduce downtime. Boosting Productivity : Employees who can solve problems independently help maintain workflow and productivity. Improving Customer Satisfaction : Solving customer issues promptly can lead to higher satisfaction and loyalty. Fostering Innovation : Problem-solving often leads to new ideas and improvements that drive innovation. Promoting Employee Development : Encouraging problem-solving helps employees grow and develop their skills. How To Highlight Problem-Solving Skills? 1. on your resume. When listing problem-solving skills on your resume, provide concrete examples. Use action verbs and quantify your achievements where possible. Resolved a customer service issue that increased customer satisfaction by 20%. Developed a new process that reduced production errors by 15%. 2. In a Cover Letter Your cover letter is a great place to elaborate on your problem-solving abilities. Describe a specific situation where you successfully addressed a challenge. “In my previous role at XYZ Company, I identified a bottleneck in our production line. I conducted a thorough analysis and implemented a new workflow, which reduced production time by 25% and saved the company $50,000 annually.” 3. During an Interview Be prepared to discuss your problem-solving skills in depth during an interview. Use the STAR (Situation, Task, Action, Result) method to structure your responses. Example: “Can you give an example of a time when you solved a difficult problem at work?” Situation: Our sales team was struggling with declining numbers. Task: I was tasked with identifying the root cause and finding a solution. Action: I analyzed sales data, conducted team meetings, and identified a lack of training as the main issue. Result: I organized comprehensive training sessions, which led to a 30% increase in sales over the next quarter. 4. On Social Media and Professional Profiles Highlight problem-solving skills on LinkedIn and other professional profiles. Share posts or articles about your problem-solving experiences and successes. “I’m thrilled to share that I recently led a project to overhaul our customer service protocol, resulting in a 40% reduction in response time and a significant boost in customer satisfaction!” 5. In Performance Reviews During performance reviews, make sure to emphasize your problem-solving contributions. Provide specific examples and outcomes. “In the past year, I resolved three major project roadblocks, enabling our team to meet all deadlines and exceed our performance goals.” 6. Through Projects and Case Studies If applicable, create case studies or detailed project descriptions that showcase your problem-solving process and results. This can be particularly useful for portfolios or presentations. Case Study: Improving IT System Efficiency Problem: Frequent system downtimes affecting productivity. Solution: Implemented a new monitoring system and revised maintenance schedules. Outcome: System downtimes were reduced by 50%, significantly improving productivity. 7. By Demonstrating Soft Skills Problem-solving often involves other soft skills such as communication, creativity, and teamwork. Highlighting these related skills can further emphasize your ability to solve problems effectively. “By fostering open communication within my team and encouraging creative brainstorming sessions, we were able to devise innovative solutions to our most pressing challenges.” How to Answer Problem-Solving Interview Questions Understand the Question : Make sure you fully understand the problem before you try to solve it. Ask clarifying questions if needed to ensure you have all the relevant information. Think Aloud : Demonstrate your thinking process by explaining your thoughts as you work through the problem. This shows your interviewer how you approach problems and organize your thoughts. Break It Down : Divide the problem into smaller, manageable parts. This can make a complex issue seem more approachable and allows you to tackle each component systematically. Use a Structured Approach : Employ frameworks or methodologies that are relevant to the question. For example, you might use the STAR method (Situation, Task, Action, Result) for behavioral questions, or a simple problem-solving framework like Define, Measure, Analyze, Improve, Control (DMAIC) for process improvements. Be Creative : Employers often look for creativity in your answers. Think outside the box and propose innovative solutions when appropriate. Prioritize Solutions : If there are multiple potential solutions, discuss the pros and cons of each and explain why you would choose one over the others. Stay Calm and Positive : Problem-solving under pressure is part of the test. Maintain a calm and positive demeanor, showing that you can handle stress effectively. Summarize Your Steps : After you have worked through the problem, summarize the steps you took and the conclusion you reached. This helps ensure the interviewer followed your process and underscores your methodical approach. Ask for Feedback : After presenting your solution, it can be beneficial to ask if there are any additional factors you might consider. This shows openness to learning and adapting. Practice Regularly : Like any skill, problem-solving improves with practice. Regularly engage in brain teasers, logic puzzles, or case studies to sharpen your skills. Why Are Problem-Solving is Important? Effective Decision-Making : Problem-solving is essential for making decisions that are logical, informed, and well-considered. This skill helps individuals and organizations make choices that lead to better outcomes. Innovation and Improvement : Solving problems effectively often requires innovative thinking. This can lead to new ideas and improvements in processes, products, and services, which are essential for business growth and adaptation. Handling Complex Situations : Many roles involve complex situations that are not straightforward to manage. Problem-solving skills enable individuals to dissect these situations and devise effective strategies to deal with them. Enhances Productivity : Efficient problem-solving contributes to higher productivity, as it allows for the identification and removal of obstacles that impede workflow and performance. Career Advancement : Individuals who are effective problem solvers are often seen as leaders and can advance more quickly in their careers. This skill is valuable because it demonstrates the ability to handle difficult situations and complex challenges. Adaptability and Resilience : Problem-solving is key to adapting to new situations and overcoming challenges. Those who can creatively navigate through difficulties are generally more resilient. Quality of Life : On a personal level, strong problem-solving skills can improve one’s quality of life by enabling better management of the challenges that come with daily living. Team Collaboration : Problem-solving often requires collaboration. Being good at solving problems can improve your ability to work with others, as it involves communication, persuasion, and negotiation skills. How to Include Problem-Solving in a Job Application Resume : Detail specific problem-solving instances in your job descriptions using action verbs like “analyzed” and “implemented”. Mention the positive outcomes achieved. Cover Letter : Narrate a specific instance where your problem-solving skills led to a successful outcome, demonstrating initiative and effectiveness. Skills Section : Include “problem-solving” in a skills section if the job ad specifically mentions it. Quantify Achievements : Use numbers to describe the impact of your solutions, such as cost savings or efficiency improvements. Job Interviews : Prepare to discuss specific examples of your problem-solving skills, focusing on the challenge, your action, and the result. References : Brief your references about your problem-solving achievements so they can provide specific examples when contacted by employers. Tips for Enhancing Problem-Solving Practice Regularly: Like any skill, problem-solving improves with regular practice. Engage in activities that challenge your thinking, such as puzzles, games, or real-world problem-solving scenarios. Learn from Others: Study how others approach and solve problems. This can provide new strategies and perspectives that you can incorporate into your own problem-solving toolkit. Stay Calm and Positive: Maintaining a calm and positive mindset can significantly improve your ability to solve problems. Stress and negativity can cloud your judgment and hinder creative thinking. Develop Critical Thinking: Sharpen your critical thinking skills by questioning assumptions, analyzing information, and evaluating evidence. This will help you make more informed and logical decisions. Collaborate with Others: Working with others can bring new insights and ideas. Collaboration can also help you see the problem from different angles and develop more effective solutions. Keep Learning: Continuously expand your knowledge and skills. The more you know, the better equipped you are to tackle a variety of problems. How can I improve my problem-solving skills? Practice regularly, learn various problem-solving techniques, and engage in activities that challenge your thinking. What are common problem-solving techniques? Common techniques include brainstorming, root cause analysis, the 5 Whys, and SWOT analysis. What are the steps in the problem-solving process? Identify the problem, analyze the problem, generate solutions, select a solution, implement, and evaluate. How do I demonstrate problem-solving skills in an interview? Discuss specific situations where you effectively solved problems, highlighting your thought process and outcomes. What’s the difference between critical thinking and problem-solving? Critical thinking involves analyzing and evaluating information, while problem-solving focuses on finding solutions to problems. How do problem-solving skills help in leadership? They enable leaders to manage challenges effectively, inspire innovation, and guide teams through obstacles. How to measure problem-solving skills? Assess through scenarios or challenges that require identifying, analyzing, and resolving problems. What role does creativity play in problem-solving? Creativity enables out-of-the-box thinking, which can lead to innovative and effective solutions. How do you use problem-solving in project management? Apply it to anticipate potential issues, plan solutions, and ensure smooth project execution. What’s an example of a problem-solving situation? Resolving customer complaints by identifying the issue, brainstorming solutions, and implementing changes to prevent future complaints. Text prompt Instructive Professional 10 Examples of Public speaking 20 Examples of Gas lighting Help | Advanced Search Quantum Physics Title: a catalyst framework for the quantum linear system problem via the proximal point algorithm. Abstract: Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system problem (QLSP) in terms of the problem dimension, but even such a theoretical advantage is bottlenecked by the condition number of the coefficient matrix. In this work, we propose a new quantum algorithm for QLSP inspired by the classical proximal point algorithm (PPA). Our proposed method can be viewed as a meta-algorithm that allows inverting a modified matrix via an existing \texttt{QLSP\_solver}, thereby directly approximating the solution vector instead of approximating the inverse of the coefficient matrix. By carefully choosing the step size $\eta$, the proposed algorithm can effectively precondition the linear system to mitigate the dependence on condition numbers that hindered the applicability of previous approaches. Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Optimization and Control (math.OC) Cite as: [quant-ph]   (or [quant-ph] for this version)   Focus to learn more arXiv-issued DOI via DataCite Submission history Access paper:. HTML (experimental) Other Formats References & Citations INSPIRE HEP Google Scholar Semantic Scholar BibTeX formatted citation Bibliographic and Citation Tools Code, data and media associated with this article, recommenders and search tools. Institution arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Advanced Search Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space New citation alert added. This alert has been successfully added and will be sent to: You will be notified whenever a record that you have chosen has been cited. To manage your alert preferences, click on the button below. New Citation Alert! Please log in to your account Information & Contributors Bibliometrics & citations, view options, recommendations, nyström method for elastic wave scattering by three-dimensional obstacles. Nyström method is developed to solve for boundary integral equations (BIE's) for elastic wave scattering by three-dimensional obstacles. To generate the matrix equation from a BIE, Nyström method applies a quadrature rule to the integrations of smooth ... Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects Multilevel fast multipole algorithm (MLFMA) is developed for solving elastic wave scattering by large three-dimensional (3D) objects. Since the governing set of boundary integral equations (BIE) for the problem includes both compressional and shear ... Numerical Solution of the Helmholtz Equation in 2D and 3D Using a High-Order Nyström Discretization We show how to solve time-harmonic scattering problems by means of a high-order Nystr m discretization of the boundary integral equations of wave scattering in 2D and 3D. The novel aspect of our new method is its use of local corrections to the ... Information Published in. Academic Press Professional, Inc. United States Publication History Author tags. Elastic scattering Windowed Green function Boundary integral equation Research-article Contributors Other metrics, bibliometrics, article metrics. 0 Total Citations 0 Total Downloads Downloads (Last 12 months) 0 Downloads (Last 6 weeks) 0 View options Login options. Check if you have access through your login credentials or your institution to get full access on this article. Full Access Share this publication link. Copying failed. Share on social media Affiliations, export citations. 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Visit our dedicated information section to learn more about MDPI. JSmol Viewer Multi-step physics-informed deep operator neural network for directly solving partial differential equations. Share and Cite Wang, J.; Li, Y.; Wu, A.; Chen, Z.; Huang, J.; Wang, Q.; Liu, F. Multi-Step Physics-Informed Deep Operator Neural Network for Directly Solving Partial Differential Equations. Appl. Sci. 2024 , 14 , 5490. https://doi.org/10.3390/app14135490 Wang J, Li Y, Wu A, Chen Z, Huang J, Wang Q, Liu F. Multi-Step Physics-Informed Deep Operator Neural Network for Directly Solving Partial Differential Equations. Applied Sciences . 2024; 14(13):5490. https://doi.org/10.3390/app14135490 Wang, Jing, Yubo Li, Anping Wu, Zheng Chen, Jun Huang, Qingfeng Wang, and Feng Liu. 2024. "Multi-Step Physics-Informed Deep Operator Neural Network for Directly Solving Partial Differential Equations" Applied Sciences 14, no. 13: 5490. https://doi.org/10.3390/app14135490 Article Metrics Article access statistics, further information, mdpi initiatives, follow mdpi. Subscribe to receive issue release notifications and newsletters from MDPI journals Is Physics All There Is? There is more to the world than just matter and energy.. Posted June 22, 2024 | Reviewed by Abigail Fagan A recent interview with the well-known physicist Sean Carroll on “the physics of consciousness” gives us a great example of a reductive physicalist view of consciousness and the world around us. In it, Carroll acknowledges that things like cats, basketball games, and consciousness exist in so far as they are “useful categories” for us to talk about in order to make sense of our world. However, he does not think they are “fundamentally real.” Instead, he thinks only the laws of physics and the particles in the Standard Model are fundamentally real. Regarding consciousness, Carroll explains that he does not think “there's any special mental realm of existence…it's all the physical world.” Ever since the scientific enlightenment, philosophers and scientists have had a hard time obtaining the right model that aligns the insights of physics with human consciousness and the rest of the world. According to the Unified Theory of Knowledge, UTOK , this failure is called the Enlightenment Gap . It refers to our inability to generate a coherent understanding that places mind in relationship to matter and scientific knowing in relationship to subjective and social knowing. In the most recent Cognitive Science Show series, Transcendent Naturalism (TN), John Vervaeke and I lay out a new worldview that allows us to resolve the Enlightenment Gap. TN is grounded in a scientific-philosophical approach called Extended Naturalism. It provides us with a better, much more coherent ontology (i.e., theory of what is real) than reductive physicalism. (It also does a better job of making sense of the world than other alternatives, such as idealism or panpsychism, but that is for another post). A reductive physicalist ontology is “flat.” As captured by Sean Carroll's description, it only considers the bottom of the layers of nature to be truly real. As John Vervaeke demonstrates in his excellent talk at last year’s UTOK Consilience Conference, Leveling Up, there are many reasons why that a flat ontology is philosophically misguided. Here I will only focus on one key aspect, which shows why a flat ontology misconstrues “reality” for that which is continuous and most widely shared. Why might folks like Sean Carroll make the claim that only the bottom layer is real? Well, it is the case that the bottom level is the most generalizable. Consider, for example, that cats, consciousness, and stars are all made up of the particles and forces in the Standard Model of elementary particle physics. It is only a short step from this to saying this is the only layer that “really” exists. Unfortunately, however, there are two problems when you conflate that which is most generalizable with that which is fundamentally real. First, there is the problem of failing to complete the reduction. You see, if we follow what modern physics tells us, all the laws and particles and space and time ultimately collapse into a singular, energy-information superforce at the time of the Big Bang. That is, the particles and laws of physics emerge from a singular superforce in a way that parallels the way life and mind emerges from more basic arrangements. So, to be genuinely consistent on this front, Carroll would have to acknowledge that the the particles in the Standard Model and the laws associated with the fundamental forces are also “useful ways of talking” about an even more fundamental, singular superforce. To be consistent, he should have just said: “Everything is really just one thing, the same thing, the singular energy superforce that simultaneously is everything and causes everything to be. We can talk about things as being different because it is useful. That is, the Standard Theory of elementary particle physics, chemistry, biology, and psychology all give us useful categories, but they are not real in a fundamental way.” I am guessing that something feels off to you here. One obvious problem with it is that the claim doesn’t allow you to make sense of the world in any way. By collapsing everything into one singular thing, there is no intelligible way to understand reality. This point is a nice way of illustrating the error of equating that which is most generalizable with that which is fundamentally real. As John Vervaeke points out in his talk, to map the real world we need to understand both the generalizable similarities and the things that create differentiation. The differences are not illusions or epiphenomena, but they are part of the real world and have real ontological status. A common term for understanding differentiation is emergence. Extended naturalism gives us a coherent way for understanding emergence. Emergence does come up in the interview with Carroll. When asked about it, he gave the example that the fluidity of the air is an emergent property that is not associated with the specific molecules that make it up. This is what we call aggregate emergence ; however, it is only one kind of emergence, and it is the least interesting. As Tyler Volk and I note , there are (at least) two other kinds of emergence, and both have more ontological significance than aggregate emergence. A second kind of emergence is when parts come together to form a new, functional wholes. An example is when an electron and a proton combine to form a hydrogen atom. As Erik Hoel demonstrates in The World Behind the World: Consciousness, Free Will , and the Limits of Science , it has been mathematically shown that emergent wholes have unique properties and causal powers that cannot be reduced to the levels beneath them. Emergent naturalism identifies yet another kind of emergence, called “dimensional” emergence. This is when a new “plane of existence” is generated. Looking back on the history of the cosmos, four dimensions or planes of existence have emerged . First, the Matter-Object plane emerged out of the Energy-Information Implicate Order at the time of the Big Bang. Second, the Life-Organism plane emerged about 4 billion years ago. Third, the Mind-Animal Plane emerged at the time of the Cambrian Explosion, which was about half a billion years ago. And fourth, the Culture-Person plane emerged during the last half million years. Why are these different planes of existence? Because they are complex adaptive systems that are connected via novel information processing and communication networks that have real causal consequences that are not reducible to the fundamental laws of physics. These are complicated concepts. And, in the Carroll interview, it is not always clear exactly what is being conveyed. Thankfully, extended naturalism comes with a visual depiction called the Tree of Knowledge System. We can compare this to the picture of reality given by physical reductionism, which only sees aggregates of emergence and only considers the basement to be what is fundamentally real. To see if we really disagree, we need to check with Carroll to see which one of these representations align with his understanding. I bring this up because I have had folks who initially identify as reductive physicalists and look at the Tree of Knowledge and say it aligns with what they are trying to say. So, much of the misunderstanding might stem from us having an inadequate language to describe the territory rather than more fundamental disagreements about the nature of reality. The natural sciences have revealed that there is a deep ontological continuity that stretches from this current moment back to the energy-information singularity that started it all. However, this fundamental starting point is not the only thing that is real. Thankfully, via extended naturalism depicted by the ToK System, we now have a coherent, naturalistic ontology that specifies both how nature is continuous and how it is differentiated, and how we have obtained real scientific knowledge of us, the energy information superforce, and the reality in between. Gregg Henriques, Ph.D. , is a professor of psychology at James Madison University. Find a Therapist Find a Treatment Center Find a Psychiatrist Find a Support Group Find Online Therapy United States Brooklyn, NY Chicago, IL Houston, TX Los Angeles, CA New York, NY Portland, OR San Diego, CA San Francisco, CA Seattle, WA Washington, DC Asperger's Bipolar Disorder Chronic Pain Eating Disorders Passive Aggression Personality Goal Setting Positive Psychology Stopping Smoking Low Sexual Desire Relationships Child Development Self Tests NEW Therapy Center Diagnosis Dictionary Types of Therapy At any moment, someone’s aggravating behavior or our own bad luck can set us off on an emotional spiral that threatens to derail our entire day. Here’s how we can face our triggers with less reactivity so that we can get on with our lives. Emotional Intelligence Gaslighting Affective Forecasting Neuroscience 224 IMAGES Physics. Problem solving. 01_13 Physics. Problem solving. 01_01 🎉 How to solve physics problem. cupsoguepictures.com: How to Solve Physics Problems Problem Solving in Physics PPT SMBC VIDEO Lecture 11 Problem solving-Potential of a charged wire-1 Problem solving-Potential of a charged wire-2 Can you solve this popular electrostatic problem type comes in #jeeadvanced Physics of a YoYo Part II: Explained Lecture 3 |Example 1| Finding current and number of electrons COMMENTS 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. 1.7 Solving Problems in Physics 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. 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. 1.7 Solving Problems in Physics 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. 6.1 Solving Problems with Newton's Laws Success in problem solving is necessary to understand and apply physical principles. We developed a pattern of analyzing and setting up the solutions to problems involving Newton's laws in Newton's Laws of Motion; in this chapter, we continue to discuss these strategies and apply a step-by-step process.. Problem-Solving Strategies 1.4: Solving Physics Problems Trigonometry and Solving Physics Problems. In physics, most problems are solved much more easily when a free body diagram is used. Free body diagrams use geometry and vectors to visually represent the problem. Trigonometry is also used in determining the horizontal and vertical components of forces and objects. 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. PDF An Expert's Approach to Solving Physics Problems problems. Here is provided a problem from the fall 2016 Quantum Mechanics exam, and its solution. Alongside the solution are annotations related to the above Expert's Approach to problem solving. Problem: Consider the spin degrees of freedom of the proton and electron in a hydrogen atom. They are 4.6: Problem-Solving Strategies 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. How To Solve Physics Problems In force problems, isolate the appropriate components of the system and sketch a force diagram for them. Put a coordinate system on each diagram. Deduce the appropriate equations of motion. In other problems, cite the appropriate laws and relations, and justify the equations you deduce where necessary. Be certain that all symbols you use have ... Problem-Solving Strategies 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 ... PDF Introductory Physics: Problems solving This collection of physics problems solutions does not intend to cover the whole Introductory Physics course. Its purpose is to show the right way to solve physics problems. Here some useful tips. 1. Always try to find out what a problem is about, which part of the physics course is in question 2. Drawings are very helpful in most cases. Phy Phy simplifies the hardest concepts. 4. Snap it. 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. Solving Physics Problems Physics is a subject that requires extensive problem-solving skills. Staying organized and on track is very important to solve any problem correctly and efficiently. The acronym GUESS stands for: PDF Some Tips for Tackling Physics Problems Conversely, physics provides some of the best formal and practical training in logical and conceptual problem-solving more broadly. In cognitive or gestalt psychology, problem-solving refers to mental processes that people go through to recognize, analyze, evaluate, and solve problems. Art of Problem Solving Acoustics is the study of sound. Sound waves are mechanical waves - they travel by actual vibrations in some material medium. Acoustics concerns itself with mechanical waves in general. Phenomena such as forced vibrations, resonance, damped vibrations and the Doppler effect come under this branch of physics. PDF Cooperative Problem Solving in Physics A User's Manual Chapter 4. Building Physics into Problem Solving 37 What Is a Problem-solving Framework? 38 A Physics Example: The Competent Problem-solving Framework 40 Example of an "Ideal" Student's Problem Solution 44 Problem Solving as A Series of Translations 53 Initial Objections to Teaching a Problem-solving Framework 55 Chapter 5. Reinforcing ... Solving Problems in Physics Solving a physics problem usually breaks down into three stages: Design a strategy. Execute that strategy. Check the resulting answer. This document treats each of these three elements in turn, and concludes with a summary. PDF Teaching Physics Through Problem Solving 4.5 Basic principles behind all physics 4.5 General qualitative problem solving skills 4.4 General quantitative problem solving skills 4.2 Apply physics topics covered to new situations 4.2 Use with confidence Goals: Algebra-based Course (24 different majors) 4.7 Basic principles behind all physics 4.2 General qualitative problem solving skills Problem Solving in Physics Physics problem solving can be learned just like you learned to drive a car, play a musical instrument, or ride a bike. What can aid you more than anything is to have a general approach to follow with each problem you encounter. You may use different tools or tactics with differing areas of physics, but the overall strategy remains the same. PDF Physics Problem Solving Jennifer L. Docktor University of Minnesota Physics Problem Solving 2 Abstract Problem solving is viewed as a fundamental part of learning physics, and research to improve the teaching and learning of physics problem solving is a primary subfield of Physics Education Research (PER). A difficult question in this field has been how to measure problem solving performance. Projectile Problems with Solutions and Explanations Problem 8. The trajectory of a projectile launched from ground is given by the equation y = -0.025 x 2 + 0.5 x, where x and y are the coordinate of the projectile on a rectangular system of axes. a) Find the initial velocity and the angle at which the projectile is launched. Solution to Problem 8. How do they solve it? An insight into the learner's approach to the results show that problem solving ability need not emerge as a consequence of conceptual clarity alone [17-19]. Therefore, an explicit training in physics problem solving may help the student to acquire the skills needed. Also, establishment of a procedural framework for problem solving in physics requires a deeper understanding of the Clever Crows Showcase Physics Knowledge in Problem-Solving Tasks The story of a crow's problem-solving with pebbles and physics to raise water in a pitcher, famously depicted in Aesop's Fable, is more than a mere tale. New Study Shed Light Recent studies ... Problem Solving Problem solving is a crucial skill in both personal and professional settings. Whether it's addressing a personal challenge or drafting a business problem solving proposal, the ability to identify a problem and develop a solution is essential.Writing a problem solving essay helps articulate the issue clearly and systematically outline potential solutions. A Catalyst Framework for the Quantum Linear System Problem via the Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system problem (QLSP) in terms of the problem dimension, but even such a theoretical advantage is bottlenecked by the condition number of the coefficient matrix. In ... Helmholtz decomposition based windowed Green function methods for This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. Applied Sciences This paper establishes a method for solving partial differential equations using a multi-step physics-informed deep operator neural network. The network is trained by embedding physics-informed constraints. Different from traditional neural networks for solving partial differential equations, the proposed method uses a deep neural operator network to indirectly construct the mapping ... Is Physics All There Is? First, there is the problem of failing to complete the reduction. You see, if we follow what modern physics tells us, all the laws and particles and space and time ultimately collapse into a ... essay homework paper phd project resume review speech study thesis