• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
  • EDIT Edit this Article
  • EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
  • Browse Articles
  • Learn Something New
  • Quizzes Hot
  • This Or That Game New
  • Train Your Brain
  • Explore More
  • Support wikiHow
  • About wikiHow
  • Log in / Sign up
  • Education and Communications

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 319,017 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.

Step 1 Calm down.

  • 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

Community Answer

Video . By using this service, some information may be shared with YouTube.

  • 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 47
  • 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 114 Not Helpful 34

how to solve a physics problem

  • 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 24
  • If an instructor tells you to draw a free body diagram, be sure that that is exactly what you draw. Thanks Helpful 88 Not Helpful 24

Things You'll Need

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

You Might Also Like

Convert Kelvin to Fahrenheit or Celsius

Expert Interview

how to solve a physics problem

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/

About This Article

Sean Alexander, MS

  • Send fan mail to authors

Reader Success Stories

Aayush P.

Did this article help you?

Aayush P.

Monish Shetty

Sep 30, 2016

U. Pathum

Oct 9, 2017

Komal Verma

Komal Verma

Dec 6, 2017

Lowella Tabbert

Lowella Tabbert

Jun 7, 2022

Am I a Narcissist or an Empath Quiz

Featured Articles

Apply for a Blue Badge

Trending Articles

Make a Snowman

Watch Articles

Clean a Laptop

  • Terms of Use
  • Privacy Policy
  • Do Not Sell or Share My Info
  • Not Selling Info

wikiHow Tech Help Pro:

Develop the tech skills you need for work and life

  • 6.1 Solving Problems with Newton’s Laws
  • Introduction
  • 1.1 The Scope and Scale of Physics
  • 1.2 Units and Standards
  • 1.3 Unit Conversion
  • 1.4 Dimensional Analysis
  • 1.5 Estimates and Fermi Calculations
  • 1.6 Significant Figures
  • 1.7 Solving Problems in Physics
  • Key Equations
  • Conceptual Questions
  • Additional Problems
  • Challenge Problems
  • 2.1 Scalars and Vectors
  • 2.2 Coordinate Systems and Components of a Vector
  • 2.3 Algebra of Vectors
  • 2.4 Products of Vectors
  • 3.1 Position, Displacement, and Average Velocity
  • 3.2 Instantaneous Velocity and Speed
  • 3.3 Average and Instantaneous Acceleration
  • 3.4 Motion with Constant Acceleration
  • 3.5 Free Fall
  • 3.6 Finding Velocity and Displacement from Acceleration
  • 4.1 Displacement and Velocity Vectors
  • 4.2 Acceleration Vector
  • 4.3 Projectile Motion
  • 4.4 Uniform Circular Motion
  • 4.5 Relative Motion in One and Two Dimensions
  • 5.2 Newton's First Law
  • 5.3 Newton's Second Law
  • 5.4 Mass and Weight
  • 5.5 Newton’s Third Law
  • 5.6 Common Forces
  • 5.7 Drawing Free-Body Diagrams
  • 6.2 Friction
  • 6.3 Centripetal Force
  • 6.4 Drag Force and Terminal Speed
  • 7.2 Kinetic Energy
  • 7.3 Work-Energy Theorem
  • 8.1 Potential Energy of a System
  • 8.2 Conservative and Non-Conservative Forces
  • 8.3 Conservation of Energy
  • 8.4 Potential Energy Diagrams and Stability
  • 8.5 Sources of Energy
  • 9.1 Linear Momentum
  • 9.2 Impulse and Collisions
  • 9.3 Conservation of Linear Momentum
  • 9.4 Types of Collisions
  • 9.5 Collisions in Multiple Dimensions
  • 9.6 Center of Mass
  • 9.7 Rocket Propulsion
  • 10.1 Rotational Variables
  • 10.2 Rotation with Constant Angular Acceleration
  • 10.3 Relating Angular and Translational Quantities
  • 10.4 Moment of Inertia and Rotational Kinetic Energy
  • 10.5 Calculating Moments of Inertia
  • 10.6 Torque
  • 10.7 Newton’s Second Law for Rotation
  • 10.8 Work and Power for Rotational Motion
  • 11.1 Rolling Motion
  • 11.2 Angular Momentum
  • 11.3 Conservation of Angular Momentum
  • 11.4 Precession of a Gyroscope
  • 12.1 Conditions for Static Equilibrium
  • 12.2 Examples of Static Equilibrium
  • 12.3 Stress, Strain, and Elastic Modulus
  • 12.4 Elasticity and Plasticity
  • 13.1 Newton's Law of Universal Gravitation
  • 13.2 Gravitation Near Earth's Surface
  • 13.3 Gravitational Potential Energy and Total Energy
  • 13.4 Satellite Orbits and Energy
  • 13.5 Kepler's Laws of Planetary Motion
  • 13.6 Tidal Forces
  • 13.7 Einstein's Theory of Gravity
  • 14.1 Fluids, Density, and Pressure
  • 14.2 Measuring Pressure
  • 14.3 Pascal's Principle and Hydraulics
  • 14.4 Archimedes’ Principle and Buoyancy
  • 14.5 Fluid Dynamics
  • 14.6 Bernoulli’s Equation
  • 14.7 Viscosity and Turbulence
  • 15.1 Simple Harmonic Motion
  • 15.2 Energy in Simple Harmonic Motion
  • 15.3 Comparing Simple Harmonic Motion and Circular Motion
  • 15.4 Pendulums
  • 15.5 Damped Oscillations
  • 15.6 Forced Oscillations
  • 16.1 Traveling Waves
  • 16.2 Mathematics of Waves
  • 16.3 Wave Speed on a Stretched String
  • 16.4 Energy and Power of a Wave
  • 16.5 Interference of Waves
  • 16.6 Standing Waves and Resonance
  • 17.1 Sound Waves
  • 17.2 Speed of Sound
  • 17.3 Sound Intensity
  • 17.4 Normal Modes of a Standing Sound Wave
  • 17.5 Sources of Musical Sound
  • 17.7 The Doppler Effect
  • 17.8 Shock Waves
  • B | Conversion Factors
  • C | Fundamental Constants
  • D | Astronomical Data
  • E | Mathematical Formulas
  • F | Chemistry
  • G | The Greek Alphabet

Learning Objectives

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

  • Apply problem-solving techniques to solve for quantities in more complex systems of forces
  • Use concepts from kinematics to solve problems using Newton’s laws of motion
  • Solve more complex equilibrium problems
  • Solve more complex acceleration problems
  • Apply calculus to more advanced dynamics problems

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

We follow here the basics of problem solving presented earlier in this text, but we emphasize specific strategies that are useful in applying Newton’s laws of motion . Once you identify the physical principles involved in the problem and determine that they include Newton’s laws of motion, you can apply these steps to find a solution. 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, so the following techniques should reinforce skills you have already begun to develop.

Problem-Solving Strategy

Applying newton’s laws of motion.

  • Identify the physical principles involved by listing the givens and the quantities to be calculated.
  • Sketch the situation, using arrows to represent all forces.
  • Determine the system of interest. The result is a free-body diagram that is essential to solving the problem.
  • Apply Newton’s second law to solve the problem. If necessary, apply appropriate kinematic equations from the chapter on motion along a straight line.
  • Check the solution to see whether it is reasonable.

Let’s apply this problem-solving strategy to the challenge of lifting a grand piano into a second-story apartment. Once we have 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 6.2 (a). Then, as in Figure 6.2 (b), we can represent all forces with arrows. Whenever sufficient information exists, it is best to label these arrows carefully and make the length and direction of each correspond to the represented force.

As with most problems, we next need to 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. It is particularly crucial to identify the system of interest, since Newton’s second law involves only external forces. We can then determine which forces are external and which are internal, a necessary step to employ Newton’s second law. (See Figure 6.2 (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 in Newton’s Laws of Motion , the system of interest depends on the question we need to answer. Only forces are shown in free-body diagrams, not acceleration or velocity. We have drawn several free-body diagrams in previous worked examples. Figure 6.2 (c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.

Once a free-body diagram is drawn, we apply Newton’s second law. This is done in Figure 6.2 (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 the forces can be handled algebraically. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. We do this 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. Generally, just write Newton’s second law in components along the different directions. Then, you have the following equations:

(If, for example, the system is accelerating horizontally, then you can then set a y = 0 . a y = 0 . ) We need this information to determine unknown forces acting on a system.

As always, we must check the solution. In some cases, it is easy to tell whether the solution is reasonable. 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; with experience, it becomes progressively easier to judge whether an answer is reasonable. Another way to check a solution is to check the units. If we are solving for force and end up with units of millimeters per second, then we have made a mistake.

There are many interesting applications of Newton’s laws of motion, a few more of which are presented in this section. These serve also to illustrate some further subtleties of physics and to help build problem-solving skills. We look first at problems involving particle equilibrium, which make use of Newton’s first law, and then consider particle acceleration, which involves Newton’s second law.

Particle Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration, but it is important to remember that these conditions are relative. For example, an object may be at rest when viewed from our frame of reference, but the same object would appear to be in motion when viewed by someone moving at a constant velocity. We now make use of the knowledge attained in Newton’s Laws of Motion , regarding the different types of forces and the use of free-body diagrams, to solve additional problems in particle equilibrium .

Example 6.1

Different tensions at different angles.

Thus, as you might expect,

This gives us the following relationship:

Note that T 1 T 1 and T 2 T 2 are not equal in this case because the angles on either side are not equal. It is reasonable that T 2 T 2 ends up being greater than T 1 T 1 because it is exerted more vertically than T 1 . T 1 .

Now consider the force components along the vertical or y -axis:

This implies

Substituting the expressions for the vertical components gives

There are two unknowns in this equation, but substituting the expression for T 2 T 2 in terms of T 1 T 1 reduces this to one equation with one unknown:

which yields

Solving this last equation gives the magnitude of T 1 T 1 to be

Finally, we find the magnitude of T 2 T 2 by using the relationship between them, T 2 = 1.225 T 1 T 2 = 1.225 T 1 , found above. Thus we obtain

Significance

Particle acceleration.

We have given a variety of examples of particles in equilibrium. We now turn our attention to particle acceleration problems, which are the result of a nonzero net force. Refer again to the steps given at the beginning of this section, and notice how they are applied to the following examples.

Example 6.2

Drag force on a barge.

The drag of the water F → D F → D is in the direction opposite to the direction of motion of the boat; this force thus works against F → app , F → app , as shown in the free-body diagram in Figure 6.4 (b). The system of interest here is the barge, since the forces on it are given as well as its acceleration. Because the applied forces are perpendicular, the x - and y -axes are in the same direction as F → 1 F → 1 and F → 2 . F → 2 . The problem quickly becomes a one-dimensional problem along the direction of F → app F → app , since friction is in the direction opposite to F → app . F → app . Our strategy is to find the magnitude and direction of the net applied force F → app F → app and then apply Newton’s second law to solve for the drag force F → D . F → D .

The angle is given by

From Newton’s first law, we know this is the same direction as the acceleration. We also know that F → D F → D is in the opposite direction of F → app , F → app , since it acts to slow down the acceleration. Therefore, the net external force is in the same direction as F → app , F → app , but its magnitude is slightly less than F → app . F → app . The problem is now one-dimensional. From the free-body diagram, we can see that

However, Newton’s second law states that

This can be solved for the magnitude of the drag force of the water F D F D in terms of known quantities:

Substituting known values gives

The direction of F → D F → D has already been determined to be in the direction opposite to F → app , F → app , or at an angle of 53 ° 53 ° south of west.

In Newton’s Laws of Motion , we discussed the normal force , which is a contact force that acts normal to the surface so that an object does not have an acceleration perpendicular to the surface. The bathroom scale is an excellent example of a normal force acting on a body. It provides a quantitative reading of how much it must push upward to support the weight of an object. But can you predict what you would see on the dial of a bathroom scale if you stood on it during an elevator ride? Will you see a value greater than your weight when the elevator starts up? What about when the elevator moves upward at a constant speed? Take a guess before reading the next example.

Example 6.3

What does the bathroom scale read in an elevator.

From the free-body diagram, we see that F → net = F → s − w → , F → net = F → s − w → , so we have

Solving for F s F s gives us an equation with only one unknown:

or, because w = m g , w = m g , simply

No assumptions were made about the acceleration, so this solution should be valid for a variety of accelerations in addition to those in this situation. ( Note: We are considering the case when the elevator is accelerating upward. If the elevator is accelerating downward, Newton’s second law becomes F s − w = − m a . F s − w = − m a . )

  • We have a = 1.20 m/s 2 , a = 1.20 m/s 2 , so that F s = ( 75.0 kg ) ( 9.80 m/s 2 ) + ( 75.0 kg ) ( 1.20 m/s 2 ) F s = ( 75.0 kg ) ( 9.80 m/s 2 ) + ( 75.0 kg ) ( 1.20 m/s 2 ) yielding F s = 825 N . F s = 825 N .
  • Now, what happens when the elevator reaches a constant upward velocity? Will the scale still read more than his weight? For any constant velocity—up, down, or stationary—acceleration is zero because a = Δ v Δ t a = Δ v Δ t and Δ v = 0 . Δ v = 0 . Thus, F s = m a + m g = 0 + m g F s = m a + m g = 0 + m g or F s = ( 75.0 kg ) ( 9.80 m/s 2 ) , F s = ( 75.0 kg ) ( 9.80 m/s 2 ) , which gives F s = 735 N . F s = 735 N .

Thus, the scale reading in the elevator is greater than his 735-N (165-lb.) weight. This means that the scale is pushing up on the person with a force greater than his weight, as it must in order to accelerate him upward. Clearly, the greater the acceleration of the elevator, the greater the scale reading, consistent with what you feel in rapidly accelerating versus slowly accelerating elevators. In Figure 6.5 (b), the scale reading is 735 N, which equals the person’s weight. This is the case whenever the elevator has a constant velocity—moving up, moving down, or stationary.

Check Your Understanding 6.1

Now calculate the scale reading when the elevator accelerates downward at a rate of 1.20 m/s 2 . 1.20 m/s 2 .

The solution to the previous example also applies to an elevator accelerating downward, as mentioned. When an elevator accelerates downward, a is negative, and the scale reading is less than the weight of the person. If a constant downward velocity is reached, the scale reading again becomes equal to the person’s weight. If the elevator is in free fall and accelerating downward at g , then the scale reading is zero and the person appears to be weightless.

Example 6.4

Two attached blocks.

For block 1: T → + w → 1 + N → = m 1 a → 1 T → + w → 1 + N → = m 1 a → 1

For block 2: T → + w → 2 = m 2 a → 2 . T → + w → 2 = m 2 a → 2 .

Notice that T → T → is the same for both blocks. Since the string and the pulley have negligible mass, and since there is no friction in the pulley, the tension is the same throughout the string. We can now write component equations for each block. All forces are either horizontal or vertical, so we can use the same horizontal/vertical coordinate system for both objects

When block 1 moves to the right, block 2 travels an equal distance downward; thus, a 1 x = − a 2 y . a 1 x = − a 2 y . Writing the common acceleration of the blocks as a = a 1 x = − a 2 y , a = a 1 x = − a 2 y , we now have

From these two equations, we can express a and T in terms of the masses m 1 and m 2 , and g : m 1 and m 2 , and g :

Check Your Understanding 6.2

Calculate the acceleration of the system, and the tension in the string, when the masses are m 1 = 5.00 kg m 1 = 5.00 kg and m 2 = 3.00 kg . m 2 = 3.00 kg .

Example 6.5

Atwood machine.

  • We have For m 1 , ∑ F y = T − m 1 g = m 1 a . For m 2 , ∑ F y = T − m 2 g = − m 2 a . For m 1 , ∑ F y = T − m 1 g = m 1 a . For m 2 , ∑ F y = T − m 2 g = − m 2 a . (The negative sign in front of m 2 a m 2 a indicates that m 2 m 2 accelerates downward; both blocks accelerate at the same rate, but in opposite directions.) Solve the two equations simultaneously (subtract them) and the result is ( m 2 − m 1 ) g = ( m 1 + m 2 ) a . ( m 2 − m 1 ) g = ( m 1 + m 2 ) a . Solving for a : a = m 2 − m 1 m 1 + m 2 g = 4 kg − 2 kg 4 kg + 2 kg ( 9.8 m/s 2 ) = 3.27 m/s 2 . a = m 2 − m 1 m 1 + m 2 g = 4 kg − 2 kg 4 kg + 2 kg ( 9.8 m/s 2 ) = 3.27 m/s 2 .
  • Observing the first block, we see that T − m 1 g = m 1 a T = m 1 ( g + a ) = ( 2 kg ) ( 9.8 m/s 2 + 3.27 m/s 2 ) = 26.1 N . T − m 1 g = m 1 a T = m 1 ( g + a ) = ( 2 kg ) ( 9.8 m/s 2 + 3.27 m/s 2 ) = 26.1 N .

Check Your Understanding 6.3

Determine a general formula in terms of m 1 , m 2 m 1 , m 2 and g for calculating the tension in the string for the Atwood machine shown above.

Newton’s Laws of Motion and Kinematics

Physics is most interesting and most powerful when applied to general situations that involve more than a narrow set of physical principles. Newton’s laws of motion can also be integrated with other concepts that have been discussed previously in this text to solve problems of motion. For example, forces produce accelerations, a topic of kinematics , and hence the relevance of earlier chapters.

When approaching problems that involve various types of forces, acceleration, velocity, and/or position, listing the givens and the quantities to be calculated will allow you to identify the principles involved. Then, you can refer to the chapters that deal with a particular topic and solve the problem using strategies outlined in the text. The following worked example illustrates how the problem-solving strategy given earlier in this chapter, as well as strategies presented in other chapters, is applied to an integrated concept problem.

Example 6.6

What force must a soccer player exert to reach top speed.

  • We are given the initial and final velocities (zero and 8.00 m/s forward); thus, the change in velocity is Δ v = 8.00 m/s Δ v = 8.00 m/s . We are given the elapsed time, so Δ t = 2.50 s . Δ t = 2.50 s . The unknown is acceleration, which can be found from its definition: a = Δ v Δ t . a = Δ v Δ t . Substituting the known values yields a = 8.00 m/s 2.50 s = 3.20 m/s 2 . a = 8.00 m/s 2.50 s = 3.20 m/s 2 .
  • Here we are asked to find the average force the ground exerts on the runner to produce this acceleration. (Remember that we are dealing with the force or forces acting on the object of interest.) This is the reaction force to that exerted by the player backward against the ground, by Newton’s third law. Neglecting air resistance, this would be equal in magnitude to the net external force on the player, since this force causes her acceleration. Since we now know the player’s acceleration and are given her mass, we can use Newton’s second law to find the force exerted. That is, F net = m a . F net = m a . Substituting the known values of m and a gives F net = ( 70.0 kg ) ( 3.20 m/s 2 ) = 224 N . F net = ( 70.0 kg ) ( 3.20 m/s 2 ) = 224 N .

This is a reasonable result: The acceleration is attainable for an athlete in good condition. The force is about 50 pounds, a reasonable average force.

Check Your Understanding 6.4

The soccer player stops after completing the play described above, but now notices that the ball is in position to be stolen. If she now experiences a force of 126 N to attempt to steal the ball, which is 2.00 m away from her, how long will it take her to get to the ball?

Example 6.7

What force acts on a model helicopter.

The magnitude of the force is now easily found:

Check Your Understanding 6.5

Find the direction of the resultant for the 1.50-kg model helicopter.

Example 6.8

Baggage tractor.

  • ∑ F x = m system a x ∑ F x = m system a x and ∑ F x = 820.0 t , ∑ F x = 820.0 t , so 820.0 t = ( 650.0 + 250.0 + 150.0 ) a a = 0.7809 t . 820.0 t = ( 650.0 + 250.0 + 150.0 ) a a = 0.7809 t . Since acceleration is a function of time, we can determine the velocity of the tractor by using a = d v d t a = d v d t with the initial condition that v 0 = 0 v 0 = 0 at t = 0 . t = 0 . We integrate from t = 0 t = 0 to t = 3 : t = 3 : d v = a d t , ∫ 0 3 d v = ∫ 0 3.00 a d t = ∫ 0 3.00 0.7809 t d t , v = 0.3905 t 2 ] 0 3.00 = 3.51 m/s . d v = a d t , ∫ 0 3 d v = ∫ 0 3.00 a d t = ∫ 0 3.00 0.7809 t d t , v = 0.3905 t 2 ] 0 3.00 = 3.51 m/s .
  • Refer to the free-body diagram in Figure 6.8 (b). ∑ F x = m tractor a x 820.0 t − T = m tractor ( 0.7805 ) t ( 820.0 ) ( 3.00 ) − T = ( 650.0 ) ( 0.7805 ) ( 3.00 ) T = 938 N . ∑ F x = m tractor a x 820.0 t − T = m tractor ( 0.7805 ) t ( 820.0 ) ( 3.00 ) − T = ( 650.0 ) ( 0.7805 ) ( 3.00 ) T = 938 N .

Recall that v = d s d t v = d s d t and a = d v d t a = d v d t . If acceleration is a function of time, we can use the calculus forms developed in Motion Along a Straight Line , as shown in this example. However, sometimes acceleration is a function of displacement. In this case, we can derive an important result from these calculus relations. Solving for dt in each, we have d t = d s v d t = d s v and d t = d v a . d t = d v a . Now, equating these expressions, we have d s v = d v a . d s v = d v a . We can rearrange this to obtain a d s = v d v . a d s = v d v .

Example 6.9

Motion of a projectile fired vertically.

The acceleration depends on v and is therefore variable. Since a = f ( v ) , a = f ( v ) , we can relate a to v using the rearrangement described above,

We replace ds with dy because we are dealing with the vertical direction,

We now separate the variables ( v ’s and dv ’s on one side; dy on the other):

Thus, h = 114 m . h = 114 m .

Check Your Understanding 6.6

If atmospheric resistance is neglected, find the maximum height for the mortar shell. Is calculus required for this solution?

Interactive

Explore the forces at work in this simulation when you try to push a filing cabinet. Create an applied force and see the resulting frictional force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a free-body diagram of all the forces (including gravitational and normal forces).

As an Amazon Associate we earn from qualifying purchases.

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

Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
  • Authors: William Moebs, Samuel J. Ling, Jeff Sanny
  • Publisher/website: OpenStax
  • Book title: University Physics Volume 1
  • Publication date: Sep 19, 2016
  • Location: Houston, Texas
  • Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
  • Section URL: https://openstax.org/books/university-physics-volume-1/pages/6-1-solving-problems-with-newtons-laws

© Jul 21, 2023 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Back Home

  • Science Notes Posts
  • Contact Science Notes
  • Todd Helmenstine Biography
  • Anne Helmenstine Biography
  • Free Printable Periodic Tables (PDF and PNG)
  • Periodic Table Wallpapers
  • Interactive Periodic Table
  • Periodic Table Posters
  • How to Grow Crystals
  • Chemistry Projects
  • Fire and Flames Projects
  • Holiday Science
  • Chemistry Problems With Answers
  • Physics Problems
  • Unit Conversion Example Problems
  • Chemistry Worksheets
  • Biology Worksheets
  • Periodic Table Worksheets
  • Physical Science Worksheets
  • Science Lab Worksheets
  • My Amazon Books

Example Physics Problems and Solutions

Equilibrium Example Problem 1

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.

well drop setup illustration

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

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 Cat 1

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

Atwood Machine

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

friction slide setup

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

Desktop Momentum Balls Toy

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

how to solve a physics problem

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

Hooke's Law Forces

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.

How To Solve Physics Problems

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? 

Solver Title

Practice

Generating PDF...

  • Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics
  • Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
  • Pre Calculus Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
  • Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
  • Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
  • Linear Algebra Matrices Vectors
  • Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
  • Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
  • Physics Mechanics
  • Chemistry Chemical Reactions Chemical Properties
  • Finance Simple Interest Compound Interest Present Value Future Value
  • Economics Point of Diminishing Return
  • Conversions Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time
  • Pre Algebra
  • Pre Calculus
  • Linear Algebra
  • Trigonometry
  • Conversions

Click to reveal more operations

Most Used Actions

Number line.

  • x^{2}-x-6=0
  • -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))
  • \int e^x\cos (x)dx
  • \int_{0}^{\pi}\sin(x)dx
  • \sum_{n=0}^{\infty}\frac{3}{2^n}
  • Is there a step by step calculator for math?
  • Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.
  • Is there a step by step calculator for physics?
  • Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go.
  • How to solve math problems step-by-step?
  • To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.
  • Practice, practice, practice Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing... Read More

Please add a message.

Message received. Thanks for the feedback.

Isaac Physics Logo

Isaac Physics

You need to enable JavaScript to access Isaac Physics.

Youtube

  • TPC and eLearning
  • Read Watch Interact
  • What's NEW at TPC?
  • Practice Review Test
  • Teacher-Tools
  • Subscription Selection
  • Seat Calculator
  • Ad Free Account
  • Edit Profile Settings
  • Student Progress Edit
  • Task Properties
  • Export Student Progress
  • Task, Activities, and Scores
  • Metric Conversions Questions
  • Metric System Questions
  • Metric Estimation Questions
  • Significant Digits Questions
  • Proportional Reasoning
  • Acceleration
  • Distance-Displacement
  • Dots and Graphs
  • Graph That Motion
  • Match That Graph
  • Name That Motion
  • Motion Diagrams
  • Pos'n Time Graphs Numerical
  • Pos'n Time Graphs Conceptual
  • Up And Down - Questions
  • Balanced vs. Unbalanced Forces
  • Change of State
  • Force and Motion
  • Mass and Weight
  • Match That Free-Body Diagram
  • Net Force (and Acceleration) Ranking Tasks
  • Newton's Second Law
  • Normal Force Card Sort
  • Recognizing Forces
  • Air Resistance and Skydiving
  • Solve It! with Newton's Second Law
  • Which One Doesn't Belong?
  • Component Addition Questions
  • Head-to-Tail Vector Addition
  • Projectile Mathematics
  • Trajectory - Angle Launched Projectiles
  • Trajectory - Horizontally Launched Projectiles
  • Vector Addition
  • Vector Direction
  • Which One Doesn't Belong? Projectile Motion
  • Forces in 2-Dimensions
  • Being Impulsive About Momentum
  • Explosions - Law Breakers
  • Hit and Stick Collisions - Law Breakers
  • Case Studies: Impulse and Force
  • Impulse-Momentum Change Table
  • Keeping Track of Momentum - Hit and Stick
  • Keeping Track of Momentum - Hit and Bounce
  • What's Up (and Down) with KE and PE?
  • Energy Conservation Questions
  • Energy Dissipation Questions
  • Energy Ranking Tasks
  • LOL Charts (a.k.a., Energy Bar Charts)
  • Match That Bar Chart
  • Words and Charts Questions
  • Name That Energy
  • Stepping Up with PE and KE Questions
  • Case Studies - Circular Motion
  • Circular Logic
  • Forces and Free-Body Diagrams in Circular Motion
  • Gravitational Field Strength
  • Universal Gravitation
  • Angular Position and Displacement
  • Linear and Angular Velocity
  • Angular Acceleration
  • Rotational Inertia
  • Balanced vs. Unbalanced Torques
  • Getting a Handle on Torque
  • Torque-ing About Rotation
  • Balloon Interactions
  • Charge and Charging
  • Charge Interactions
  • Charging by Induction
  • Conductors and Insulators
  • Coulombs Law
  • Electric Field
  • Electric Field Intensity
  • Polarization
  • Case Studies: Electric Power
  • Know Your Potential
  • Light Bulb Anatomy
  • I = ∆V/R Equations as a Guide to Thinking
  • Parallel Circuits - ∆V = I•R Calculations
  • Resistance Ranking Tasks
  • Series Circuits - ∆V = I•R Calculations
  • Series vs. Parallel Circuits
  • Equivalent Resistance
  • Period and Frequency of a Pendulum
  • Pendulum Motion: Velocity and Force
  • Energy of a Pendulum
  • Period and Frequency of a Mass on a Spring
  • Horizontal Springs: Velocity and Force
  • Vertical Springs: Velocity and Force
  • Energy of a Mass on a Spring
  • Decibel Scale
  • Frequency and Period
  • Closed-End Air Columns
  • Name That Harmonic: Strings
  • Rocking the Boat
  • Wave Basics
  • Matching Pairs: Wave Characteristics
  • Wave Interference
  • Waves - Case Studies
  • Color Addition and Subtraction
  • Color Filters
  • If This, Then That: Color Subtraction
  • Light Intensity
  • Color Pigments
  • Converging Lenses
  • Curved Mirror Images
  • Law of Reflection
  • Refraction and Lenses
  • Total Internal Reflection
  • Who Can See Who?
  • Formulas and Atom Counting
  • Atomic Models
  • Bond Polarity
  • Entropy Questions
  • Cell Voltage Questions
  • Heat of Formation Questions
  • Reduction Potential Questions
  • Oxidation States Questions
  • Measuring the Quantity of Heat
  • Hess's Law
  • Oxidation-Reduction Questions
  • Galvanic Cells Questions
  • Thermal Stoichiometry
  • Molecular Polarity
  • Quantum Mechanics
  • Balancing Chemical Equations
  • Bronsted-Lowry Model of Acids and Bases
  • Classification of Matter
  • Collision Model of Reaction Rates
  • Density Ranking Tasks
  • Dissociation Reactions
  • Complete Electron Configurations
  • Enthalpy Change Questions
  • Equilibrium Concept
  • Equilibrium Constant Expression
  • Equilibrium Calculations - Questions
  • Equilibrium ICE Table
  • Ionic Bonding
  • Lewis Electron Dot Structures
  • Line Spectra Questions
  • Measurement and Numbers
  • Metals, Nonmetals, and Metalloids
  • Metric Estimations
  • Metric System
  • Molarity Ranking Tasks
  • Mole Conversions
  • Name That Element
  • Names to Formulas
  • Names to Formulas 2
  • Nuclear Decay
  • Particles, Words, and Formulas
  • Periodic Trends
  • Precipitation Reactions and Net Ionic Equations
  • Pressure Concepts
  • Pressure-Temperature Gas Law
  • Pressure-Volume Gas Law
  • Chemical Reaction Types
  • Significant Digits and Measurement
  • States Of Matter Exercise
  • Stoichiometry - Math Relationships
  • Subatomic Particles
  • Spontaneity and Driving Forces
  • Gibbs Free Energy
  • Volume-Temperature Gas Law
  • Acid-Base Properties
  • Energy and Chemical Reactions
  • Chemical and Physical Properties
  • Valence Shell Electron Pair Repulsion Theory
  • Writing Balanced Chemical Equations
  • Mission CG1
  • Mission CG10
  • Mission CG2
  • Mission CG3
  • Mission CG4
  • Mission CG5
  • Mission CG6
  • Mission CG7
  • Mission CG8
  • Mission CG9
  • Mission EC1
  • Mission EC10
  • Mission EC11
  • Mission EC12
  • Mission EC2
  • Mission EC3
  • Mission EC4
  • Mission EC5
  • Mission EC6
  • Mission EC7
  • Mission EC8
  • Mission EC9
  • Mission RL1
  • Mission RL2
  • Mission RL3
  • Mission RL4
  • Mission RL5
  • Mission RL6
  • Mission KG7
  • Mission RL8
  • Mission KG9
  • Mission RL10
  • Mission RL11
  • Mission RM1
  • Mission RM2
  • Mission RM3
  • Mission RM4
  • Mission RM5
  • Mission RM6
  • Mission RM8
  • Mission RM10
  • Mission LC1
  • Mission RM11
  • Mission LC2
  • Mission LC3
  • Mission LC4
  • Mission LC5
  • Mission LC6
  • Mission LC8
  • Mission SM1
  • Mission SM2
  • Mission SM3
  • Mission SM4
  • Mission SM5
  • Mission SM6
  • Mission SM8
  • Mission SM10
  • Mission KG10
  • Mission SM11
  • Mission KG2
  • Mission KG3
  • Mission KG4
  • Mission KG5
  • Mission KG6
  • Mission KG8
  • Mission KG11
  • Mission F2D1
  • Mission F2D2
  • Mission F2D3
  • Mission F2D4
  • Mission F2D5
  • Mission F2D6
  • Mission KC1
  • Mission KC2
  • Mission KC3
  • Mission KC4
  • Mission KC5
  • Mission KC6
  • Mission KC7
  • Mission KC8
  • Mission AAA
  • Mission SM9
  • Mission LC7
  • Mission LC9
  • Mission NL1
  • Mission NL2
  • Mission NL3
  • Mission NL4
  • Mission NL5
  • Mission NL6
  • Mission NL7
  • Mission NL8
  • Mission NL9
  • Mission NL10
  • Mission NL11
  • Mission NL12
  • Mission MC1
  • Mission MC10
  • Mission MC2
  • Mission MC3
  • Mission MC4
  • Mission MC5
  • Mission MC6
  • Mission MC7
  • Mission MC8
  • Mission MC9
  • Mission RM7
  • Mission RM9
  • Mission RL7
  • Mission RL9
  • Mission SM7
  • Mission SE1
  • Mission SE10
  • Mission SE11
  • Mission SE12
  • Mission SE2
  • Mission SE3
  • Mission SE4
  • Mission SE5
  • Mission SE6
  • Mission SE7
  • Mission SE8
  • Mission SE9
  • Mission VP1
  • Mission VP10
  • Mission VP2
  • Mission VP3
  • Mission VP4
  • Mission VP5
  • Mission VP6
  • Mission VP7
  • Mission VP8
  • Mission VP9
  • Mission WM1
  • Mission WM2
  • Mission WM3
  • Mission WM4
  • Mission WM5
  • Mission WM6
  • Mission WM7
  • Mission WM8
  • Mission WE1
  • Mission WE10
  • Mission WE2
  • Mission WE3
  • Mission WE4
  • Mission WE5
  • Mission WE6
  • Mission WE7
  • Mission WE8
  • Mission WE9
  • Vector Walk Interactive
  • Name That Motion Interactive
  • Kinematic Graphing 1 Concept Checker
  • Kinematic Graphing 2 Concept Checker
  • Graph That Motion Interactive
  • Rocket Sled Concept Checker
  • Force Concept Checker
  • Free-Body Diagrams Concept Checker
  • Free-Body Diagrams The Sequel Concept Checker
  • Skydiving Concept Checker
  • Elevator Ride Concept Checker
  • Vector Addition Concept Checker
  • Vector Walk in Two Dimensions Interactive
  • Name That Vector Interactive
  • River Boat Simulator Concept Checker
  • Projectile Simulator 2 Concept Checker
  • Projectile Simulator 3 Concept Checker
  • Turd the Target 1 Interactive
  • Turd the Target 2 Interactive
  • Balance It Interactive
  • Go For The Gold Interactive
  • Egg Drop Concept Checker
  • Fish Catch Concept Checker
  • Exploding Carts Concept Checker
  • Collision Carts - Inelastic Collisions Concept Checker
  • Its All Uphill Concept Checker
  • Stopping Distance Concept Checker
  • Chart That Motion Interactive
  • Roller Coaster Model Concept Checker
  • Uniform Circular Motion Concept Checker
  • Horizontal Circle Simulation Concept Checker
  • Vertical Circle Simulation Concept Checker
  • Race Track Concept Checker
  • Gravitational Fields Concept Checker
  • Orbital Motion Concept Checker
  • Balance Beam Concept Checker
  • Torque Balancer Concept Checker
  • Aluminum Can Polarization Concept Checker
  • Charging Concept Checker
  • Name That Charge Simulation
  • Coulomb's Law Concept Checker
  • Electric Field Lines Concept Checker
  • Put the Charge in the Goal Concept Checker
  • Circuit Builder Concept Checker (Series Circuits)
  • Circuit Builder Concept Checker (Parallel Circuits)
  • Circuit Builder Concept Checker (∆V-I-R)
  • Circuit Builder Concept Checker (Voltage Drop)
  • Equivalent Resistance Interactive
  • Pendulum Motion Simulation Concept Checker
  • Mass on a Spring Simulation Concept Checker
  • Particle Wave Simulation Concept Checker
  • Boundary Behavior Simulation Concept Checker
  • Slinky Wave Simulator Concept Checker
  • Simple Wave Simulator Concept Checker
  • Wave Addition Simulation Concept Checker
  • Standing Wave Maker Simulation Concept Checker
  • Color Addition Concept Checker
  • Painting With CMY Concept Checker
  • Stage Lighting Concept Checker
  • Filtering Away Concept Checker
  • Young's Experiment Interactive
  • Plane Mirror Images Interactive
  • Who Can See Who Concept Checker
  • Optics Bench (Mirrors) Concept Checker
  • Name That Image (Mirrors) Interactive
  • Refraction Concept Checker
  • Total Internal Reflection Concept Checker
  • Optics Bench (Lenses) Concept Checker
  • Kinematics Preview
  • Velocity Time Graphs Preview
  • Moving Cart on an Inclined Plane Preview
  • Stopping Distance Preview
  • Cart, Bricks, and Bands Preview
  • Fan Cart Study Preview
  • Friction Preview
  • Coffee Filter Lab Preview
  • Friction, Speed, and Stopping Distance Preview
  • Up and Down Preview
  • Projectile Range Preview
  • Ballistics Preview
  • Juggling Preview
  • Marshmallow Launcher Preview
  • Air Bag Safety Preview
  • Colliding Carts Preview
  • Collisions Preview
  • Engineering Safer Helmets Preview
  • Push the Plow Preview
  • Its All Uphill Preview
  • Energy on an Incline Preview
  • Modeling Roller Coasters Preview
  • Hot Wheels Stopping Distance Preview
  • Ball Bat Collision Preview
  • Energy in Fields Preview
  • Weightlessness Training Preview
  • Roller Coaster Loops Preview
  • Universal Gravitation Preview
  • Keplers Laws Preview
  • Kepler's Third Law Preview
  • Charge Interactions Preview
  • Sticky Tape Experiments Preview
  • Wire Gauge Preview
  • Voltage, Current, and Resistance Preview
  • Light Bulb Resistance Preview
  • Series and Parallel Circuits Preview
  • Thermal Equilibrium Preview
  • Linear Expansion Preview
  • Heating Curves Preview
  • Electricity and Magnetism - Part 1 Preview
  • Electricity and Magnetism - Part 2 Preview
  • Vibrating Mass on a Spring Preview
  • Period of a Pendulum Preview
  • Wave Speed Preview
  • Slinky-Experiments Preview
  • Standing Waves in a Rope Preview
  • Sound as a Pressure Wave Preview
  • DeciBel Scale Preview
  • DeciBels, Phons, and Sones Preview
  • Sound of Music Preview
  • Shedding Light on Light Bulbs Preview
  • Models of Light Preview
  • Electromagnetic Radiation Preview
  • Electromagnetic Spectrum Preview
  • EM Wave Communication Preview
  • Digitized Data Preview
  • Light Intensity Preview
  • Concave Mirrors Preview
  • Object Image Relations Preview
  • Snells Law Preview
  • Reflection vs. Transmission Preview
  • Magnification Lab Preview
  • Reactivity Preview
  • Ions and the Periodic Table Preview
  • Periodic Trends Preview
  • Gaining Teacher Access
  • Tasks and Classes
  • Tasks - Classic
  • Subscription
  • Subscription Locator
  • 1-D Kinematics
  • Newton's Laws
  • Vectors - Motion and Forces in Two Dimensions
  • Momentum and Its Conservation
  • Work and Energy
  • Circular Motion and Satellite Motion
  • Thermal Physics
  • Static Electricity
  • Electric Circuits
  • Vibrations and Waves
  • Sound Waves and Music
  • Light and Color
  • Reflection and Mirrors
  • About the Physics Interactives
  • Task Tracker
  • Usage Policy
  • Newtons Laws
  • Vectors and Projectiles
  • Forces in 2D
  • Momentum and Collisions
  • Circular and Satellite Motion
  • Balance and Rotation
  • Waves and Sound
  • 1-Dimensional Kinematics
  • Circular, Satellite, and Rotational Motion
  • Einstein's Theory of Special Relativity
  • Waves, Sound and Light
  • QuickTime Movies
  • Forces in Two Dimensions
  • Work, Energy, and Power
  • Circular Motion and Gravitation
  • Sound Waves
  • About the Concept Builders
  • Pricing For Schools
  • Directions for Version 2
  • Measurement and Units
  • Relationships and Graphs
  • Rotation and Balance
  • Vibrational Motion
  • Reflection and Refraction
  • Teacher Accounts
  • Task Tracker Directions
  • Kinematic Concepts
  • Kinematic Graphing
  • Wave Motion
  • Sound and Music
  • About CalcPad
  • 1D Kinematics
  • Vectors and Forces in 2D
  • Simple Harmonic Motion
  • Rotational Kinematics
  • Rotation and Torque
  • Rotational Dynamics
  • Electric Fields, Potential, and Capacitance
  • Transient RC Circuits
  • Electromagnetism
  • Light Waves
  • Units and Measurement
  • Stoichiometry
  • Molarity and Solutions
  • Thermal Chemistry
  • Acids and Bases
  • Kinetics and Equilibrium
  • Solution Equilibria
  • Oxidation-Reduction
  • Nuclear Chemistry
  • NGSS Alignments
  • 1D-Kinematics
  • Projectiles
  • Circular Motion
  • Magnetism and Electromagnetism
  • Graphing Practice
  • About the ACT
  • ACT Preparation
  • For Teachers
  • Other Resources
  • Newton's Laws of Motion
  • Work and Energy Packet
  • Static Electricity Review
  • Solutions Guide
  • Solutions Guide Digital Download
  • Motion in One Dimension
  • Work, Energy and Power
  • Purchasing the CD
  • Purchasing the Digital Download
  • About the NGSS Corner
  • NGSS Search
  • Force and Motion DCIs - High School
  • Energy DCIs - High School
  • Wave Applications DCIs - High School
  • Force and Motion PEs - High School
  • Energy PEs - High School
  • Wave Applications PEs - High School
  • Crosscutting Concepts
  • The Practices
  • Physics Topics
  • NGSS Corner: Activity List
  • NGSS Corner: Infographics
  • About the Toolkits
  • Position-Velocity-Acceleration
  • Position-Time Graphs
  • Velocity-Time Graphs
  • Newton's First Law
  • Newton's Second Law
  • Newton's Third Law
  • Terminal Velocity
  • Projectile Motion
  • Forces in 2 Dimensions
  • Impulse and Momentum Change
  • Momentum Conservation
  • Work-Energy Fundamentals
  • Work-Energy Relationship
  • Roller Coaster Physics
  • Satellite Motion
  • Electric Fields
  • Circuit Concepts
  • Series Circuits
  • Parallel Circuits
  • Describing-Waves
  • Wave Behavior Toolkit
  • Standing Wave Patterns
  • Resonating Air Columns
  • Wave Model of Light
  • Plane Mirrors
  • Curved Mirrors
  • Teacher Guide
  • Using Lab Notebooks
  • Current Electricity
  • Light Waves and Color
  • Reflection and Ray Model of Light
  • Refraction and Ray Model of Light
  • Teacher Resources
  • Subscriptions

how to solve a physics problem

  • Newton's Laws
  • Einstein's Theory of Special Relativity
  • About Concept Checkers
  • School Pricing
  • Newton's Laws of Motion
  • Newton's First Law
  • Newton's Third Law
  • Horizontally Launched Projectile Problems
  • What is a Projectile?
  • Motion Characteristics of a Projectile
  • Horizontal and Vertical Velocity
  • Horizontal and Vertical Displacement
  • Initial Velocity Components
  • Non-Horizontally Launched Projectile Problems

how to solve a physics problem

There are two basic types of projectile problems that we will discuss in this course. While the general principles are the same for each type of problem, the approach will vary due to the fact the problems differ in terms of their initial conditions. The two types of problems are:

A projectile is launched with an initial horizontal velocity from an elevated position and follows a parabolic path to the ground. Predictable unknowns include the initial speed of the projectile, the initial height of the projectile, the time of flight, and the horizontal distance of the projectile.

Examples of this type of problem are

  • A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location.

A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. Predictable unknowns include the time of flight, the horizontal range, and the height of the projectile when it is at its peak.

  • A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the football.
  • A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

The second problem type will be the subject of the next part of Lesson 2 . In this part of Lesson 2, we will focus on the first type of problem - sometimes referred to as horizontally launched projectile problems. Three common kinematic equations that will be used for both type of problems include the following:

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

Equations for the Horizontal Motion of a Projectile

The above equations work well for motion in one-dimension, but a projectile is usually moving in two dimensions - both horizontally and vertically. Since these two components of motion are independent of each other, two distinctly separate sets of equations are needed - one for the projectile's horizontal motion and one for its vertical motion. Thus, the three equations above are transformed into two sets of three equations. For the horizontal components of motion, the equations are

x = v i x •t + 0.5*a x *t 2

v f x  = v i x  + a x •t

v f x 2  = v i x 2  + 2*a x •x

Of these three equations, the top equation is the most commonly used. An application of projectile concepts to each of these equations would also lead one to conclude that any term with a x in it would cancel out of the equation since a x = 0 m/s/s . Once this cancellation of ax terms is performed, the only equation of usefulness is:

x = v i x •t

Equations for the Vertical Motion of a Projectile

For the vertical components of motion, the three equations are

y = v iy •t + 0.5*a y *t 2

v fy  = v iy  + a y •t

v fy 2  = v iy 2  + 2*a y •y

In each of the above equations, the vertical acceleration of a projectile is known to be -9.8 m/s/s (the acceleration of gravity). Furthermore, for the special case of the first type of problem (horizontally launched projectile problems), v iy = 0 m/s. Thus, any term with v iy in it will cancel out of the equation.

The two sets of three equations above are the kinematic equations that will be used to solve projectile motion problems.

Solving Projectile Problems

To illustrate the usefulness of the above equations in making predictions about the motion of a projectile, consider the solution to the following problem.

The solution of this problem begins by equating the known or given values with the symbols of the kinematic equations - x, y, v ix , v iy , a x , a y , and t. Because horizontal and vertical information is used separately, it is a wise idea to organized the given information in two columns - one column for horizontal information and one column for vertical information. In this case, the following information is either given or implied in the problem statement:

As indicated in the table, the unknown quantity is the horizontal displacement (and the time of flight) of the pool ball. The solution of the problem now requires the selection of an appropriate strategy for using the kinematic equations and the known information to solve for the unknown quantities. It will almost always be the case that such a strategy demands that one of the vertical equations be used to determine the time of flight of the projectile and then one of the horizontal equations be used to find the other unknown quantities (or vice versa - first use the horizontal and then the vertical equation). An organized listing of known quantities (as in the table above) provides cues for the selection of the strategy. For example, the table above reveals that there are three quantities known about the vertical motion of the pool ball. Since each equation has four variables in it, knowledge of three of the variables allows one to calculate a fourth variable. Thus, it would be reasonable that a vertical equation is used with the vertical values to determine time and then the horizontal equations be used to determine the horizontal displacement (x). The first vertical equation (y = v iy •t +0.5•a y •t 2 ) will allow for the determination of the time. Once the appropriate equation has been selected, the physics problem becomes transformed into an algebra problem. By substitution of known values, the equation takes the form of

Since the first term on the right side of the equation reduces to 0, the equation can be simplified to

If both sides of the equation are divided by -5.0 m/s/s, the equation becomes

By taking the square root of both sides of the equation, the time of flight can then be determined .

Once the time has been determined, a horizontal equation can be used to determine the horizontal displacement of the pool ball. Recall from the given information , v ix = 2.4 m/s and a x = 0 m/s/s. The first horizontal equation (x = v ix •t + 0.5•a x •t 2 ) can then be used to solve for "x." With the equation selected, the physics problem once more becomes transformed into an algebra problem. By substitution of known values, the equation takes the form of

Since the second term on the right side of the equation reduces to 0, the equation can then be simplified to

The answer to the stated problem is that the pool ball is in the air for 0.35 seconds and lands a horizontal distance of 0.84 m from the edge of the pool table.

The following procedure summarizes the above problem-solving approach.

  • Carefully read the problem and list known and unknown information in terms of the symbols of the kinematic equations. For convenience sake, make a table with horizontal information on one side and vertical information on the other side.
  • Identify the unknown quantity that the problem requests you to solve for.
  • Select either a horizontal or vertical equation to solve for the time of flight of the projectile.
  • With the time determined, use one of the other equations to solve for the unknown. (Usually, if a horizontal equation is used to solve for time, then a vertical equation can be used to solve for the final unknown quantity.)

One caution is in order. The sole reliance upon 4- and 5-step procedures to solve physics problems is always a dangerous approach. Physics problems are usually just that - problems! While problems can often be simplified by the use of short procedures as the one above, not all problems can be solved with the above procedure. While steps 1 and 2 above are critical to your success in solving horizontally launched projectile problems, there will always be a problem that doesn't fit the mold . Problem solving is not like cooking; it is not a mere matter of following a recipe. Rather, problem solving requires careful reading, a firm grasp of conceptual physics, critical thought and analysis, and lots of disciplined practice. Never divorce conceptual understanding and critical thinking from your approach to solving problems.

Check Your Understanding

Use y = v iy • t + 0.5 • a y • t 2 to solve for time; the time of flight is 2.12 seconds.

Now use x = v ix • t + 0.5 • a x • t 2 to solve for v ix

Note that a x is 0 m/s/s so the last term on the right side of the equation cancels. By substituting 35.0 m for x and 2.12 s for t, the v ix can be found to be 16.5 m/s.

We Would Like to Suggest ...

how to solve a physics problem

  • Addition of Forces
  • For a new problem, you will need to begin a new live expert session.
  • You can contact support with any questions regarding your current subscription.
  • You will be able to enter math problems once our session is over.
  • I am only able to help with one math problem per session. Which problem would you like to work on?
  • Does that make sense?
  • I am currently working on this problem.
  • Are you still there?
  • It appears we may have a connection issue. I will end the session - please reconnect if you still need assistance.
  • Let me take a look...
  • Can you please send an image of the problem you are seeing in your book or homework?
  • If you click on "Tap to view steps..." you will see the steps are now numbered. Which step # do you have a question on?
  • Please make sure you are in the correct subject. To change subjects, please exit out of this live expert session and select the appropriate subject from the menu located in the upper left corner of the Mathway screen.
  • What are you trying to do with this input?
  • While we cover a very wide range of problems, we are currently unable to assist with this specific problem. I spoke with my team and we will make note of this for future training. Is there a different problem you would like further assistance with?
  • Mathway currently does not support this subject. We are more than happy to answer any math specific question you may have about this problem.
  • Mathway currently does not support Ask an Expert Live in Chemistry. If this is what you were looking for, please contact support.
  • Mathway currently only computes linear regressions.
  • We are here to assist you with your math questions. You will need to get assistance from your school if you are having problems entering the answers into your online assignment.
  • Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.
  • Have a great day!
  • Hope that helps!
  • You're welcome!
  • Per our terms of use, Mathway's live experts will not knowingly provide solutions to students while they are taking a test or quiz.

Please ensure that your password is at least 8 characters and contains each of the following:

  • a special character: @$#!%*?&

Advertisement

Google wants to solve tricky physics problems with quantum computers

Quantum computers could become more useful now researchers at Google have designed an algorithm that can translate complex physical problems into the language of quantum physics

By Alex Wilkins

19 December 2023

A quantum computer

Quantum computers don’t have many practical uses yet

Bartlomiej Wroblewski/Getty Images

Researchers at Google have created an algorithm that can translate complex physical problems into the language of quantum mechanics, which could make quantum computers able to tackle more tasks.

IBM’s 'Condor' quantum computer has more than 1000 qubits

Once they become powerful enough, quantum computers might become useful for specific jobs, such as breaking encryption or modelling quantum mechanics, but it is still largely unknown how useful they will be for many other scientific problems that classical computers…

To continue reading, subscribe today with our introductory offers

No commitment, cancel anytime*

Offer ends 28th October 2023.

*Cancel anytime within 14 days of payment to receive a refund on unserved issues.

Inclusive of applicable taxes (VAT)

Existing subscribers

More from New Scientist

Explore the latest news, articles and features

Quantum computer sets record on path towards error-free calculations

Why the quantum universe is weirder than you think.

Subscriber-only

IBM quantum computer beat a supercomputer in a head-to-head test

Quantum twist on common computer algorithm promises useful speed boost, popular articles.

Trending New Scientist articles

Engineering Mathematics and Sciences

Your virtual study buddy in mathematics, engineering sciences, and civil engineering, problem 6-4: period, angular velocity, and linear velocity of the earth, (a) what is the period of rotation of earth in seconds (b) what is the angular velocity of earth (c) given that earth has a radius of 6.4×10 6 m at its equator, what is the linear velocity at earth’s surface.

The period of a rotating body is the time it takes for 1 full revolution. The Earth rotates about its axis, and complete 1 full revolution in 24 hours. Therefore, the period is

The angular velocity \omega is the rate of change of an angle,

where a rotation \Delta \theta takes place in a time \Delta t .

From the given problem, we are given the following: \Delta \theta = 2\pi \text{radian} = 1 \ \text{revolution} , and \Delta t =24\ \text{hours} = 1440 \ \text{minutes}= 86400 \ \text{seconds} . Therefore, the angular velocity is

We can also express the angular velocity in units of radians per second. That is

The linear velocity v , and the angular velocity \omega are related by the formula

From the given problem, we are given the following values: r=6.4 \times 10^{6} \ \text{meters} , and \omega = 7.27 \times 10^{-5}\ \text{radians/second} . Therefore, the linear velocity at the surface of the earth is

December 22, 2023

The Most Important Unsolved Problem in Computer Science

Here’s a look at the million-dollar math problem at the heart of computation

By Jack Murtagh

mathematic formulas on a computer display, blue text on black screen

alengo/Getty Images

When the Clay Mathematics Institute put individual $1-million prize bounties on seven unsolved mathematical problems , they may have undervalued one entry—by a lot. If mathematicians were to resolve, in the right way, computer science’s “P versus NP” question, the result could be worth worlds more than $1 million—they’d be cracking most online-security systems, revolutionizing science and even mechanistically solving the other six of the so-called Millennium Problems, all of which were chosen in the year 2000. It’s hard to overstate the stakes surrounding the most important unsolved problem in computer science .

P versus NP concerns the apparent asymmetry between finding solutions to problems and verifying solutions to problems. For example, imagine you’re planning a world tour to promote your new book. You pull up Priceline and start testing routes, but each one you try blows your total trip budget. Unfortunately, as the number of cities grows on your worldwide tour, the number of possible routes to check skyrockets exponentially, rapidly making it infeasible even for computers to exhaustively search through every case. But when you complain, your agent writes back with a solution sequence of flights. You can easily verify whether or not their route stays in budget by simply checking that it hits every city and summing the fares to compare against the budget limit. Notice the asymmetry here: finding a solution is hard, but verifying a solution is easy.

The P versus NP question asks whether this asymmetry is real or an illusion. If you can efficiently verify a solution to a problem, does that imply that you can also efficiently find a solution? Perhaps a clever shortcut can circumvent searching through zillions of potential routes. For example, if your agent instead wanted you to find a sequence of flights between two specific remote airports while obeying the budget, you might also throw up your hands at the similarly immense number of possible routes to check, but in fact, this problem contains enough structure that computer scientists have developed a fast procedure (algorithm) for it that bypasses the need for exhaustive search.

You might think this asymmetry is obvious: of course one would sometimes have a harder time finding a solution to a problem than verifying it. But researchers have been surprised before in thinking that that’s the case, only to discover last-minute that the solution is just as easy. So every attempt in which they try to resolve this question for any single scenario only further exposes how monumentally difficult it is to prove one way or another. P versus NP also rears its head everywhere we look in the computational world well beyond the specifics of our travel scenario—so much so that it has come to symbolize a holy grail in our understanding of computation.

In the subfield of theoretical computer science called complexity theory, researchers try to pin down how easily computers can solve various types of problems. P represents the class of problems they can solve efficiently, such as sorting a column of numbers in a spreadsheet or finding the shortest path between two addresses on a map. NP represents the class of problems for which computers can verify solutions efficiently. Our book tour problem, called the Traveling Salesperson Problem by academics, lives in NP because we have an efficient procedure for verifying that our agent’s solution worked.

Notice that NP actually contains P as a subset because solving a problem outright is one way to verify a solution to it. For example, how would you verify that 27 x 89 = 2,403? You would solve the multiplication problem yourself and check that your answer matches the claimed one. We typically depict the relationship between P and NP with a simple Venn diagram:

Venn diagram shows one large circle labeled “NP” encompassing a smaller one labeled “P.” The entire circle is labeled “Problems with solutions that computers can verify easily.” The area inside of P is labeled “Problems with solutions that computers can find easily.” The area in NP but outside of P is labeled “Problems with solutions that computers can verify but not find easily.”

The region inside of NP but not inside of P contains problems that can’t be solved with any known efficient algorithm. (Theoretical computer scientists use a technical definition for “efficient” that can be debated, but it serves as a useful proxy for the colloquial concept.) But we don’t know if that’s because such algorithms don’t exist or we just haven’t mustered the ingenuity to discover them. Here’s another way to phrase the P versus NP question: Are these classes actually distinct? Or does the Venn diagram collapse into one circle? Do all NP problems admit efficient algorithms? Here are some examples of problems in NP that are not currently known to be in P:

  • Given a social network, is there a group of a specified size in which all of the people in it are friends with one another?
  • Given a varied collection of boxes to be shipped, can all of them be fit into a specified number of trucks?
  • Given a sudoku (generalized to n x n puzzle grids), does it have a solution?
  • Given a map, can the countries be colored with only three colors such that no two neighboring countries are the same color?

Ask yourself how you would verify proposed solutions to some of the problems above and then how you would find a solution. Note that approximating a solution or solving a small instance (most of us can solve a 9 x 9 sudoku ) doesn’t suffice. To qualify as solving a problem, an algorithm needs to find an exact solution on all instances, including very large ones.

Each of the problems can be solved via brute-force search (e.g., try every possible coloring of the map and check if any of them work), but the number of cases to try grows exponentially with the size of the problem. This means that if we call the size of the problem n (e.g., the number of countries on the map or the number of boxes to pack into trucks), then the number of cases to check looks something like 2 n . The world’s fastest supercomputers have no hope against exponential growth. Even when n equals 300, a tiny input size by modern data standards, 2 300 exceeds the number of atoms in the observable universe. After hitting “go” on such an algorithm, your computer would display a spinning pinwheel that would outlive you and your descendants.

Thousands of other problems belong on our list. From cell biology to game theory, the P versus NP question reaches into far corners of science and industry. If P = NP (i.e., our Venn diagram dissolves into a single circle) and we obtain fast algorithms for these seemingly hard problems, then the whole digital economy would become vulnerable to collapse. This is because much of the cryptography that secures such things as your credit card number and passwords works by shrouding private information behind computationally difficult problems that can only become easy to solve if you know the secret key. Online security as we know it rests on unproven mathematical assumptions that crumble if P = NP.

Amazingly, we can even cast math itself as an NP problem because we can program computers to efficiently verify proofs. In fact, legendary mathematician Kurt Gödel first posed the P versus NP problem in a letter to his colleague John von Neumann in 1956, and he expressed (in older terminology) that P = NP “would have consequences of the greatest importance. Namely, it would obviously mean that ... the mental work of a mathematician concerning yes-or-no questions could be completely replaced by a machine.”

If you’re a mathematician worried for your job, rest assured that most experts believe that P does not equal NP. Aside from the intuition that sometimes solutions should be harder to find than to verify, thousands of the hardest NP problems that are not known to be in P have sat unsolved across disparate fields, glowing with incentives of fame and fortune, and yet not one person has designed an efficient algorithm for a single one of them.

Of course, gut feeling and a lack of counterexamples don’t constitute a proof. To prove that P is different from NP, you somehow have to rule out all potential algorithms for all of the hardest NP problems, a task that appears out of reach for current mathematical techniques. In fact, the field has coped by proving so-called barrier theorems, which say that entire categories of tempting proof strategies to resolve P versus NP cannot succeed. Not only have we failed to find a proof but we also have no clue what an eventual proof might look like.

IMAGES

  1. How to solve a physics problem (with an example)?

    how to solve a physics problem

  2. How to Solve Any Physics Problem: 10 Steps (with Pictures)

    how to solve a physics problem

  3. Physics: 5 Step Problem Solving Process with Examples

    how to solve a physics problem

  4. How To Solve Physics Problems Easily?

    how to solve a physics problem

  5. How to Be a Better Physics Problem Solver: Tips for High School and

    how to solve a physics problem

  6. 🎉 How to solve physics problem. cupsoguepictures.com: How to Solve

    how to solve a physics problem

VIDEO

  1. Don't do THIS in A Level Physics

  2. STEPS TO SOLVE PHYSICS PROBLEMS EASILY

  3. Physics Chapter 3 probem 3

  4. Physics Example 4.7

  5. Physics Chapter 3 problem 2

  6. Derivative by First Principles turned simple!

COMMENTS

  1. How to Solve Any Physics Problem: 10 Steps (with Pictures)

    1 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.

  2. PDF An Expert's Approach to Solving Physics Problems

    Focus on the Problem. Establish a clear mental image of the problem. Visualize the situation and events by sketching a useful picture. Identify physics concepts and approaches that might be useful to reach a solution. In your own words, precisely state the question to be answered in terms you can calculate. Describe the Physics.

  3. 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.

  4. 1.7 Solving Problems in Physics

    Strategy 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.

  5. How To Solve Any Physics Problem

    How To Solve Any Physics Problem Jesse Mason 100K subscribers Subscribe 6.2K 403K views 10 years ago Tutorials Learn five simple steps in five minutes! In this episode we cover the most...

  6. 6.1 Solving Problems with Newton's Laws

    A classic problem in physics, similar to the one we just solved, is that of the Atwood machine, which consists of a rope running over a pulley, with two objects of different mass attached. It is particularly useful in understanding the connection between force and motion. In Figure 6.7, m 1 = 2.00 kg and m 2 = 4.00 kg.

  7. 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.

  8. 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. Free body diagrams are very ...

  9. Solving Physics Problems

    Activities How do you utilize the GUESS method in physics? To use the GUESS method in physics, first identify the givens, or knowns, in the problem. Second, identify the unknowns and which...

  10. How To Solve Physics Problems

    ( a) Find the acceleration of the system if B is initially at rest. ( b) Find the acceleration if B is moving up the plane. ( c) What is the acceleration if B is moving down the plane?

  11. How To

    General Approach to Solving Physics Problems. 1. Identify the problem. In order to identify the type of problem that you have, think about the key physics behind your problem. The surface features (in a car, on an incline, on a rope, with or without friction, horizontal or vertical, etc.) do not affect how you solve the problem.

  12. 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.

  13. Kinematic Equations and Problem-Solving

    d = vi • t + ½ • a • t2. 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. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s 2) • (4.10 s) 2.

  14. How to Solve Physics Problems THOROUGHLY

    These study tips will help you systematically work through physics problems a lot more easily.Timestamps:00:45 - Perform a sanity check03:47 - Dimensional an...

  15. CC

    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?

  16. Step-by-Step Calculator

    Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go. How to solve math problems step-by-step?

  17. How To Solve Physics Problems

    The problem-solving skills illustrated in this book will help you to solve physics problems on Isaac Physics and beyond, as well as problems in other spheres of life. See our worked solution videos below which demonstrate the methods used to solve two questions from the book. Worked Example: Crossing a River.

  18. Kinematic Equations: Sample Problems and Solutions

    See solution below. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.83 seconds, then what is the acceleration and what is the distance that the sled travels? See Answer See solution below.

  19. Introduction to Inclined Planes

    This physics video tutorial provides a basic introduction into inclined planes. It covers the most common equations and formulas that you need to solve incl...

  20. Horizontally Launched Projectile Problems

    Problem Type 1: A projectile is launched with an initial horizontal velocity from an elevated position and follows a parabolic path to the ground. Predictable unknowns include the initial speed of the projectile, the initial height of the projectile, the time of flight, and the horizontal distance of the projectile.

  21. Mathway

    Free math problem solver answers your physics homework questions with step-by-step explanations.

  22. How to Solve a Physics Problem

    which means we can get an answer by solving for t in terms of θ or vice versa. Looking at the y equation yields. where we chose the nonzero solution of t since the cannonball is at (0, 0) at t = 0. Since we have t in terms of θ, we can plug it back into the equation for the range, which gets us.

  23. The Guess Method to Solve Every Physics Problem (Easy)

    Mathematically solving problems is a large part in understanding physics. In this video I am going to teach you a process that will help you solve many physi...

  24. Google wants to solve tricky physics problems with quantum computers

    Bartlomiej Wroblewski/Getty Images. Researchers at Google have created an algorithm that can translate complex physical problems into the language of quantum mechanics, which could make quantum ...

  25. How to Solve Physics Problems: Period, Angular Velocity, and Linear

    Learn how to solve physics problems involving period, angular velocity, and linear velocity of the Earth. This post explains the concepts and formulas with a step-by-step solution. ... College Physics by Openstax Problems Solution Guide. Chapter 1: Introduction: The Nature of Science and Physics. Chapter 2: Kinematics. Chapter 3: Two ...

  26. The Most Important Unsolved Problem in Computer Science

    Note that approximating a solution or solving a small instance (most of us can solve a 9 x 9 sudoku) doesn't suffice. To qualify as solving a problem, an algorithm needs to find an exact ...

  27. Numerical Modeling of the Interaction of Dark Atoms with Nuclei to

    The puzzle of the direct dark matter search can be resolved by examining the concept of «dark atoms», which consist of hypothetical stable lepton-like particles with a charge of −2n, where n is any natural number, bound to n nuclei of primordial helium. These «dark atoms», known as «XHe» (X-helium) atoms, remain undiscovered in experiments due to their neutral atom-like states.