- âș Force and Motion
- âș This article

## Solving problems which involve forces, friction, and Newton's Laws: A step-by-step guide

This step-by-step guide is meant to show you how to approach problems where you have to deal with moving objects subject to friction and other forces, and you need to apply Newton's Laws. We will go through many problems, so you can have a clear idea of the process involved in solving them.

The problems we will examine include objects that

- are pushed/pulled horizontally with an angle
- move up or down an incline
- hang from ropes attached to the ceiling
- hang from ropes that run over pulleys
- move connected by a string
- are pushed in contact with each other (Coming soon!)
- Box pulled at an angle over a horizontal surface
- Block pushed over the floor with a downward and forward force
- Object moving at constant velocity over a horizontal surface
- Block pushed up a frictionless ramp
- Mass pulled up an incline with friction
- A mass hanging from two ropes
- Two hanging objects connected by a rope
- Two masses on a pulley
- Two blocks connected by a string are pulled horizontally

## HIGH SCHOOL

- ACT Tutoring
- SAT Tutoring
- PSAT Tutoring
- ASPIRE Tutoring
- SHSAT Tutoring
- STAAR Tutoring

## GRADUATE SCHOOL

- MCAT Tutoring
- GRE Tutoring
- LSAT Tutoring
- GMAT Tutoring
- AIMS Tutoring
- HSPT Tutoring
- ISAT Tutoring
- SSAT Tutoring

## Search 50+ Tests

Loading Page

## math tutoring

- Elementary Math
- Pre-Calculus
- Trigonometry

## science tutoring

Foreign languages.

- Mandarin Chinese

## elementary tutoring

- Computer Science

## Search 350+ Subjects

- Video Overview
- Tutor Selection Process
- Online Tutoring
- Mobile Tutoring
- Instant Tutoring
- How We Operate
- Our Guarantee
- Impact of Tutoring
- Reviews & Testimonials
- Media Coverage
- About Varsity Tutors

## High School Physics : Calculating Force

Study concepts, example questions & explanations for high school physics, all high school physics resources, example questions, example question #1 : net force.

Plug these into the equation to solve for acceleration.

## Example Question #2 : Calculating Force

Plug in the values given to us and solve for the force.

## Example Question #3 : Calculating Force

Plug in the given values to solve for the mass.

## Example Question #4 : Calculating Force

(Assume the only two forces acting on the object are friction and Derek).

Plug in the information we've been given so far to find the force of friction.

Friction will be negative because it acts in the direction opposite to the force of Derek.

## Example Question #5 : Calculating Force

Newton's third law states that when one object exerts a force on a second object, the second object exerts a force equal in size, but opposite in direction to the first. That means that the force of the hammer on the nail and the nail on the hammer will be equal in size, but opposite in direction.

## Example Question #6 : Calculating Force

We can find the net force by adding the individual force together.

## Example Question #7 : Calculating Force

If the object has a constant velocity, that means that the net acceleration must be zero.

In conjunction with Newton's second law, we can see that the net force is also zero. If there is no net acceleration, then there is no net force.

Since Franklin is lifting the weight vertically, that means there will be two force acting upon the weight: his lifting force and gravity. The net force will be equal to the sum of the forces acting on the weight.

We know the mass of the weight and we know the acceleration, so we can solve for the lifting force.

## Example Question #1 : Calculating Force

We are given the mass, but we will need to calculate the acceleration to use in the formula.

Plug in our given values and solve for acceleration.

Now we know both the acceleration and the mass, allowing us to solve for the force.

## Example Question #9 : Calculating Force

We can calculate the gravitational force using the mass.

## Example Question #10 : Calculating Force

## Report an issue with this question

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

## DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (âInfringement Noticeâ) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneysâ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question â an image, a link, the text, etc â your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such ownerâs agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below:

## Contact Information

Complaint details.

## Dynamics: Force and Newton’s Laws of Motion

Problem-solving strategies, learning objective.

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

- Understand and apply a problem-solving procedure to solve problems using Newton’s laws of motion.

Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams. The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newtonâs laws of motion are emphasized. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop.

## Problem-Solving Strategy for Newtonâs Laws of Motion

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newtonâs laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation . Such a sketch is shown in Figure 1(a). Then, as in Figure 1(b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists).

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

Step 2. Identify what needs to be determined and what is known or can be inferred from the problem as stated. That is, make a list of knowns and unknowns. Then carefully determine the system of interest . This decision is a crucial step, since Newtonâs second law involves only external forces. Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newtonâs second law. (See Figure 1(c).) Newtonâs third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). As illustrated earlier in this chapter, the system of interest depends on what question we need to answer. This choice becomes easier with practice, eventually developing into an almost unconscious process. Skill in clearly defining systems will be beneficial in later chapters as well.

A diagram showing the system of interest and all of the external forces is called a free-body diagram . Only forces are shown on free-body diagrams, not acceleration or velocity. We have drawn several of these in worked examples. Figure 1(c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.

Step 3. Once a free-body diagram is drawn, Newtonâs second law can be applied to solve the problem . This is done in Figure 1(d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensionalâthat is, if all forces are parallelâthen they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.

## Applying Newtonâs Second Law

F net xÂ = ma ,

F net y = 0.

You will need this information in order to determine unknown forces acting in a system.

Step 4. As always, check the solution to see whether it is reasonable . In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.

## Section Summary

To solve problems involving Newtonâs laws of motion, follow the procedure described:

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

## Problems & Exercises

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Selected Solutions to Problems & Exercises

1. Using the free-body diagram:

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

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

3.Â Use Newtonâs laws of motion.

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

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

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

7. (a) 910 N (b) 1.11 Ă 10 3

9. (a) a = 0.139 m/s, Îž = 12.4Âș

11.Â Use Newtonâs laws since we are looking for forces.

- Draw a free-body diagram:

- The tension is given as T = 25.0 N. Find F app .Â Using Newtonâs laws gives:[latex]\sigma{F}_{y}=0\\[/latex], so that applied force is due to the y -components of the two tensions: F app = 2 T Â sinÂ ÎžÂ = 2(25.0 N) sin(15Âș) = 12.9 NÂ The x -components of the tension cancel. [latex]\sum{F}_{x}=0\\[/latex].
- This seems reasonable, since the applied tensions should be greater than the force applied to the tooth.
- College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics . License : CC BY: Attribution . License Terms : Located at License

## Physics Problems with Solutions

Forces in physics, tutorials and problems with solutions.

Free tutorials on forces with questions and problems with detailed solutions and examples. The concepts of forces, friction forces, action and reaction forces, free body diagrams, tension of string, inclined planes, etc. are discussed and through examples, questions with solutions and clear and self explanatory diagrams. Questions to practice for the SAT Physics test on forces are also included with their detailed solutions. The discussions of applications of forces engineering system are also included.

## Forces: Tutorials with Examples and Detailed Solutions

- Forces in Physics .
- Components of a Force in a System of Coordinates .
- Free Body Diagrams, Tutorials with Examples and Explanations .
- Forces of Friction .
- Addition of Forces .
- What is the Tension of a String or rope? .
- Newton's Laws in Physics .
- Hooke's Law, Examples with solutions .

## Problems on Forces with Detailed Solutions

- Inclined Planes Problems in Physics with Solutions .
- Tension, String, Forces Problems with Solutions .

## SAT Questions on Forces with Solutions

- Physics Practice Questions with Solutions on Forces and Newton's Laws .

## Formulas and Constants

- Physics Formulas Reference
- SI Prefixes Used with Units in Physics, Chemistry and Engineering
- Constants in Physics, Chemistry and Engineering

## Popular Pages

- Privacy Policy

About me and why I created this physics website.

## Force Problems

- Search Website

## Real World Applications â for high school level and above

- Amusement Parks
- Battle & Weapons
- Engineering
- Miscellaneous

## Education & Theory â for high school level and above

- Useful Formulas
- Physics Questions
- Example Mechanics Problems
- Learn Physics Compendium

## Kids Section

- Physics For Kids
- Science Experiments
- Science Fair Ideas
- Science Quiz
- Science Toys
- Teacher Resources
- Commercial Disclosure
- Privacy Policy

Â© Copyright 2009-2024 real-world-physics-problems.com

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Physics library

Course: physics library Â > Â unit 4, centripetal force problem solving.

- What is a centripetal force?
- Yo-yo in vertical circle example
- Bowling ball in vertical loop
- Mass swinging in a horizontal circle

## Want to join the conversation?

- Upvote Button navigates to signup page
- Downvote Button navigates to signup page
- Flag Button navigates to signup page

## Video transcript

- 8.1 Linear Momentum, Force, and Impulse
- Introduction
- 1.1 Physics: Definitions and Applications
- 1.2 The Scientific Methods
- 1.3 The Language of Physics: Physical Quantities and Units
- Section Summary
- Key Equations
- Concept Items
- Critical Thinking Items
- Performance Task
- Multiple Choice
- Short Answer
- Extended Response
- 2.1 Relative Motion, Distance, and Displacement
- 2.2 Speed and Velocity
- 2.3 Position vs. Time Graphs
- 2.4 Velocity vs. Time Graphs
- 3.1 Acceleration
- 3.2 Representing Acceleration with Equations and Graphs
- 4.2 Newton's First Law of Motion: Inertia
- 4.3 Newton's Second Law of Motion
- 4.4 Newton's Third Law of Motion
- 5.1 Vector Addition and Subtraction: Graphical Methods
- 5.2 Vector Addition and Subtraction: Analytical Methods
- 5.3 Projectile Motion
- 5.4 Inclined Planes
- 5.5 Simple Harmonic Motion
- 6.1 Angle of Rotation and Angular Velocity
- 6.2 Uniform Circular Motion
- 6.3 Rotational Motion
- 7.1 Kepler's Laws of Planetary Motion
- 7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity
- 8.2 Conservation of Momentum
- 8.3 Elastic and Inelastic Collisions
- 9.1 Work, Power, and the WorkâEnergy Theorem
- 9.2 Mechanical Energy and Conservation of Energy
- 9.3 Simple Machines
- 10.1 Postulates of Special Relativity
- 10.2 Consequences of Special Relativity
- 11.1 Temperature and Thermal Energy
- 11.2 Heat, Specific Heat, and Heat Transfer
- 11.3 Phase Change and Latent Heat
- 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium
- 12.2 First law of Thermodynamics: Thermal Energy and Work
- 12.3 Second Law of Thermodynamics: Entropy
- 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators
- 13.1 Types of Waves
- 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period
- 13.3 Wave Interaction: Superposition and Interference
- 14.1 Speed of Sound, Frequency, and Wavelength
- 14.2 Sound Intensity and Sound Level
- 14.3 Doppler Effect and Sonic Booms
- 14.4 Sound Interference and Resonance
- 15.1 The Electromagnetic Spectrum
- 15.2 The Behavior of Electromagnetic Radiation
- 16.1 Reflection
- 16.2 Refraction
- 16.3 Lenses
- 17.1 Understanding Diffraction and Interference
- 17.2 Applications of Diffraction, Interference, and Coherence
- 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge
- 18.2 Coulomb's law
- 18.3 Electric Field
- 18.4 Electric Potential
- 18.5 Capacitors and Dielectrics
- 19.1 Ohm's law
- 19.2 Series Circuits
- 19.3 Parallel Circuits
- 19.4 Electric Power
- 20.1 Magnetic Fields, Field Lines, and Force
- 20.2 Motors, Generators, and Transformers
- 20.3 Electromagnetic Induction
- 21.1 Planck and Quantum Nature of Light
- 21.2 Einstein and the Photoelectric Effect
- 21.3 The Dual Nature of Light
- 22.1 The Structure of the Atom
- 22.2 Nuclear Forces and Radioactivity
- 22.3 Half Life and Radiometric Dating
- 22.4 Nuclear Fission and Fusion
- 22.5 Medical Applications of Radioactivity: Diagnostic Imaging and Radiation
- 23.1 The Four Fundamental Forces
- 23.2 Quarks
- 23.3 The Unification of Forces
- A | Reference Tables

## Section Learning Objectives

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

- Describe momentum, what can change momentum, impulse, and the impulse-momentum theorem
- Describe Newtonâs second law in terms of momentum
- Solve problems using the impulse-momentum theorem

## Teacher Support

The learning objectives in this section will help your students master the following standards:

- (C) calculate the mechanical energy of, power generated within, impulse applied to, and momentum of a physical system.

## Section Key Terms

[BL] [OL] Review inertia and Newtonâs laws of motion.

[AL] Start a discussion about movement and collision. Using the example of football players, point out that both the mass and the velocity of an object are important considerations in determining the impact of collisions. The direction as well as the magnitude of velocity is very important.

## Momentum, Impulse, and the Impulse-Momentum Theorem

Linear momentum is the product of a systemâs mass and its velocity . In equation form, linear momentum p is

You can see from the equation that momentum is directly proportional to the objectâs mass ( m ) and velocity ( v ). Therefore, the greater an objectâs mass or the greater its velocity, the greater its momentum. A large, fast-moving object has greater momentum than a smaller, slower object.

Momentum is a vector and has the same direction as velocity v . Since mass is a scalar , when velocity is in a negative direction (i.e., opposite the direction of motion), the momentum will also be in a negative direction; and when velocity is in a positive direction, momentum will likewise be in a positive direction. The SI unit for momentum is kg m/s.

Momentum is so important for understanding motion that it was called the quantity of motion by physicists such as Newton. Force influences momentum, and we can rearrange Newtonâs second law of motion to show the relationship between force and momentum.

Recall our study of Newtonâs second law of motion ( F net = m a ). Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. The change in momentum is the difference between the final and initial values of momentum.

In equation form, this law is

where F net is the net external force, Î p Î p is the change in momentum, and Î t Î t is the change in time.

We can solve for Î p Î p by rearranging the equation

F net Î t F net Î t is known as impulse and this equation is known as the impulse-momentum theorem . From the equation, we see that the impulse equals the average net external force multiplied by the time this force acts. It is equal to the change in momentum. The effect of a force on an object depends on how long it acts, as well as the strength of the force. Impulse is a useful concept because it quantifies the effect of a force. A very large force acting for a short time can have a great effect on the momentum of an object, such as the force of a racket hitting a tennis ball. A small force could cause the same change in momentum, but it would have to act for a much longer time.

[OL] [AL] Explain that a large, fast-moving object has greater momentum than a smaller, slower object. This quality is called momentum.

[BL] [OL] Review the equation of Newtonâs second law of motion. Point out the two different equations for the law.

## Newtonâs Second Law in Terms of Momentum

When Newtonâs second law is expressed in terms of momentum, it can be used for solving problems where mass varies, since Î p = Î ( m v ) Î p = Î ( m v ) . In the more traditional form of the law that you are used to working with, mass is assumed to be constant. In fact, this traditional form is a special case of the law, where mass is constant. F net = m a F net = m a is actually derived from the equation:

For the sake of understanding the relationship between Newtonâs second law in its two forms, letâs recreate the derivation of F net = m a F net = m a from

by substituting the definitions of acceleration and momentum.

The change in momentum Î p Î p is given by

If the mass of the system is constant, then

By substituting m Î v m Î v for Î p Î p , Newtonâs second law of motion becomes

for a constant mass.

we can substitute to get the familiar equation

when the mass of the system is constant.

[BL] [OL] [AL] Show the two different forms of Newtonâs second law and how one can be derived from the other.

## Tips For Success

We just showed how F net = m a F net = m a applies only when the mass of the system is constant. An example of when this formula would not apply would be a moving rocket that burns enough fuel to significantly change the mass of the rocket. In this case, you can use Newtonâs second law expressed in terms of momentum to account for the changing mass without having to know anything about the interaction force by the fuel on the rocket.

## Hand Movement and Impulse

In this activity you will experiment with different types of hand motions to gain an intuitive understanding of the relationship between force, time, and impulse.

- one tub filled with water
- Try catching a ball while giving with the ball, pulling your hands toward your body.
- Next, try catching a ball while keeping your hands still.
- Hit water in a tub with your full palm. Your full palm represents a swimmer doing a belly flop.
- After the water has settled, hit the water again by diving your hand with your fingers first into the water. Your diving hand represents a swimmer doing a dive.
- Explain what happens in each case and why.
- a football player colliding with another, or a car moving at a constant velocity
- a car moving at a constant velocity, or an object moving in the projectile motion
- a car moving at a constant velocity, or a racket hitting a ball
- a football player colliding with another, or a racket hitting a ball

[OL] [AL] Discuss the impact one feels when one falls or jumps. List the factors that affect this impact.

## Links To Physics

Engineering: saving lives using the concept of impulse.

Cars during the past several decades have gotten much safer. Seat belts play a major role in automobile safety by preventing people from flying into the windshield in the event of a crash. Other safety features, such as airbags, are less visible or obvious, but are also effective at making auto crashes less deadly (see Figure 8.2 ). Many of these safety features make use of the concept of impulse from physics. Recall that impulse is the net force multiplied by the duration of time of the impact. This was expressed mathematically as Î p = F net Î t Î p = F net Î t .

Airbags allow the net force on the occupants in the car to act over a much longer time when there is a sudden stop. The momentum change is the same for an occupant whether an airbag is deployed or not. But the force that brings the occupant to a stop will be much less if it acts over a larger time. By rearranging the equation for impulse to solve for force F net = Î p Î t , F net = Î p Î t , you can see how increasing Î t Î t while Î p Î p stays the same will decrease F net . This is another example of an inverse relationship. Similarly, a padded dashboard increases the time over which the force of impact acts, thereby reducing the force of impact.

Cars today have many plastic components. One advantage of plastics is their lighter weight, which results in better gas mileage. Another advantage is that a car will crumple in a collision , especially in the event of a head-on collision. A longer collision time means the force on the occupants of the car will be less. Deaths during car races decreased dramatically when the rigid frames of racing cars were replaced with parts that could crumple or collapse in the event of an accident.

## Grasp Check

You may have heard the advice to bend your knees when jumping. In this example, a friend dares you to jump off of a park bench onto the ground without bending your knees. You, of course, refuse. Explain to your friend why this would be a foolish thing. Show it using the impulse-momentum theorem.

- Bending your knees increases the time of the impact, thus decreasing the force.
- Bending your knees decreases the time of the impact, thus decreasing the force.
- Bending your knees increases the time of the impact, thus increasing the force.
- Bending your knees decreases the time of the impact, thus increasing the force.

## Solving Problems Using the Impulse-Momentum Theorem

Talk about the different strategies to be used while solving problems. Make sure that students know the assumptions made in each equation regarding certain quantities being constant or some quantities being negligible.

## Worked Example

Calculating momentum: a football player and a football.

(a) Calculate the momentum of a 110 kg football player running at 8 m/s. (b) Compare the playerâs momentum with the momentum of a 0.410 kg football thrown hard at a speed of 25 m/s.

No information is given about the direction of the football player or the football, so we can calculate only the magnitude of the momentum, p . (A symbol in italics represents magnitude.) In both parts of this example, the magnitude of momentum can be calculated directly from the definition of momentum:

To find the playerâs momentum, substitute the known values for the playerâs mass and speed into the equation.

To find the ballâs momentum, substitute the known values for the ballâs mass and speed into the equation.

The ratio of the playerâs momentum to the ballâs momentum is

Although the ball has greater velocity, the player has a much greater mass. Therefore, the momentum of the player is about 86 times greater than the momentum of the football.

## Calculating Force: Venus Williamsâ Racquet

During the 2007 French Open, Venus Williams ( Figure 8.3 ) hit the fastest recorded serve in a premier womenâs match, reaching a speed of 58 m/s (209 km/h). What was the average force exerted on the 0.057 kg tennis ball by Williamsâ racquet? Assume that the ballâs speed just after impact was 58 m/s, the horizontal velocity before impact is negligible, and that the ball remained in contact with the racquet for 5 ms (milliseconds).

Recall that Newtonâs second law stated in terms of momentum is

As noted above, when mass is constant, the change in momentum is given by

where v f is the final velocity and v i is the initial velocity. In this example, the velocity just after impact and the change in time are given, so after we solve for Î p Î p , we can use F net = Î p Î t F net = Î p Î t to find the force.

To determine the change in momentum, substitute the values for mass and the initial and final velocities into the equation above.

Now we can find the magnitude of the net external force using F net = Î p Î t F net = Î p Î t

This quantity was the average force exerted by Venus Williamsâ racquet on the tennis ball during its brief impact. This problem could also be solved by first finding the acceleration and then using F net = m a , but we would have had to do one more step. In this case, using momentum was a shortcut.

## Practice Problems

- 0.5 kg â m/s
- 15 kg â m/s
- 50 kg â m/s

A 155-g baseball is incoming at a velocity of 25 m/s. The batter hits the ball as shown in the image. The outgoing baseball has a velocity of 20 m/s at the angle shown.

What is the magnitudde of the impulse acting on the ball during the hit?

- 2.68 kgâ m/s.
- 5.42 kgâ m/s.
- 6.05 kgâ m/s.
- 8.11 kgâ m/s.

## Check Your Understanding

What is linear momentum?

- the sum of a systemâs mass and its velocity
- the ratio of a systemâs mass to its velocity
- the product of a systemâs mass and its velocity
- the product of a systemâs moment of inertia and its velocity

If an objectâs mass is constant, what is its momentum proportional to?

- Its velocity
- Its displacement
- Its moment of inertia

What is the equation for Newtonâs second law of motion, in terms of mass, velocity, and time, when the mass of the system is constant?

- F net = Î v Î m Î t F net = Î v Î m Î t
- F net = m Î t Î v F net = m Î t Î v
- F net = m Î v Î t F net = m Î v Î t
- F net = Î m Î v Î t F net = Î m Î v Î t

Give an example of a system whose mass is not constant.

- A spinning top
- A baseball flying through the air
- A rocket launched from Earth
- A block sliding on a frictionless inclined plane

Use the Check Your Understanding questions to assess whether students master the learning objectives of this section. If students are struggling with a specific objective, the assessment will help identify which objective is causing the problem and direct students to the relevant content.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction

- Authors: Paul Peter Urone, Roger Hinrichs
- Publisher/website: OpenStax
- Book title: Physics
- Publication date: Mar 26, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/physics/pages/1-introduction
- Section URL: https://openstax.org/books/physics/pages/8-1-linear-momentum-force-and-impulse

Â© Jan 19, 2024 Texas Education Agency (TEA). 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.

- 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
- Classes (Version 2)
- 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
- Properties of Matter
- Fluid Pressure
- Buoyant Force
- Sinking, Floating, and Hanging
- Pascal's Principle
- Flow Velocity
- 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 = âV/R Equations as a Guide to Thinking
- Parallel Circuits - âV = IâąR Calculations
- Resistance Ranking Tasks
- Series Circuits - âV = IâąR 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 (âV-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
- InterferencePatterns 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
- Electromagnetism
- Waves and Sound
- Forces in Two Dimensions
- Work, Energy, and Power
- Circular Motion and Gravitation
- Sound Waves
- 1-Dimensional Kinematics
- Circular, Satellite, and Rotational Motion
- Einstein's Theory of Special Relativity
- Waves, Sound and Light
- QuickTime Movies
- 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
- 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
- Frequently Asked Questions
- Purchasing the Download
- 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
- Classes (Legacy Version)
- Teacher Resources
- Subscriptions

- 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
- Sample Problems and Solutions
- Kinematic Equations Introduction
- Solving Problems with Kinematic Equations
- Kinematic Equations and Free Fall
- Kinematic Equations and Kinematic Graphs

## Check Your Understanding

Answer: d = 1720 m

Answer: a = 8.10 m/s/s

Answers: d = 33.1 m and v f = 25.5 m/s

Answers: a = 11.2 m/s/s and d = 79.8 m

Answer: t = 1.29 s

Answers: a = 243 m/s/s

Answer: a = 0.712 m/s/s

Answer: d = 704 m

Answer: d = 28.6 m

Answer: v i = 7.17 m/s

Answer: v i = 5.03 m/s and hang time = 1.03 s (except for in sports commericals)

Answer: a = 1.62*10 5 m/s/s

Answer: d = 48.0 m

Answer: t = 8.69 s

Answer: a = -1.08*10^6 m/s/s

Answer: d = -57.0 m (57.0 meters deep)

Answer: v i = 47.6 m/s

Answer: a = 2.86 m/s/s and t = 30. 8 s

Answer: a = 15.8 m/s/s

Answer: v i = 94.4 mi/hr

## Solutions to Above Problems

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s 2 )*(32.8 s) 2

Return to Problem 1

110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s) 2

110 m = (13.57 s 2 )*a

a = (110 m)/(13.57 s 2 )

a = 8.10 m/ s 2

Return to Problem 2

d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s 2 )*(2.60 s) 2

d = -33.1 m (- indicates direction)

v f = v i + a*t

v f = 0 + (-9.8 m/s 2 )*(2.60 s)

v f = -25.5 m/s (- indicates direction)

Return to Problem 3

a = (46.1 m/s - 18.5 m/s)/(2.47 s)

a = 11.2 m/s 2

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

d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s 2 )*(2.47 s) 2

d = 45.7 m + 34.1 m

(Note: the d can also be calculated using the equation v f 2 = v i 2 + 2*a*d)

Return to Problem 4

-1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s 2 )*(t) 2

-1.40 m = 0+ (-0.835 m/s 2 )*(t) 2

(-1.40 m)/(-0.835 m/s 2 ) = t 2

1.68 s 2 = t 2

Return to Problem 5

a = (444 m/s - 0 m/s)/(1.83 s)

a = 243 m/s 2

d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s 2 )*(1.83 s) 2

d = 0 m + 406 m

Return to Problem 6

(7.10 m/s) 2 = (0 m/s) 2 + 2*(a)*(35.4 m)

50.4 m 2 /s 2 = (0 m/s) 2 + (70.8 m)*a

(50.4 m 2 /s 2 )/(70.8 m) = a

a = 0.712 m/s 2

Return to Problem 7

(65 m/s) 2 = (0 m/s) 2 + 2*(3 m/s 2 )*d

4225 m 2 /s 2 = (0 m/s) 2 + (6 m/s 2 )*d

(4225 m 2 /s 2 )/(6 m/s 2 ) = d

Return to Problem 8

d = (22.4 m/s + 0 m/s)/2 *2.55 s

d = (11.2 m/s)*2.55 s

Return to Problem 9

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(2.62 m)

0 m 2 /s 2 = v i 2 - 51.35 m 2 /s 2

51.35 m 2 /s 2 = v i 2

v i = 7.17 m/s

Return to Problem 10

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(1.29 m)

0 m 2 /s 2 = v i 2 - 25.28 m 2 /s 2

25.28 m 2 /s 2 = v i 2

v i = 5.03 m/s

To find hang time, find the time to the peak and then double it.

0 m/s = 5.03 m/s + (-9.8 m/s 2 )*t up

-5.03 m/s = (-9.8 m/s 2 )*t up

(-5.03 m/s)/(-9.8 m/s 2 ) = t up

t up = 0.513 s

hang time = 1.03 s

Return to Problem 11

(521 m/s) 2 = (0 m/s) 2 + 2*(a)*(0.840 m)

271441 m 2 /s 2 = (0 m/s) 2 + (1.68 m)*a

(271441 m 2 /s 2 )/(1.68 m) = a

a = 1.62*10 5 m /s 2

Return to Problem 12

- (NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.)

First use: v f = v i + a*t

0 m/s = v i + (-9.8 m/s 2 )*(3.13 s)

0 m/s = v i - 30.7 m/s

v i = 30.7 m/s (30.674 m/s)

Now use: v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = (30.7 m/s) 2 + 2*(-9.8 m/s 2 )*(d)

0 m 2 /s 2 = (940 m 2 /s 2 ) + (-19.6 m/s 2 )*d

-940 m 2 /s 2 = (-19.6 m/s 2 )*d

(-940 m 2 /s 2 )/(-19.6 m/s 2 ) = d

Return to Problem 13

-370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s 2 )*(t) 2

-370 m = 0+ (-4.9 m/s 2 )*(t) 2

(-370 m)/(-4.9 m/s 2 ) = t 2

75.5 s 2 = t 2

Return to Problem 14

(0 m/s) 2 = (367 m/s) 2 + 2*(a)*(0.0621 m)

0 m 2 /s 2 = (134689 m 2 /s 2 ) + (0.1242 m)*a

-134689 m 2 /s 2 = (0.1242 m)*a

(-134689 m 2 /s 2 )/(0.1242 m) = a

a = -1.08*10 6 m /s 2

(The - sign indicates that the bullet slowed down.)

Return to Problem 15

d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s 2 )*(3.41 s) 2

d = 0 m+ 0.5*(-9.8 m/s 2 )*(11.63 s 2 )

d = -57.0 m

(NOTE: the - sign indicates direction)

Return to Problem 16

(0 m/s) 2 = v i 2 + 2*(- 3.90 m/s 2 )*(290 m)

0 m 2 /s 2 = v i 2 - 2262 m 2 /s 2

2262 m 2 /s 2 = v i 2

v i = 47.6 m /s

Return to Problem 17

( 88.3 m/s) 2 = (0 m/s) 2 + 2*(a)*(1365 m)

7797 m 2 /s 2 = (0 m 2 /s 2 ) + (2730 m)*a

7797 m 2 /s 2 = (2730 m)*a

(7797 m 2 /s 2 )/(2730 m) = a

a = 2.86 m/s 2

88.3 m/s = 0 m/s + (2.86 m/s 2 )*t

(88.3 m/s)/(2.86 m/s 2 ) = t

t = 30. 8 s

Return to Problem 18

( 112 m/s) 2 = (0 m/s) 2 + 2*(a)*(398 m)

12544 m 2 /s 2 = 0 m 2 /s 2 + (796 m)*a

12544 m 2 /s 2 = (796 m)*a

(12544 m 2 /s 2 )/(796 m) = a

a = 15.8 m/s 2

Return to Problem 19

v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(91.5 m)

0 m 2 /s 2 = v i 2 - 1793 m 2 /s 2

1793 m 2 /s 2 = v i 2

v i = 42.3 m/s

Now convert from m/s to mi/hr:

v i = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

v i = 94.4 mi/hr

Return to Problem 20

- school Campus Bookshelves
- menu_book Bookshelves
- perm_media Learning Objects
- login Login
- how_to_reg Request Instructor Account
- hub Instructor Commons
- Download Page (PDF)
- Download Full Book (PDF)
- Periodic Table
- Physics Constants
- Scientific Calculator
- Reference & Cite
- Tools expand_more
- Readability

selected template will load here

This action is not available.

## 1.4: Solving Physics Problems

- Last updated
- Save as PDF
- Page ID 16926

## Dimensional Analysis

Any physical quantity can be expressed as a product of a combination of the basic physical dimensions.

learning objectives

- Calculate the conversion from one kind of dimension to another

The dimension of a physical quantity indicates how it relates to one of the seven basic quantities. These fundamental quantities are:

- [A] Current
- [K] Temperature
- [mol] Amount of a Substance
- [cd] Luminous Intensity

As you can see, the symbol is enclosed in a pair of square brackets. This is often used to represent the dimension of individual basic quantity. An example of the use of basic dimensions is speed, which has a dimension of 1 in length and -1 in time; \(\mathrm{\frac{[L]}{[T]}=[LT^{−1}]}\). Any physical quantity can be expressed as a product of a combination of the basic physical dimensions.

Dimensional analysis is the practice of checking relations between physical quantities by identifying their dimensions. The dimension of any physical quantity is the combination of the basic physical dimensions that compose it. Dimensional analysis is based on the fact that physical law must be independent of the units used to measure the physical variables. It can be used to check the plausibility of derived equations, computations and hypotheses.

## Derived Dimensions

The dimensions of derived quantities may include few or all dimensions in individual basic quantities. In order to understand the technique to write dimensions of a derived quantity, we consider the case of force. Force is defined as:

\[\begin{align} \mathrm{F} &= \mathrm{m⋅a} \\ \mathrm{F} &= \mathrm{[M][a]} \end{align}\]

The dimension of acceleration, represented as [a], is itself a derived quantity being the ratio of velocity and time. In turn, velocity is also a derived quantity, being ratio of length and time.

\[\begin{align} \mathrm{F} &= \mathrm{[M][a]=[M][vT^{−1}]} \\ \mathrm{F} &= \mathrm{[M][LT^{−1}T^{−1}]=[MLT^{−2}]} \end{align}\]

## Dimensional Conversion

In practice, one might need to convert from one kind of dimension to another. For common conversions, you might already know how to convert off the top of your head. But for less common ones, it is helpful to know how to find the conversion factor:

\[\mathrm{Q=n_1u_1=n_2u_2}\]

where n represents the amount per u dimensions. You can then use ratios to figure out the conversion:

\[\mathrm{n_2=\dfrac{u_2}{u_1}⋅n_1}\]

## Trigonometry

Trigonometry is central to the use of free body diagrams, which help visually represent difficult physics problems.

- Explain why trigonometry is useful in determining horizontal and vertical components of forces

## 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 helpful in visually identifying which components are unknown and where the moments are applied. They can help analyze a problem, whether it is static or dynamic.

When people draw free body diagrams, often not everything is perfectly parallel and perpendicular. Sometimes people need to analyze the horizontal and vertical components of forces and object orientation. When the force or object is not acting parallel to the x or y axis, people can employ basic trigonometry to use the simplest components of the action to analyze it. Basically, everything should be considered in terms of x and y , which sometimes takes some manipulation.

Free Body Diagram : The rod is hinged from a wall and is held with the help of a string.

A rod ‘AB’ is hinged at ‘A’ from a wall and is held still with the help of a string, as shown in. This exercise involves drawing the free body diagram. To make the problem easier, the force F will be expressed in terms of its horizontal and vertical components. Removing all other elements from the image helps produce the finished free body diagram.

Free Body Diagram : The free body diagram as a finished product

Given the finished free body diagram, people can use their knowledge of trigonometry and the laws of sine and cosine to mathematically and numerical represent the horizontal and vertical components:

## General Problem-Solving Tricks

Free body diagrams use geometry and vectors to visually represent the problem.

- Construct a free-body diagram for a physical scenario

In physics, most problems are solved much more easily when a free body diagram is used. This uses geometry and vectors to visually represent to problem, and trigonometry is also used in determining horizontal and vertical components of forces and objects.

Purpose: Free body diagrams are very helpful in visually identifying which components are unknown, where the moments are applied, and help analyze a problem, whether static or dynamic.

## How to Make A Free Body Diagram

To draw a free body diagram, do not worry about drawing it to scale, this will just be what you use to help yourself identify the problems. First you want to model the body, in one of three ways:

- As a particle. This model may be used when any turning effects are zero or have zero interest even though the body itself may be extended. The body may be represented by a small symbolic blob and the diagram reduces to a set of concurrent arrows. A force on a particle is a bound vector.
- rigid extended . Stresses and strains are of no interest but turning effects are. A force arrow should lie along the line of force, but where along the line is irrelevant. A force on an extended rigid body is a sliding vector.
- non-rigid extended . The point of application of a force becomes crucial and has to be indicated on the diagram. A force on a non-rigid body is a bound vector. Some engineers use the tail of the arrow to indicate the point of application. Others use the tip.

## Do’s and Don’ts

What to include: Since a free body diagram represents the body itself and the external forces on it. So you will want to include the following things in the diagram:

- The body: This is usually sketched in a schematic way depending on the body – particle/extended, rigid/non-rigid – and on what questions are to be answered. Thus if rotation of the body and torque is in consideration, an indication of size and shape of the body is needed.
- The external forces: These are indicated by labelled arrows. In a fully solved problem, a force arrow is capable of indicating the direction, the magnitude the point of application. These forces can be friction, gravity, normal force, drag, tension, etc…

## Do not include:

- Do not show bodies other than the body of interest.
- Do not show forces exerted by the body.
- Internal forces acting on various parts of the body by other parts of the body.
- Any velocity or acceleration is left out.

How To Solve Any Physics Problem : Learn five simple steps in five minutes! In this episode we cover the most effective problem-solving method I’ve encountered and call upon some fuzzy friends to help us remember the steps.

Free Body Diagram : Use this figure to work through the example problem.

- Dimensional analysis is the practice of checking relations amount physical quantities by identifying their dimensions.
- It is common to be faced with a problem that uses different dimensions to express the same basic quantity. The following equation can be used to find the conversion factor between the two derived dimensions: \(\mathrm{n_2=\frac{u_2}{u_1} \times n_1}\).
- Dimensional analysis can also be used as a simple check to computations, theories and hypotheses.
- It is important to identify the problem and the unknowns and draw them in a free body diagram.
- The laws of cosine and sine can be used to determine the vertical and horizontal components of the different elements of the diagram.
- Free body diagrams use geometry and vectors to visually represent physics problems.
- A free body diagram lets you visually isolate the problem you are trying to solve, and simplify it into simple geometry and trigonometry.
- When drawing these diagrams, it is helpful to only draw the body it self, and the forces acting on it.
- Drawing other objects and internal forces can condense the diagram and cause it to be less helpful.
- dimension : A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
- trigonometry : The branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, particularly the trigonometric functions.
- static : Fixed in place; having no motion.
- dynamic : Changing; active; in motion.

LICENSES AND ATTRIBUTIONS

CC LICENSED CONTENT, SHARED PREVIOUSLY

- Curation and Revision. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike

CC LICENSED CONTENT, SPECIFIC ATTRIBUTION

- Dimensional analysis. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Dimensional_analysis . License : CC BY-SA: Attribution-ShareAlike
- Sunil Kumar Singh, Dimensional Analysis. September 18, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m15037/latest/ . License : CC BY: Attribution
- dimension. Provided by : Wiktionary. Located at : http://en.wiktionary.org/wiki/dimension . License : CC BY-SA: Attribution-ShareAlike
- Sunil Kumar Singh, Free Body Diagram (Application). September 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m14720/latest/ . License : CC BY: Attribution
- trigonometry. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/trigonometry . License : CC BY-SA: Attribution-ShareAlike
- Sunil Kumar Singh, Free Body Diagram (Application). February 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m14720/latest/ . License : CC BY: Attribution
- Free body diagram. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Free_body_diagram . License : CC BY-SA: Attribution-ShareAlike
- dynamic. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/dynamic . License : CC BY-SA: Attribution-ShareAlike
- static. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/static . License : CC BY-SA: Attribution-ShareAlike
- Free Body Diagram. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Free_Body_Diagram.png . License : CC BY-SA: Attribution-ShareAlike
- How To Solve Any Physics Problem. Located at : http://www.youtube.com/watch?v=YocWuzi4JhY . License : Public Domain: No Known Copyright . License Terms : Standard YouTube license

- MyU : For Students, Faculty, and Staff

## Jacquelyn Burt Earns 2024 John Tate Award for Excellence in Undergraduate Advising

Department of Computer Science & Engineering Undergraduate Academic Advisor Jacquelyn Burt was awarded the 2024 John Tate Award for Excellence in Undergraduate Advising. Named in honor of John Tate, Professor of Physics and first Dean of University College (1930-41), the Tate Awards serve to recognize and reward high-quality academic advising, calling attention to the contribution academic advising makes to helping students formulate and achieve intellectual, career, and personal goals.

âI thought it was a trick when I got the email that I was being nominated,â said Jacquelyn. âWithin the advising field, this award is a big deal; I described it to my parents as âthe advising Grammysâ. Part of what makes it so cool is the nomination process, which involves several letters of support from students and colleagues as well as putting together a kind of portfolio of some of the programs and resources Iâve helped develop. So many different people contributed to that on my behalf, so it was really powerful to be reminded of the impact of my work and the amazing colleagues and students I get to love!â

Jacquelyn is a lifelong Gopher, earning her B.S. in business marketing education in 2014 and her M.Ed. in education policy and leadership in 2019. She joined the CS&E student services team in 2019, where she quickly developed a reputation as a staunch ally and advocate for her students. In 2021, Jacquelyn received the Gopher Spirit Award , recognizing the U of M advisor who contributes to a positive office culture, is inclusive, and brings others up. âI feel the most useful when a student or colleague is misunderstanding something, or experiencing a lot of stress, and I am able to help separate it into smaller pieces or come up with a different way of looking at it,â said Jacquelyn. âIf I can shine light on something, help shift a lens or perspective, or give an idea or experience a bit of breathing room, Iâm doing my job.â

When asked about what inspired her to work in advising, Jacquelyn replied, âWhen I first came to the University of Minnesota as a freshman, I was a family and social sciences major - I love relationships and helping, and so figured a career in marriage and family therapy sounded good. However, Iâve also always loved education and felt most at home at school - when I finished my undergraduate degree, I didnât want to leave college because I loved it so much! Student advising seemed like a cool sweet spot between classroom teaching, advocacy, and being in a helping role. Ultimately, Iâve really come to see advising as facilitation work: I help students identify and navigate barriers to their goals, experiences, and personal development.â

As an undergraduate advisor, Jacquelyn manages a caseload of over 450 students in multiple majors, minors and other departmental programs. On top of her advising duties, Jacquelyn has undertaken a number of projects to better the undergraduate student experience, including establishing a weekly newsletter; designing, promoting, and executing departmental events and programs; and developing and teaching students through a variety of training and credit-bearing coursework. Most notably, Jacquelyn created and now facilitates mandatory implicit bias training for all 200+ undergraduate teaching assistants, as well as teaching CSCI 2915: Teaching Methods in Computer Science (a leadership and communication skills seminar) each semester.

âWithin our student services team, weâve developed a great culture of initiative and problem-solving: like, if you identify a problem and have or can create tools to help address it, amazing - you go get it!â said Jacquelyn. âWe all believe that students deserve to have positive and supportive experiences while they are here, and weâve built an advising team that trusts each of us to help bear that belief out. I definitely could not do my job without the collaboration, encouragement, and love of the whole team.â

On top of her work within CS&E, Jacquelyn has personally designed advising resources that have made an impact for undergraduate students across the entire university. Her âExplore & Expandâ tool (originally developed for the collegeâs major/minor expo) is used widely throughout the entire University, particularly within the Center for Academic Planning and Exploration office. Additionally, her âAcademic Progress Audit System Guideâ resource (originally used within the departmental âWelcome to the Majorâ workshops) has been used in advisor training and onboarding. Above all, Jacquelyn has a keen eye for making connections, and for communicating things that can be overwhelmingly complex with both clarity and compassion.

âWhen I applied for this job, I had to come up with an âadvising philosophy,ââ said Jacquelyn. âWhat I landed on is anytime a student leaves an interaction with me, I want them to feel a little bit more seen, supported, and celebrated. I am a naturally celebratory person, which Iâve learned to embrace - and this award is a wonderful way to celebrate the work of advising!â

Learn more about the John Tate Award at the Provost website .Â

## Related news releases

- Professors Shekhar and Mokbel part of Institute Grant on Spatial Data Science for Arctic and Antarctic Regions
- Computing Ethics Project Receives $400,000 Grant
- Kelly Thomas wins 2022 Outstanding Community Service Award
- CS&Eâs Jacquelyn Burt wins Gopher Spirit Award
- Graduate staff recognized by Center for Educational Innovation
- Publications
- Future undergraduate students
- Future transfer students
- Future graduate students
- Future international students
- Diversity and Inclusion Opportunities
- Learn abroad
- Living Learning Communities
- Mentor programs
- Programs for women
- Student groups
- Visit, Apply & Next Steps
- Information for current students
- Departments and majors overview
- Departments
- Undergraduate majors
- Graduate programs
- Integrated Degree Programs
- Additional degree-granting programs
- Online learning
- Academic Advising overview
- Academic Advising FAQ
- Academic Advising Blog
- Appointments and drop-ins
- Academic support
- Commencement
- Four-year plans
- Honors advising
- Policies, procedures, and forms
- Career Services overview
- Resumes and cover letters
- Jobs and internships
- Interviews and job offers
- CSE Career Fair
- Major and career exploration
- Graduate school
- Collegiate Life overview
- Scholarships
- Diversity & Inclusivity Alliance
- Anderson Student Innovation Labs
- Information for alumni
- Get engaged with CSE
- Upcoming events
- CSE Alumni Society Board
- Alumni volunteer interest form
- Golden Medallion Society Reunion
- 50-Year Reunion
- Alumni honors and awards
- Outstanding Achievement
- Alumni Service
- Distinguished Leadership
- Honorary Doctorate Degrees
- Nobel Laureates
- Alumni resources
- Alumni career resources
- Alumni news outlets
- CSE branded clothing
- International alumni resources
- Inventing Tomorrow magazine
- Update your info
- CSE giving overview
- Why give to CSE?
- College priorities
- Give online now
- External relations
- Giving priorities
- Donor stories
- Impact of giving
- Ways to give to CSE
- Matching gifts
- CSE directories
- Invest in your company and the future
- Recruit our students
- Connect with researchers
- K-12 initiatives
- Diversity initiatives
- Research news
- Give to CSE
- CSE priorities
- Corporate relations
- Information for faculty and staff
- Administrative offices overview
- Office of the Dean
- Academic affairs
- Finance and Operations
- Communications
- Human resources
- Undergraduate programs and student services
- CSE Committees
- CSE policies overview
- Academic policies
- Faculty hiring and tenure policies
- Finance policies and information
- Graduate education policies
- Human resources policies
- Research policies
- Research overview
- Research centers and facilities
- Research proposal submission process
- Research safety
- Award-winning CSE faculty
- National academies
- University awards
- Honorary professorships
- Collegiate awards
- Other CSE honors and awards
- Staff awards
- Performance Management Process
- Work. With Flexibility in CSE
- K-12 outreach overview
- Summer camps
- Outreach events
- Enrichment programs
- Field trips and tours
- CSE K-12 Virtual Classroom Resources
- Educator development
- Sponsor an event

## IMAGES

## VIDEO

## COMMENTS

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.

Solving problems which involve forces, friction, and Newton's Laws: A step-by-step guide | Phyley Support Ukraine đșđŠ Help Ukrainian Army Humanitarian Assistance to Ukrainians In this tutorial you will learn how to examine and solve problems which involve forces and applications of Newton's Laws.

Correct answer: The formula for force is. We are given the mass, but we will need to calculate the acceleration to use in the formula. We know the initial velocity (zero because the box starts from rest), final velocity, and distance traveled. Using these values, we can find the acceleration using the formula.

Unit 1 One-dimensional motion. Unit 2 Two-dimensional motion. Unit 3 Forces and Newton's laws of motion. Unit 4 Centripetal force and gravitation. Unit 5 Work and energy. Unit 6 Impacts and linear momentum. Unit 7 Torque and angular momentum. Unit 8 Oscillations and mechanical waves. Unit 9 Fluids.

Resolution of Forces Equilibrium and Statics Net Force Problems Revisited Inclined Planes Two-Body Problems This part of Lesson 3 focuses on net force-acceleration problems in which an applied force is directed at an angle to the horizontal.

Newton's second law: Solving for force, mass, and acceleration. A stunt woman of mass m falls into a net during the filming of an action movie. Assume she experiences upward acceleration magnitude a while touching the net.

Tension. A tension is a force along the length of a medium, especially a force carried by a flexible medium, such as a rope or cable. The word "tension " comes from a Latin word meaning "to stretch.". Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons.

Problem-Solving Strategy for Newton's Laws of Motion. Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton's laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation. Such a sketch is shown in Figure(a).

Problem-Solving Strategy: Drawing Free-Body Diagrams. Draw the object under consideration. If you are treating the object as a particle, represent the object as a point. Place this point at the origin of an xy-coordinate system. Include all forces that act on the object, representing these forces as vectors.

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.

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton's laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation. Such a sketch is shown in Figure 4.20 (a).

Namely, we use Newton's second law to relate the motion of the object to the forces involved. To be specific we can, Draw the forces exerted on the object in question. Write down Newton's second law ( a = ÎŁ F m) â. for a direction in which the tension is directed. Solve for the tension using the Newton's second law equation a = ÎŁ F m.

Problem 1: For each collection of listed forces, determine the vector sum or the net force. Audio Guided Solution Show Answer Problem 2: Hector is walking his dog (Fido) around the neighborhood. Upon arriving at Fidella's house (a friend of Fido's), Fido turns part mule and refuses to continue on the walk.

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton's laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation. Such a sketch is shown in Figure 1 (a).

SAT Questions on Forces with Solutions Physics Practice Questions with Solutions on Forces and Newton's Laws. Formulas and Constants Physics Formulas Reference SI Prefixes Used with Units in Physics, Chemistry and Engineering Constants in Physics, Chemistry and Engineering {ezoic-ad-1}

Example 2.4.3. A block is attached to one end of a massless spring, the other end of which is attached to a vertical fixed peg in a frictionless horizontal surface. The block is spun around a circle, and the spring stretches as a result of this motion. In fact, the faster the motion, the more the spring stretches.

Problem 22: Brandon is the catcher for the Varsity baseball team. He exerts a forward force on the .145-kg baseball to bring it to rest from a speed of 38.2 m/s. During the process, his hand recoils a distance of 0.135 m. Determine the acceleration of the ball and the force which is applied to it by Brandon.

Force Problems On this page I put together a collection of force problems to help you understand forces better. The required equations and background reading to solve these problems are given on the friction page, the equilibrium page, and Newton's second law page . Problem # 1 A ball of mass m is hanging on a wall with a string, as shown.

You divide by the radius which was 0.5, and you get that the force of tension had to be 100 Newtons. So in this case, the force of tension, which is the centripetal force, is equal to 100 Newtons. Now, some of you might be thinking, hey, this was way too much work for what ended up being a really simple problem.

We can solve for Î p by rearranging the equation. F net = Î p Î t. to be. Î p = F net Î t . F net Î t is known as impulse and this equation is known as the impulse-momentum theorem. From the equation, we see that the impulse equals the average net external force multiplied by the time this force acts.

Problem 1 A block of mass 5 Kg is suspended by a string to a ceiling and is at rest. Find the force Fc exerted by the ceiling on the string. Assume the mass of the string to be negligible. Solution a) The free body diagram below shows the weight W and the tension T 1 acting on the block.

237 likes, 13 comments - physics_ontable on February 3, 2024: "Question:- Consider a wire bent in the shape of a semi-circle with a radius of 2 meters. If a cur..." Physics_ontable on Instagram: "Question:- Consider a wire bent in the shape of a semi-circle with a radius of 2 meters.

A useful problem-solving strategy was presented for use with these equations and two examples were given that illustrated the use of the strategy. Then, the application of the kinematic equations and the problem-solving strategy to free-fall motion was discussed and illustrated. In this part of Lesson 6, several sample problems will be presented.

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.

Department of Computer Science & Engineering Undergraduate Academic Advisor Jacquelyn Burt was awarded the 2024 John Tate Award for Excellence in Undergraduate Advising. Named in honor of John Tate, Professor of Physics and first Dean of University College (1930-41), the Tate Awards serve to recognize and reward high-quality academic advising, calling attention to the contribution academic ...