Slide 1 / 127 Slide 2 / 127 Work and Energy www.njctl.org Slide 3 / 127 Slide 4 / 127 Table of Contents How to Use this File Click on the topic to go to that section Each topic is composed of brief direct instruction · Energy and Work · There are formative assessment questions after every topic · · Conservative and Non-Conservative Forces denoted by black text and a number in the upper left. Conservation of Total Mechanical Energy · >Students work in groups to solve these problems but use · Two Dimensional Forces and Work student responders to enter their own answers. · Work done by a Position Dependent Force >Designed for SMART Response PE student response · Position Dependent Potential Energy Graphical Analysis systems. · Power >Use only as many questions as necessary for a sufficient · Placeholder number of students to learn a topic. Full information on how to teach with NJCTL courses can be · found at njctl.org/courses/teaching methods Slide 5 / 127 Slide 6 / 127 Energy The concept of energy is so fundamental, like space and time, that there is no real good definition of what it "is." Energy and Work However, just like space and time, that doesn't stop us from doing very useful calculations with energy. There are some things we can say about it: It is the ability to do work. · It can be stored. · It can be changed from one form to another (light to thermal · energy, mechanical to thermal energy, gravitational potential energy to kinetic energy). It can be measured and compared. · Return to Table of Contents Did you notice a term in the bullet list above that hasn't been defined yet?
Slide 7 / 127 Slide 8 / 127 Work Work You're not! Work has the ability to increase or decrease the amount of Energy at a certain position and time in space. Work, in physics terms, is defined as the exertion of a force over a displacement where only the component of the force in Work has the same units as energy - Joules. the direction of the motion is relevant. For now, we'll assume a constant force. What is Work? If you're just holding a box, you are certainly exerting an It is not what is talked about in common language. It is upward force on the box (to keep gravity from pulling it to the unfortunate that sometimes Physics uses words that are used ground), but it's not moving, so there is no displacement. everyday - in a quite different fashion. For example - if you're Therefore, there is no work. holding up a heavy box, do you think you're doing work? You learned the following equation: W = Fd parallel = Fdcosθ where θ is the angle between the Force and the displacement. Slide 9 / 127 Slide 10 / 127 Work System and Environment A more elegant way to represent this is by using vector The system and the environment. notation and a specific type of vector multiplication called the A system is a small segment of the universe that will be vector dot product, or just dot product. considered in solving a specific problem, and we will erect a boundary around it. Any force or object outside this boundary The result of the dot product of two vectors is a scalar - and is will not be considered. the length of one vector projected on the other - so this The environment is everything outside the system boundary. achieves the goal of just using the component of force along the direction of the displacement. The system can be a particle, a group of particles, an object, an area of space, and its size and shape is totally determined by how you want to solve the problem. But where is the work being done? Where is the energy being increased or decreased? The entire universe? We need two more definitions to bound these questions. Why are we defining a system and its environment? Slide 11 / 127 Slide 12 / 127 1 Which of the following are characteristics of energy? System and Environment A Thermal energy can be changed to mechanical energy. So we can make the problem solvable. B Mechanical energy can be changed to thermal energy. By defining an appropriate system, we can isolate the forces that are within the system from the forces that act on the C Energy can be stored. system from the environment. If the forces are internal to the system, then there is no change D Energy has the ability to do work. in the energy of the system (as long as we don't consider thermal energy - which we won't for now). E All of the above. If the forces are external, then there will be a change in the energy of the system.
Slide 12 (Answer) / 127 Slide 13 / 127 1 Which of the following are characteristics of energy? 2 A system is defined as: A Thermal energy can be changed to mechanical energy. A All the forces that are external to the boundary between it and the rest of the universe. B Mechanical energy can be changed to thermal energy. B A small segment of the universe that has no internal forces. Answer C Energy can be stored. E C A small segment of the universe that is chosen to solve a D Energy has the ability to do work. problem. Forces internal to the system can change its total mechanical energy. E All of the above. D A small segment of the universe that is chosen to solve a problem. Forces internal to the system cannot change its [This object is a pull tab] total mechanical energy. E Uniquely for a problem. Only one specific system can be used to solve a problem. Slide 13 (Answer) / 127 Slide 14 / 127 2 A system is defined as: 3 In solving an energy problem, the environment is defined as: A All the forces that are external to the boundary between it A An area that contains no forces. and the rest of the universe. B An area that is partially in, and partially outside the system. Answer B A small segment of the universe that has no internal forces. D C The source of the external forces on the system. C A small segment of the universe that is chosen to solve a problem. Forces internal to the system can change its total D The source of the internal forces on the system. mechanical energy. E A small area within the system. D A small segment of the universe that is chosen to solve a [This object is a pull tab] problem. Forces internal to the system cannot change its total mechanical energy. E Uniquely for a problem. Only one specific system can be used to solve a problem. Slide 14 (Answer) / 127 Slide 15 / 127 3 In solving an energy problem, the environment is defined as: Work A An area that contains no forces. If the force acts in the same direction as the object's motion, B An area that is partially in, and partially outside the system. · then the work done is positive, and the energy of the object increases. C The source of the external forces on the system. Answer If the force acts in the opposite direction as the object's · C D The source of the internal forces on the system. motion, then the work done is negative and the energy of the object decreases. E A small area within the system. If the object does not move, then zero work is done. · Work is a scalar - it has magnitude, but not direction. · [This object is a pull tab] The unit of work is the Joule - just like energy. ·
Slide 16 / 127 Slide 17 / 127 Units of Work and Energy James Prescott Joule Joule was instrumental in showing that different forms of energy can be converted into other forms - most notably This equation gives us the units of work. Since force is mechanical to thermal energy. measured in Newtons (N) and distance is measured in meters (m) the unit of work is the Newton-meter (N-m). Before Joule, it was commonly accepted that thermal energy is conserved. This was disproved by Joule's And since N = kg-m/s 2 ; a N-m also equals a kg-m 2 /s 2 . extremely accurate and precise measurements showing how thermal energy is just another form of energy. In honor of James Joule, who made critical contributions in developing the idea of energy, the unit of work and energy This was made possible by his experience as a brewer is also known as the Joule (J). which relied on very accurate measurements of temperature, time and volume! 1 Joule = 1 Newton-meter = 1 kilogram-meter 2 /second 2 1 J = 1 N-m = 1 kg-m 2 /s 2 Slide 18 / 127 Slide 18 (Answer) / 127 4 Which is a valid unit for work? 4 Which is a valid unit for work? A N/m A N/m B N-s B N-s Answer C W C W E D J/s D J/s E J E J [This object is a pull tab] Slide 19 / 127 Slide 20 / 127 Force and Work 5 A 36.0 N force is applied to an object that moves 11.0 m in the same direction as the applied force on a frictionless surface. How F much work is done on the object? v F # x F v # x F v # x
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