Work Energy Principle

10 Key excerpts on "Work Energy Principle"

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  Conceptual Dynamics

  • Richard C. Hill, Kirstie Plantenberg(Authors)
  • 2013(Publication Date)
  • SDC Publications

    (Publisher)

  However, the work-energy method is not very useful for determining a body's acceleration or the direction of its velocity. The main idea with an energy approach is to analyze how a body's energy changes as it moves. The amount and form of a body's energy will change due to the body either doing work or due to work being done on the body. Conceptual Dynamics Kinetics: Chapter 7 – Particle Work and Energy 7 - 3 7.1) WORK Work is a concept that has meaning in our everyday lives. Everyone has done “work.” We “work” for a living, we “work”out and we “work” hard. This is not exactly what we will be talking about here. If you are doing physical “work” like pushing or lifting something, then you are doing the type of work that we will learn how to calculate in this chapter. In the study of dynamics, work has a very specific mathematical definition that is given by Equation 7.1-1. This equation gives the most general equation for work; however, work in its most basic form is simply a force applied over a distance (U = Fd ). So if you push a box across the floor from the living room to the kitchen, then you are doing work. However, if the box is very heavy and you push and push and sweat and sweat and the box does not move, then you have done no work. Even though you are exhausted, the box did not move and, therefore, the force you applied to the box did not do any work. Work: 2 1 1 2 U d     r r F r (7.1-1) U 1-2 = work done by F from r 1 to r 2 (work is a scalar) F = force vector r = position vector Work is the amount of energy transferred by a force acting through a distance. One definition of work is “The amount of energy transferred by a force acting through a distance.” What does that mean in the context of dynamics? If a force is applied to a particle and the force causes that particle to move through a distance, the force has done work. This also means that the force has transferred some energy to (or from) the particle.

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  Principles of Physics: Extended, International Adaptation

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  3. Only the component of F → that is along the displacement d → can do work on the object. 4. When two or more forces act on an object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force F → net of those forces. 5. For a particle, a change ΔK in the kinetic energy equals the net work W done on the particle: ΔK = K f − K i = W (work–kinetic energy theorem), in which K i is the initial kinetic energy of the particle and K f is the kinetic energy after the work is done. The equation rearranged gives us K f = K i + W. LEARNING OBJECTIVES 7.2 Work and Kinetic Energy 149 Work If you accelerate an object to a greater speed by applying a force to the object, you increase the kinetic energy K (= 1 _ 2 mv 2 ) of the object. Similarly, if you decelerate the object to a lesser speed by applying a force, you decrease the kinetic energy of the object. We account for these changes in kinetic energy by saying that your force has transferred energy to the object from yourself or from the object to yourself. In such a transfer of energy via a force, work W is said to be done on the object by the force. More formally, we define work as follows: Work W is energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, and energy trans- ferred from the object is negative work. “Work,” then, is transferred energy; “doing work” is the act of transferring the energy. Work has the same units as energy and is a scalar quantity. The term transfer can be misleading. It does not mean that anything material flows into or out of the object; that is, the transfer is not like a flow of water. Rather, it is like the electronic transfer of money between two bank accounts: The number in one account goes up while the number in the other account goes down, with nothing material passing between the two accounts.

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  Fundamentals of Physics, Volume 1

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  More formally, we define work as follows: Work W is energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, and energy trans- ferred from the object is negative work. “Work,” then, is transferred energy; “doing work” is the act of transferring the energy. Work has the same units as energy and is a scalar quantity. The term transfer can be misleading. It does not mean that anything mate- rial flows into or out of the object; that is, the transfer is not like a flow of water. Rather, it is like the electronic transfer of money between two bank accounts: The number in one account goes up while the number in the other account goes down, with nothing material passing between the two accounts. Note that we are not concerned here with the common meaning of the word “work,” which implies that any physical or mental labor is work. For example, if you push hard against a wall, you tire because of the continuously repeated muscle contractions that are required, and you are, in the common sense, work- ing. However, such effort does not cause an energy transfer to or from the wall and thus is not work done on the wall as defined here. To avoid confusion in this chapter, we shall use the symbol W only for work and shall represent a weight with its equivalent mg. Work and Kinetic Energy Finding an Expression for Work Let us find an expression for work by considering a bead that can slide along a frictionless wire that is stretched along a horizontal x axis (Fig. 7.2.1). A con- stant force F → , directed at an angle ϕ to the wire, accelerates the bead along the wire. We can relate the force and the acceleration with Newton’s second law, written for components along the x axis: F x = ma x , (7.2.1) where m is the bead’s mass. As the bead moves through a displacement d → , the force changes the bead’s velocity from an initial value v → 0 to some other value v → .

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  Introduction to Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  In physics, when a net force performs work on an object, there is always a result from the effort. The result is a change in the kinetic energy of the object. As we will now see, the relation- ship that relates work to the change in kinetic energy is known as the work–energy theorem. This theorem is obtained by bringing together three basic concepts that we’ve already learned about. First, we’ll apply Newton’s second law of motion, SF 5 ma, which relates the net force SF to the acceleration a of an object. Then, we’ll determine the work done by the net force when the object moves through a certain distance. Finally, we’ll use Equation 2.9, one of the equations of kinematics, to relate the distance and acceleration to the initial and final speeds of the object. The result of this approach will be the work–energy theorem. To gain some insight into the idea of kinetic energy and the work–energy theorem, look at Figure 6.5, where a constant net external force S F B acts on an airplane of mass m. This net force is the vector sum of all the external forces acting on the plane, and, for simplicity, it is assumed to have the same direction as the displacement s B . According to Newton’s second law, the net force produces an acceleration a, given by a 5 SF/m. Check Your Understanding (The answers are given at the end of the book.) 1. Two forces F B 1 and F B 2 are acting on the box shown in the drawing, causing the box to move across the floor. The two force vectors are drawn to scale. Which one of the following statements is correct? (a) F B 2 does more work than F B 1 does. (b) F B 1 does more work than F B 2 does. (c) Both forces do the same amount of work. (d) Neither force does any work. 2. A box is being moved with a velocity v B by a force P B (in the same direction as v B ) along a level horizontal floor. The normal force is F B N , the kinetic frictional force is f B k , and the weight is m g B .

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Kinetic energy, like work, is a scalar quantity. These are not surprising observations, because work and kinetic energy are closely related, as is clear from the following statement of the work–energy theorem. THEWORK– ENERGYTHEOREM WhenanetexternalforcedoesworkWonanobject,thekineticenergyofthe objectchangesfromitsinitialvalueofKE 0 toafinalvalueofKE f ,thedifference betweenthetwovaluesbeingequaltothework:   W= KE f − KE 0 = 1  _  2  m υ f  2 − 1  _  2  m υ 0  2  (6.3) Work done by net ext. force *For extra emphasis, the final speed is now represented by the symbol υ f , rather than υ. INTERACTIVE FIGURE 6.5 A constant net external force Σ →  Facts over a displacement → s and does work on the plane. As a result of the work done, the plane’s kinetic energy changes. s v 0 v f Final kinetic energy = m f 2 _ 1 2 1 2 Initial kinetic energy = m 0 2 _ ΣF ΣF υ υ 6.2 The Work–Energy Theorem and Kinetic Energy 163 The work–energy theorem may be derived for any direction of the force relative to the displacement, not just the situation in InteractiveFigure6.5. In fact, the force may even vary from point to point along a path that is curved rather than straight, and the theorem remains valid. According to the work–energy theorem, a moving object has kinetic energy, because work was done to accelerate the object from rest to a speed υ f . † Conversely, an object with kinetic energy can perform work, if it is allowed to push or pull on another object. Example 4 illustrates the work–energy theorem and considers a single force that does work to change the kinetic energy of a space probe. Description Symbol Value Comment ExplicitData Mass m 474 kg Initial speed υ 0 275 m/s Magnitude of force F 5.60 × 10 −2 N Magnitude of displacement s 2.42 × 10 9 m ImplicitData Angle between force → Fand displacement → s θ 0° The force is parallel to the displacement.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  6.2 The Work–Energy Theorem and Kinetic Energy 149 The work–energy theorem may be derived for any direction of the force relative to the displace- ment, not just the situation in Interactive Figure 6.5. In fact, the force may even vary from point to point along a path that is curved rather than straight, and the theorem remains valid. According to the work–energy theorem, a moving object has kinetic energy, because work was done to accelerate the object from rest to a speed υ f . † Conversely, an object with kinetic energy can perform work, if it is allowed to push or pull on another object. Example 4 illustrates the work–energy theorem and considers a single force that does work to change the kinetic energy of a space probe. † Strictly speaking, the work–energy theorem, as given by Equation 6.3, applies only to a single particle, which occupies a mathematical point in space. A macroscopic object, however, is a collection or system of particles and is spread out over a region of space. Therefore, when a force is applied to a macroscopic object, the point of application of the force may be anywhere on the object. To take into account this and other factors, a discussion of work and energy is required that is beyond the scope of this text. The interested reader may refer to A. B. Arons, The Physics Teacher, October 1989, p. 506. Analyzing Multiple-Concept Problems EXAMPLE 4 The Physics of an Ion Propulsion Drive The space probe Deep Space 1 was launched October 24, 1998, and it used a type of engine called an ion propulsion drive. An ion propulsion drive generates only a weak force (or thrust), but can do so for long periods of time using only small amounts of fuel. Suppose the probe, which has a mass of 474 kg, is traveling at an initial speed of 275 m/s. No forces act on it except the 5.60 × 10 ‒2 -N thrust of its engine. This external force F → is directed parallel to the displacement s → , which has a magnitude of 2.42 × 10 9 m (see Figure 6.6).

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  Physics, Volume 1

  • Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  F B CHAPTER 11 CHAPTER 11 ENERGY 1: WORK AND KINETIC ENERGY W e have seen how Newton’s laws are useful in un- derstanding and analyzing a wide variety of problems in mechanics. In this and the following two chapters we consider a different approach based on one of the truly fundamental and universal concepts in physics: energy. There are many kinds of energy. In this chapter we consider one particular form — kinetic energy, the energy associated with a body because of its motion. We also introduce the concept of work, which is re- lated to kinetic energy through the work – energy theorem. This theorem, derived from Newton’s laws, pro- vides new and different insight into the behavior of mechanical systems. In Chapter 12 we introduce a sec- ond kind of energy — potential energy — and begin developing a conservation law for energy. In Chapter 13 we discuss energy in a more comprehensive way and generalize the law of conservation of energy, which is one of the most useful laws of physics. application moves through some distance, and one way to define the energy of a system is a measure of its capacity to do work. In the case of the wheelchair rider, he does work because he exerts a force as the wheelchair moves forward through some distance. For him to do work, he must ex- pend some of his supply of energy — that is, the chemical energy stored in his muscle fibers — which can be replen- ished from his body’s store of energy through resting and which ultimately comes from the food he eats. The energy stored in a system may take many forms: for example, chemical, electrical, gravitational, or mechanical. In this chapter we study the relationship between work and one particular type of energy — the energy of motion of a body, which we call kinetic energy. 11- 2 WORK DONE BY A CONSTANT FORCE Figure 11-2a shows a block of mass m being lifted through a vertical distance h by a winch that is turned by a motor.

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  The Engineering Dynamics Course Companion, Part 1

  ParticlesKinematics and Kinetics

  • Edward Diehl(Author)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  where KE 1 D Kinetic Energy at state 1 PE 1 D Potential Energy at state 1 U 1!2 D External Work acting on system between states 1 and 2 KE 2 D Kinetic Energy at state 2 PE 2 D Potential Energy at state 2 The Work-Energy equation might seem familiar to students who have taken or are taking Fluid Mechanics or Thermodynamics. You can think of this as the solid mechanics form of energy accounting. It’s good to use the following grouping to organize how you think of energy accounting: KE 1 C PE 1 „ ƒ‚ … Initial Energy C U 1!2 „ƒ‚… Outside Work Happens D KE 2 C PE 2 „ ƒ‚ … Final Energy : Note that this equation can be used in multiple locations in between, not just initial and final. We can break problems apart into stages, and this can be a very useful solution strategy in many problems. 8.2. WORK (U) 131 F F ∆x ∆y Figure 8.2: Newtdog works by applying forces in the direction of motion (©E. Diehl). Energy methods are powerful tools to solve many kinds of engineering problems, often as an alternative to other solution techniques that become excessively complicated. We’ll see that the kinetic energy change is closely related to N2L since it’s derived from it. We’ll start the derivation/explanation with the definition of work. 8.2 WORK (U) What is the definition of “work”? You might answer with an equation, but perhaps a layman’s answer like “effort to move stuff ” or “getting stuff done” is more descriptive. As a technical definition we might phrase this as “work is force through a distance.” There is emphasis on the word “through” because this is a necessary part of the concept. Work requires both force and movement, and only when the force and movement align is work done. In Figure 8.2, Newtdog is pushing the loaded wheel barrow up the hill. He’s specifically pushing the handles in the direction of motion. The force he’s exerting on the wheel barrow multiplied by the distance it moves in the direction of the force is the work he is applying.

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  Applied Mathematics

  Made Simple

  • Patrick Murphy(Author)
  • 2014(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The simplest mechanical example is the typical hydroelectric scheme where a lake of water is dammed and the water flow then regulated to feed through tunnels to drive machinery in order to generate electricity. This is a straightforward conversion of the water's potential energy into kinetic energy. But our task here is to summarize these results into a form for applying energy principles to solve our problems. For simplicity we restrict ourselves to two methods of solution. Method 1: In any motion of a body where the force of gravity is the only force on the body which does any work, the sum of the potential energy and the kinetic energy is constant. We express this in the form F p + E k = constant Method 2: If the body moves under the action of a system of constant forces, let this system have a resultant of magnitude R. Since this acts on the body it follows from Newton's Second Law that R = ma, where a is the acceleration of the body. If the body moves a distance s under the action of the resultant R, then the work done by all the forces in the system is the same as the work done by the resultant R of the system, and the work done is Rs. From the equation v 2 = u 2 + las multiplied by m we have mas — imv 2 — mu 2 Rs = mas = imv 2 — mu 2 We see therefore that the change in kinetic energy of the body is equal to the total work done by all the forces acting on the body. We shall now apply these two methods to some problems. Example: A bullet of mass 15 g is fired into a fixed block of wood with a horizontal velocity of 400 m s 1 . If the bullet comes to rest after penetrating a distance of 80 mm, calculate the resistance of the block assuming the resistance to be constant. SOLUTION: The only two forces on the bullet are its weight and the resistance F of the block. The work done by the weight is zero since the displacement of the bullet is at right-angles to the line of action of mg.

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  Workshop Physics Activity Guide Module 2

  Mechanics II

  • Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  Name Section Date UNIT 10: WORK AND ENERGY VIAVAL TOURS / Shutterstock A roller coaster presents a challenge for using Newton’s laws of motion to predict the position of the carts as a function of time. The slope of the track is continually changing; imagine trying to figure out the net force on each cart on a moment-by-moment basis as the carts go uphill, downhill, and even upside down. As opposed to Newton’s laws, the concepts of work and energy can be used to simplify the analysis of such complex motions. We will examine these powerful new concepts in Units 10 and 11. 314 WORKSHOP PHYSICS ACTIVITY GUIDE UNIT 10: WORK AND ENERGY OBJECTIVES 1. To extend the intuitive notion of work as relating to effort into a more formal mathematical definition of physical work. 2. To learn to use the definition of physical work to calculate the work done by a constant force or a force that depends on position. 3. To introduce the concept of power as the rate at which work is done. 4. To define the concept of kinetic energy and its relationship to the net work done on a point mass as embodied in the work-energy principle. 10.1 OVERVIEW Although we have seen that momentum is generally conserved in collisions, different outcomes are still possible. For example, two carts can collide and stick together, or they can bounce off each other after the collision. Two carts can even “explode” apart if you release a compressed spring between them. In this unit we will introduce two new concepts that are useful for studying the interactions just described—work and energy. We start by considering both intuitive and mathematical definitions of the work done on objects.

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