Physics
Kinetic Energy
Kinetic energy is the energy possessed by an object due to its motion. It depends on the object's mass and its velocity, with the formula KE = 0.5 * mass * velocity^2. The greater the mass and velocity of an object, the more kinetic energy it possesses.
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10 Key excerpts on "Kinetic Energy"
eBook - PDF- Richard C. Hill, Kirstie Plantenberg(Authors)
- 2013(Publication Date)
- SDC Publications(Publisher)
7.2.2) Kinetic Energy Kinetic Energy is the energy due to an object’s motion. If a body has mass and is moving, then it has Kinetic Energy. The body's motion can be used to perform work. If a body is at rest, then it has no Kinetic Energy. The mathematical definition of Kinetic Energy is given by Equation 7.2-1. Kinetic Energy: 2 1 2 T mv (7.2-1) T = Kinetic Energy of a particle m = particle's mass v = particle's speed Kinetic Energy is the energy possessed by a body due to its motion. There are a few things that we can surmise by looking at Equation 7.2-1. First, this equation is not a vector equation, therefore, Kinetic Energy is a scalar. It has no direction. Second, Kinetic Energy depends on both mass and speed. Consider two identical balls. One ball is red and the other blue. The red ball is rolling with twice the speed of the blue one. Which one has the higher Kinetic Energy? The red one is moving faster, therefore, it has more energy. Now let’s look at the case where the balls are moving with the same speed, but now the red ball has twice the mass as the blue ball. Which ball has the higher Kinetic Energy in this case? The red ball has more mass and, therefore, has more energy (i.e. a greater capacity to do work) even though both balls are moving at the same speed. Note that Kinetic Energy is always positive. Mathematically, this is due to the fact that mass cannot be negative and that the speed, in Equation 7.2-1, is squared. More intuitively, a moving body can always perform work regardless of the direction of its velocity. It is also interesting to note that the Kinetic Energy of a particle captures a particle’s current state and not the particle’s history. A particle's Units of Kinetic Energy SI units: Newton–meter [N-m] Joule [J = 1 N-m] erg [erg = 1 x 10 -7 J] US customary units: foot–pound [ft-lb = 1.3558 J] kilocalorie [kcal = 4187 J] British thermal unit [Btu = 778.16 ft-lb = 1055 J]
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
With this history in mind, we can now state the classical definition of Kinetic Energy. Note that when we say “classical,” we mean non-relativistic, that is, at speeds much less that the speed of light. At speeds comparable to the speed of light, the special theory of relativity requires a different expression for the Kinetic Energy of a particle, as discussed in Relativity (http://cnx.org/content/m58555/latest/) . Since objects (or systems) of interest vary in complexity, we first define the Kinetic Energy of a particle with mass m. Kinetic Energy The Kinetic Energy of a particle is one-half the product of the particle’s mass m and the square of its speed v: (7.6) K = 1 2 mv 2 . We then extend this definition to any system of particles by adding up the kinetic energies of all the constituent particles: (7.7) K = ∑ 1 2 mv 2 . Note that just as we can express Newton’s second law in terms of either the rate of change of momentum or mass times the rate of change of velocity, so the Kinetic Energy of a particle can be expressed in terms of its mass and momentum ( p → = m v → ), instead of its mass and velocity. Since v = p/m , we see that K = 1 2 m ⎛ ⎝ p m ⎞ ⎠ 2 = p 2 2m also expresses the Kinetic Energy of a single particle. Sometimes, this expression is more convenient to use than Equation 7.6. The units of Kinetic Energy are mass times the square of speed, or kg · m 2 /s 2 . But the units of force are mass times acceleration, kg · m/s 2 , so the units of Kinetic Energy are also the units of force times distance, which are the units of work, or joules. You will see in the next section that work and Kinetic Energy have the same units, because they are different forms of the same, more general, physical property.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
156 7.1 Kinetic Energy Learning Objectives After reading this module, you should be able to . . . 7.1.1 Apply the relationship between a particle’s Kinetic Energy, mass, and speed. 7.1.2 Identify that Kinetic Energy is a scalar quantity. Key Idea ● The Kinetic Energy K associated with the motion of a particle of mass m and speed v, where v is well below the speed of light, is K = 1 _ 2 mv 2 (Kinetic Energy). What Is Physics? One of the fundamental goals of physics is to investigate something that everyone talks about: energy. The topic is obviously important. Indeed, our civilization is based on acquiring and effectively using energy. For example, everyone knows that any type of motion requires energy: Flying across the Pacific Ocean requires it. Lifting material to the top floor of an office building or to an orbiting space station requires it. Throwing a fastball requires it. We spend a tremendous amount of money to acquire and use energy. Wars have been started because of energy resources. Wars have been ended because of a sudden, overpowering use of energy by one side. Everyone knows many examples of energy and its use, but what does the term energy really mean? What Is Energy? The term energy is so broad that a clear definition is difficult to write. Techni- cally, energy is a scalar quantity associated with the state (or condition) of one or more objects. However, this definition is too vague to be of help to us now. A looser definition might at least get us started. Energy is a number that we associate with a system of one or more objects. If a force changes one of the objects by, say, making it move, then the energy number changes. After count- less experiments, scientists and engineers realized that if the scheme by which we assign energy numbers is planned carefully, the numbers can be used to predict the outcomes of experiments and, even more important, to build machines, such as flying machines.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
This minimum Kinetic Energy contributes to the system's invariant mass, which is independent of the reference frame. According to classical mechanics (ie ignoring relativistic effects) the Kinetic Energy of a non-rotating object of mass m traveling at a speed v is mv 2 /2. This will be a good approximation provided v is much less than the speed of light. History and etymology The adjective kinetic has its roots in the Greek word κίνησις (kinesis) meaning motion , which is the same root as in the word cinema, referring to motion pictures. The principle in classical mechanics that E ∝ mv² was first developed by Gottfried Leibniz and Johann Bernoulli, who described Kinetic Energy as the living force , vis viva . Willem 's Gravesande of the Netherlands provided experimental evidence of this relation-ship. By dropping weights from different heights into a block of clay, 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms Kinetic Energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of Kinetic Energy. William Thomson, later Lord Kelvin, is given the credit for coining the term Kinetic Energy c. 1849 - 1851. ________________________ WORLD TECHNOLOGIES ________________________ Introduction There are various forms of energy: chemical energy, heat, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, rest energy. These can be categorized in two main classes: potential energy and Kinetic Energy. Kinetic Energy can be best understood by examples that demonstrate how it is tran-sformed to and from other forms of energy.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
This minimum Kinetic Energy contributes to the system's invariant mass, which is independent of the reference frame. According to classical mechanics (ie ignoring relativistic effects) the Kinetic Energy of a non-rotating object of mass m traveling at a speed v is mv 2 /2. This will be a good approximation provided v is much less than the speed of light. History and etymology The adjective kinetic has its roots in the Greek word κίνησις (kinesis) meaning motion , which is the same root as in the word cinema, referring to motion pictures. The principle in classical mechanics that E ∝ mv² was first developed by Gottfried Leibniz and Johann Bernoulli, who described Kinetic Energy as the living force , vis viva . Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms Kinetic Energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of Kinetic Energy. William Thomson, later Lord Kelvin, is given the credit for coining the t erm Kinetic Energy c. 1849 - 1851. ________________________ WORLD TECHNOLOGIES ________________________ Introduction There are various forms of energy: chemical energy, heat, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, rest energy. These can be categorized in two main classes: potential energy and Kinetic Energy. Kinetic Energy can be best understood by examples that demonstrate how it is transformed to and from other forms of energy.
eBook - PDF- Stephen Lee(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
● The Kinetic Energy of a moving object 1 2 mass ( speed ) 2 . Potential energy is the energy which a body possesses because of its position. It may be thought of as stored energy which can be converted into kinetic or other forms of energy. You will meet this again on page 208. The energy of an object is usually changed when it is acted on by a force. When a force is applied to an object which moves in the direction of its line of action, the force is said to do work. For a constant force this is defined as follows. ● The work done by a constant force force distance moved in the direction of the force . The following examples illustrate how to use these ideas. A brick, initially at rest, is raised by a force averaging 40 N to a height 5 m above the ground where it is left stationary. How much work is done by the force? S OLUTION The work done by the force raising the brick is 40 5 200 J. Figure 9.1 Examples 9.2 and 9.3 show how the work done by a force can be related to the change in Kinetic Energy of an object. A train travelling on level ground is subject to a resisting force (from the brakes and air resistance) of 250 kN for a distance of 5 km. How much Kinetic Energy does the train lose? 5 m 40 N 202 AN INTRODUCTION TO MATHEMATICS FOR ENGINEERS : MECHANICS E XAMPLE 9.1 E XAMPLE 9.2 S OLUTION The forward force is 250 000 N. The work done by it is 250 000 5000 1 250 000 000 J. Hence 1 250 000 000 J of Kinetic Energy are gained by the train, in other words 1 250 000 000 J of Kinetic Energy are lost and the train slows down. This energy is converted to other forms such as heat and perhaps a little sound. A car of mass m kg is travelling at u ms 1 when the driver applies a constant driving force of F N. The ground is level and the road is straight and air resistance can be ignored. The speed of the car increases to v ms 1 in a period of t s over a distance of s m.
eBook - PDFApplied Mathematics
Made Simple
- Patrick Murphy(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
We can therefore summarize these last two results by what is called the principle of the conservation of energy: for any body moving under the force of gravity alone the sum of the potential and kinetic energies is constant. An equation such as $mv 2 + mgy = mu 2 above is called the energy equation for the body in motion. Since energy is defined as the capacity for doing work, any form of pent-up or sealed-in energy may be used to perform work; the potential energy due to the height and weight of a body is just one of many ways in which energy may be stored. For example, a watch spring when fully wound has a store of energy or potential energy which is used up in turning the hands to register the time. The old grandfather clocks have large masses suspended by cords which gradually unwind so that the work done by the weight as it descends is used to turn the hands of the clock. When the weight has descended to the bottom of the clock we wind it back up again to replace its potential energy. A piece of elastic also has potential energy when it is held in a stretched state. Thus a catapult releases the energy of the stretched elastic and in so doing imparts a velocity to a stone, i.e. the potential energy of the elastic is converted into Kinetic Energy for the stone. There are other forms of energy such as heat, chemical, and electrical energy. One very familiar example is the chemical action in a battery which can be converted to electrical energy to start the engine of a car. Considering the principle of the conservation of energy in the widest sense, we suggest that although energy can be converted from one form to another it can never be destroyed. This means that the sum of all the different energies in a system remains constant. To illustrate this point consider the energy stored in a gallon of petrol.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
No exception to this principle of energy conservation has ever been found. Money. Think of the many types of energy as being numbers representing money in many types of bank accounts. Rules have been made about what such money numbers mean and how they can be changed. You can transfer money numbers from one account to another or from one system to another, perhaps electronically with nothing material actually moving. However, the total amount (the total of all the money numbers) can always be accounted for: It is always conserved. In this chapter we focus on only one type of energy (Kinetic Energy) and on only one way in which energy can be transferred (work). After reading this module, you should be able to . . . 7.1.1 Apply the relationship between a particle’s Kinetic Energy, mass, and speed. 7.1.2 Identify that Kinetic Energy is a scalar quantity. 7.1 Kinetic Energy LEARNING OBJECTIVES Kinetic Energy and Work KEY IDEA 1. The Kinetic Energy K associated with the motion of a particle of mass m and speed v, where v is well below the speed of light, is K = 1 _ 2 mv 2 (Kinetic Energy). 147 148 CHAPTER 7 Kinetic Energy and Work Kinetic Energy Kinetic Energy K is energy associated with the state of motion of an object. The faster the object moves, the greater is its Kinetic Energy. When the object is stationary, its Kinetic Energy is zero. For an object of mass m whose speed v is well below the speed of light, K = 1 _ 2 mv 2 (Kinetic Energy). (7.1.1) For example, a 3.0 kg duck flying past us at 2.0 m/s has a Kinetic Energy of 6.0 kg ⋅ m 2 /s 2 ; that is, we associate that number with the duck’s motion. The SI unit of Kinetic Energy (and all types of energy) is the joule (J), named for James Prescott Joule, an English scientist of the 1800s, and defined as 1 joule = 1 J = 1 kg ⋅ m 2 /s 2 . (7.1.2) Thus, the flying duck has a Kinetic Energy of 6.0 J. CHECKPOINT 7.1.1 The speed of a car (treat it as being a particle) increases from 5.0 m/s to 15.0 m/s.
No longer available |Learn more- Ping YI, Jun LIU, Feng JIANG(Authors)
- 2022(Publication Date)
- EDP Sciences(Publisher)
Chapter 9 Kinetics: Work and Energy Objectives Calculate the work done by a force or a couple. Understand the concepts of power and efficiency of a mechanical system. Calculate the Kinetic Energy of a particle, a system of particles, a rigid body or a system of rigid bodies undergoing planar motion. Derive and apply the principle of work and energy to solve kinetic problems that involve force, displacement and velocity. Understand the concept of conservative force and calculate the gravitational and elastic potential energy of a mechanical system. Solve kinetic problems using conservation of energy. Chapter 8 relates force and acceleration through Newton’s second law, i.e., the equation of motion F = ma. Once F is given, we can solve for the acceleration a from this equation; then from kinematics, the velocity and position of the particle at any time can be obtained from integration of a. However, using the equation of motion together with kinematics allows us to derive the principle of work and energy, which directly relates force, displacement and velocity and make the determination of the acceleration unnecessary. We will discuss the principle of work and energy in this chapter. The concepts of conservative force and potential energy and the principle of conservation of mechanical energy will also be examined. 9.1 Work and Power 9.1.1 Work In mechanics, work has a very specific definition that involves force and displace- ment. Force F does work on a particle when the particle acted upon by the force undergoes a displacement in the direction of the force. For example, constant force DOI: 10.1051/978-2-7598-2901-9.c009 © Science Press, EDP Sciences, 2022 F is exerted on a particle that moves along a straight line and has a displacement s, figure 9.1. Then its work equals the magnitude of the force times the component of displacement in the direction of the force, i.e., W ¼ Fs cos h.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
We see that in at least two frames of reference (the cen- ter-of-mass frame and the laboratory frame) the total initial and final kinetic energies of the two-body system are equal. In fact, because the laboratory frame is an arbitrarily chosen frame, the total Kinetic Energy remains constant in all iner- tial frames of reference. We can understand this result by imagining that there is a spring at its relaxed length between the two bodies. As the bodies collide, they compress the spring, and some of their Kinetic Energy is lost due to the K i K f (elastic). K f 1 2 m 1 v 1f 2 1 2 m 2 v 2f 2 . K i 1 2 m 1 v 2 1i 1 2 m 2 v 2 2i , K f K 1f K 2f , K i K 1i K 2i , K 2i K 2f K 1i K 1f v 2i v 2f ), (v 1i v 1f work done by the spring. When the spring expands again, it does an equal amount of work on the bodies, which in- creases their Kinetic Energy. If the spring returns to its re- laxed length, there is no net work done on the system con- sisting of the two bodies, and so the total final Kinetic Energy of the system must equal the total initial Kinetic Energy. Of course, there are no springs in collisions between real bodies — it is the colliding objects themselves that be- have elastically, just like springs. The interatomic forces of the objects can be regarded as elastic; the objects do work on one another in changing each other’s Kinetic Energy, but the net work done by the entire system of the two objects is zero, so the change in Kinetic Energy of the system is zero. On the other hand, imagine a spring between the two bodies in an inelastic collision (compare lines 1 and 3 in Fig. 11-22b). The spring will be compressed in the colli- sion, but it does not return to its full relaxed length after the collision.
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