Physics
Power Physics
Power in physics refers to the rate at which work is done or energy is transferred. It is measured in watts and is the product of force and velocity. In simple terms, power is the amount of energy converted or transferred per unit time, and it plays a crucial role in understanding the dynamics of various physical systems.
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12 Key excerpts on "Power Physics"
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
* The definition that we like best is this: † Work is any interaction at the boundary of a system that is not heat transfer or the transfer of matter. For example, when electrical power is supplied to a motor, the electric current is classified as a work term. Power Power, which expresses a rate of work or energy, is defined by P ≡ quantity of work (or energy) ________________________ interval of time = lim Δt→0 ΔW _ Δt = W ˙ (7.2) Equation (7.2) is defined at an instant in time because power can vary with time. To calculate power, engineers use several different equations. For rectilinear motion, such as a car or bicy- cle, the amount of work is the product of force and displacement: ΔW = FΔx. Then, power can be found using P = lim Δt→0 FΔx _ Δt = FV (7.3a) where V is the velocity of the moving body. When a shaft is rotating (Fig. 7.1b), the amount of work is given by the product of torque and angular displacement, ΔW = TΔθ. In this case, the power equation is P = lim Δt→0 TΔθ _ Δt = Tω (7.3b) where ω is the angular speed. The SI units of angular speed are rad/s. Because power has units of energy per time, the SI unit is a joule/second, which is called a watt. Common units for power are the watt (W), horsepower (hp), and the ft-lbf/s. Some typical values of power include the following: *This generalized kind of work is sometimes called thermodynamic work to distinguish it from mechanical work. In this text, we use the label work to represent all types of work, including mechanical work. † This definition comes from chemical engineering professor and Nobel Prize winner John Fenn in his book Engines, Energy, and Entropy: A Thermodynamics Primer, p. 5. Chapter 7: The Energy Equation 250 • An incandescent lightbulb can use 60–100 J/s of energy. • A well-conditioned athlete can sustain a power output of about 300 J/s for an hour. This is about four-tenths of a horsepower. One horsepower is the approximate power that a draft horse can supply.
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
For example, when electrical power is supplied to a motor, the electric current is clas- sified as a work term. Power Power , which expresses a rate of work or energy, is defined by P ≡ quantity of work (or energy) interval of time = lim Δt →0 ΔW Δt = W · (7.2) *This generalized kind of work is sometimes called thermodynamic work to distinguish it from mechanical work. In this text, we use the label work to represent all types of work, including mechanical work. † This definition comes from chemical engineering professor and Nobel Prize winner John Fenn in his book Engines, Energy, and Entropy: A Thermodynamics Primer, p. 5. Return spring Closed check valve Spray (a) Force Piston (b) Torque FIGURE 7.2 (a) For a spray bottle, the force acting through a distance is an example of mechanical work. (b) For the wind turbine, the pressure of the air causes a torque that acts through an angular displacement. This is also an example of mechanical work. Conservation of Energy 187 Eq. (7.2) is defined at an instant in time because power can vary with time. To calculate power, engineers use several different equations. For rectilinear motion, such as a car or bicycle, the amount of work is the product of force and displacement: ∆W = F∆x. Then, power can be found using P = lim Δt →0 FΔx Δt = FV (7.3a) where V is the velocity of the moving body. When a shaft is rotating (Fig. 7.2b), the amount of work is given by the product of torque and angular displacement, ∆W = T∆θ. In this case, the power equation is P = lim Δt →0 TΔθ Δt = Tω (7.3b) where ω is the angular speed. The SI units of angular speed are rad/s. Because power has units of energy per time, the SI unit is a joule/second, which is called a watt. Common units for power are the watt (W), horsepower (hp), and the ft-lbf/s. Some typi- cal values of power include the following: • An incandescent lightbulb can use 60–100 J/s of energy. • A well-conditioned athlete can sustain a power output of about 300 J/s for an hour.
eBook - PDFEngineering Mechanics
Problems and Solutions
- Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
13.4. If the particle is infinitesimally displaced by displacement ‘ ds ’ during time ‘ dt ’ then the work done by pushing force will be given by δ δ w F ds w m a ds a dv dt = = = . . . where Substituting the value of a in equation (1), δ δ δ w m dv dt ds w m ds dt dv w m v dv = = = . . . . . . ..... (1) 594 Engineering Mechanics If the particle is finally displaced by distance ‘s’ from position 1 to position 2 (not shown), then work done can be determine by integrating the above equation, δ δ w m v dv w m v dv W m v v 1 2 1 2 1 2 1 2 2 2 1 2 1 2 ∫ ∫ ∫ ∫ = = = -( ) . . . Work done = Change in kinetic energy of the particle Thus according to this principle, the work done on a moving particle is equal to the change in its kinetic energy. This principle is useful when kinetic problems are required to be exclusively dealt with in variation of velocities. 13.6 Power Power is a term which designates the work performed with minimum time. For example, a person wants to travel a distance of 5 km. Suppose he travels the same distance by three different modes, i.e., by walking, bicycle and motor cycle, and takes time 70 min, 25 min, and 8 min, respectively. Thus the work performed in the third case is most meaningful as it is conducted with the least time. Hence power is the capacity of a machine to perform work with respect to time or it is the rate at which work is performed. If a machine performs work W in total time duration t then, the average power of such machine will be given by P W t avg = F mg ds v 1 v 2 Fig. 13.4 Work and Energy 595 If a machine performs work δw for instant time dt then the instantaneous power of machine will be given by P w dt w F ds P F ds dt P F dv inst inst inst = = = = δ δ as . . . Hence, Power P = F. v Power is expressed in watt or joule per second in S.I. units. However, in electrical and mechanical equipment devices like motor and engine, the power is defined in terms of horsepower (hp).
eBook - PDF- David R. Sokoloff, Ronald K. Thornton, Priscilla W. Laws(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
You will begin by comparing your intuitive, everyday understanding of work to its formal mathematical definition. You will first consider the work done on a small point-like object by a constant force. There are, however, many cases where the force is not constant. For example, the force exerted by a spring increases the 234 REALTIME PHYSICS: MECHANICS more you stretch the spring. In this lab you will learn how to measure and cal- culate the work done by any force that acts on a moving object (even a force that changes with time). Often it is useful to know both the total amount of work that is done, and also the rate at which it is done. The rate at which work is done is known as the power. Energy (and the concept of conservation of energy, which we will explore in the next lab) is a powerful and useful concept in all the sciences. It is one of the more challenging concepts to understand. You will begin the study of energy in this lab by considering kinetic energy—a type of energy that depends on the ve- locity of an object and on its mass. By comparing the change of an object’s kinetic energy to the net work done on it, it is possible to understand the relationship between these two quantities in idealized situations. This relationship is known as the work–energy principle. You will study a cart being pulled by the force applied by a spring. How much net work is done on the cart? What is the kinetic energy change of the cart? How is the change in kinetic energy related to the net work done on the cart by the spring? INVESTIGATION 1: THE CONCEPTS OF PHYSICAL WORK AND POWER While you all have an everyday understanding of the word “work” as being re- lated to expending effort, the actual physical definition is very precise, and there are situations where this precise scientific definition does not agree with the every- day use of the word.
eBook - PDF- Patrick N. McDermott, Colin G. Orton(Authors)
- 2018(Publication Date)
- Medical Physics Publishing(Publisher)
2.2.3 Work Energy Theorem and Energy Conservation When work is done on an object, its energy changes. Energy is found in vari- ous forms: kinetic, potential, heat, light, chemical, etc. Kinetic energy is the energy associated with motion. A particle of mass m traveling with speed v has kinetic energy equal to Figure 2.2 Illustration of the work done on an object traveling in a straight line and acted on by a constant force. The object moves through a distance d. In this case, the work done on the object can be calculated using Equation (2.7). (2.7) W Fd , (2.8) T m 1 2 2 v . THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY 2-6 The connection between work and energy is provided by the work-energy theorem, which states: the work done on an object in going from an initial state i to a final state f is equal to the change in the kinetic energy, If the object starts from rest, then T i = 0 and W = T f = ½ mv 2 , where v rep- resents the final speed of the object. The units of kinetic energy are the same as those of work; that is, [T] = joule. The total energy of an isolated system must have the same value after an event or process as before that event or process. Energy can be transformed from one type to another, but the total amount must be the same before and after. This principle is known as the conservation of energy. 2.2.4 Power Power is the rate at which work is done. If the symbol t represents the time interval over which the work is done, then the power is given by the equation The units of power can be determined from the defining equation: [P] = [W]/ [t] = joule/s. This unit has a special name: 1 watt = 1 W = 1 joule/s. When you pay your “power” bill, what you are really paying for is energy or work, not power. The power company expresses your usage in kilowatt- hours (kW-h). This is a nonstandard quantity that has the units of work because it is a power multiplied by a time.
eBook - PDF- Nelson Bolívar(Author)
- 2020(Publication Date)
- Arcler Press(Publisher)
These motions signify increased thermal energy in the system. Figure 5.9 displays a system in which a thermally isolated water tank has a shaft deferred in it. There are two paddles are attached to the shaft which is established to rotate on its axis. In this system, any work is done in revolving the shaft effects in a transfer of kinetic energy to the water. There will still be some residual motion if the driving force is removed from the shaft after some time. Though, the motion will ultimately die down and increase the thermal energy of the water. Remarkably, a system similar to that shown in Figure 5.9 was used by James Prescott Joule (1818–1889), for whom the SI unit of energy is termed. By using a paddle wheel immersed in a tank of whale oil and driven by falling weights, he was able to regulate the relationship between heat and mechanical energy. This guide to the 1 ˢᵗ law of thermodynamics and law of conservation of energy. General Physics 132 Figure 5.9. A paddlewheel rotating in a water tank. Source: http://www.engineeringexpert.net/Engineering-Expert-Witness-Blog/ james-prescott-joule-and-the-joule-apparatus. 5.9. POWER Alike energy , the power is a word we hear a lot. In daily life, it has an extensive range of meanings. In physics though, it has a very precise meaning. The measure of the rate at which work is done (or similarly, at which energy is transferred) is called power (Abhat, 1983; Hawlader et al., 2003). The capability to precisely measure power was one of the important abilities which gave early engineers to make the steam engines which drove the industrial revolution. It remains to be important for knowing how to make usage of the energy resources which drive the modern world (Inaba, 2000; Sharma et al., 2009). 5.9.1. Measurement of Power Watt is the standard unit used to measure power which has the symbol W. It was named after the Scottish inventor and industrialist James Watt. You have perhaps encountered the watt often in everyday life.
eBook - PDFApplied Mathematics
Made Simple
- Patrick Murphy(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
Work, Energy, and Power 217 CHAPTER TWELVE WORK, E N E R G Y A N D P O W E R (1) Work In applied mathematics, work is associated with the movement of bodies from one position to another. Since the movement of a body from rest re-quires force, and the change in position is represented by displacement, we shall define work by relating it to force and displacement. If you help to push-start a car with a flat battery on a winter's morning you will readily agree on three things : pushing the car 20 m will be only half the 'work' of pushing it 40 m ; directing your push in the line of motion is better than pushing in any other direction ; finally, the sooner you can find a down-ward slope the better. If a young child helps you push she will not do the same amount of work as you, even though she will move just as far. The differ-ence between your work contribution and hers will have something to do with the magnitude of the force applied to the car. We therefore conclude that a definition of work involving force and distance looks promising. In order to keep the early ideas as simple as possible we shall consider first, the work done by a force acting on a particle. DEFINITION : / / a constant force of magnitude Fis applied to a particle which then moves a distance s along the line of action of F, the product Fs is called work and is said to be a measure of the work done by the force on the particle. To measure anything we must have a standard unit. The search for a unit need only be brief because we have already obtained units for F and s. Since the standard units are newtons for F and metres for s, it follows that Fs must be measured in newton metres. Unfortunately this is the same measurement as for moment of a force, so it would be helpful to have some means of distinguishing between the two. We therefore refer to the newton metre, when it is a unit of work, as a joule (pronounced 'jewel').
eBook - PDFThermodynamics
Concepts and Applications
- Stephen R. Turns(Author)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
Like heat, work is not possessed by a thermodynamic system or a control volume but is just the name of a particular form of energy transfer from a system to the surroundings, or vice versa. For this reason we draw arrows representing work or heat that start or stop at the system or control volume boundary without crossing. In this context, we offer the following formal definition of work: Work is the transfer of energy across a system or control-volume boundary, exclusive of energy carried across the boundary by a flow, and not the result of a temperature gradient at the boundary or a difference in temperature between the system and the surroundings. Before presenting examples of work, it is useful to convert Eq. 4.6 to a form expressing the rate at which work is done. The time rate of doing work W 2 . W 1 ¢E E 2 E 1 . 1 W 2 1 W 2 F ds, dW k ˆ j ˆ i ˆ ds i ˆ dx j ˆ dy k ˆ dz, W F ds; CH. 4 ENERGY AND ENERGY TRANSFER 225 F Fcosθ ds Path 1 2 θ Q out Q in Boundary W out W in is called power, defined as (4.7a) or (4.7b) where we recognize that is the velocity vector V. From this definition, we see that power enters or exits a system or control volume wherever a component of a force is aligned with the velocity at the boundary. Types Some common types of work are listed in Table 4.1. In many situations, the power, or rate of working, is the important quantify; therefore, expressions to evaluate the power are also shown. Expansion (or Compression) Work In systems or control volumes where a boundary moves, work is performed by the system if it expands, whereas work is done on the system if the system is compressed. Concomitantly, work is done on the surroundings by an expanding system, and work is done by the surroundings when the system contracts. As an example of this type of work, consider the expansion of a gas contained in a piston–cylinder assembly as shown in Fig.
eBook - PDFGeneral Engineering Science in SI Units
The Commonwealth and International Library: Mechanical Engineering Division
- G. W. Marr, N. Hiller(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
Section 4 Power and Energy 4.1. Introduction In volume 1, section 6, the reader was introduced to the terms energy and work, and the scientific meaning of these terms was explained. It was stated that work was done whenever a force underwent a displacement. The work done, or energy expended, when a force of magnitude F moved its point of application a distance d along its line of action was said to be measured by the product F.d. In addition it was shown that the work done could be represented, in the case of a constant force, by the area under the force-displacement graph. This section begins by showing that this graphical method of representation can be extended to include the work done by a variable force. Thereafter, the section deals with other aspects of the relationship between force, energy, and power. 4.2. Graphical Representation of the Work Done by a Variable Force The following simple argument may be used to show that the work done by a force is represented by the area under the force-displacement graph even when the force varies in magnitude. The curve in Fig. 4.1 represents the manner in which the magni-tude of a force varies as the point of application of the force moves along the line of action of the force. 76 POWER AND ENERGY When the force is applied throughout a distance AB = work done = average value of the force X distance moved d, the In the diagram, the ordinates represent force, and hence the average value of the force is represented by the average value of the ordinates, which is the average height of the curve al ove the axis. But (average height of curve)X (base length) = area ABCD under the curve. Thus area under curve = F av X
eBook - PDFGeneral Engineering Science in SI Units
In Two Volumes
- G. W. Marr, N. Hiller(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
Section 4 Power and Energy 4.1. Introduction In volume 1, section 6, the reader was introduced to the terms energy and work, and the scientific meaning of these terms was explained. It was stated that work was done whenever a force underwent a displacement. The work done, or energy expended, when a force of magnitude F moved its point of application a distance d along its line of action was said to be measured by the product F.d. In addition it was shown that the work done could be represented, in the case of a constant force, by the area under the force-displacement graph. This section begins by showing that this graphical method of representation can be extended to include the work done by a variable force. Thereafter, the section deals with other aspects of the relationship between force, energy, and power. 4.2. Graphical Representation of the Work Done by a Variable Force The following simple argument may be used to show that the work done by a force is represented by the area under the force-displacement graph even when the force varies in magnitude. The curve in Fig. 4.1 represents the manner in which the magni-tude of a force varies as the point of application of the force moves along the line of action of the force. 76 POWER AND ENERGY vVhen the force is applied throughout a distance AB = work done = average value of the force X distance moved = F av Xrf.
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
vertical height is raised mm 0.2342 m G GO GA = - = - = = 309 2 75 234 2 . . work done weight vertical lift of J = × = × = G 1040 0 2342 243 5 . . Ans. (ii) Power POWER is the rate of doing work, or the quantity of work completed in a given time. The unit of power is the watt, which is equal to the rate 1 joule of work being done every second. power J/s Nm/s) force velocity work done (for small ( W F ds = = = × = displacement) power (for small time interval) (i = = F ds dt P Fv nstantaneous velocity ) v 84 • Applied Mechanics When describing the power generated in marine engineering applications, either mechanical, electrical or hydraulic, the kilowatt (kW) is usually a more convenient unit of measure, due to the size of the power that is being generated. Example 4.2. A pump lifts fresh water from one tank to another through an effective height of 12 m. If the mass flow of water is 40 t/h, find the output power of the pump. 40 40 10 9 81 3 3 t kg weight of water lifted per second 40 10 3 = × = × × . 600 9 81 1 N power weight lifted per second height = 40 10 3 = × × × × . 2 3600 1308 W W or 1.308 kW P = MECHANICAL EFFICIENCY is the ratio of power that comes out of a machine compared to the power that is put in, therefore: mechanical efficiency output power input power = This will always give a fraction less than unity; however, it is common practice to multiply the result by 100 and express the efficiency as a percentage. For example, if the input power of the pump in Example 4.2 was 1.75 kW, then the efficiency would be ℑ= = = output power input power or 74.74% 1 308 1 75 0 7474 . . . PRESSURE is defined as the force per unit area. It is measured in units of N/m 2 and is used in calculating power. POWER OF RECIPROCATING ENGINES. When a gas or a liquid acts on a piston in a closed cylinder, the pressure multiplied by the piston area on which the pressure acts gives the total force on the piston.
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
This type of analysis is representative of a microscopic description of the processes occurring within the boundaries of the defined system, because the history of a single particle was followed in detail. Rather than pursue further the microscopic concept of matter, we shall be concerned with the macroscopic, or average, behavior of the particles composing a system. The macroscopic viewpoint essen-tially assumes that it is possible to describe the average behavior of these particles at a given time and at some subsequent time after changes have occurred to the system. The 60 Thermodynamics and Heat Power system changes of concern to us in this study are temperature, pressure, density, work, energy, velocity, and position. The power of the macroscopic approach lies in its ability to describe the changes that have occurred to the system without having to detail all the events of the processes involved. 2.2 Work The work done by a force is the product of the displacement of the body multiplied by the component of the force in the direction of the displacement. Thus, in Figure 2.1, the dis-placement of the body on the horizontal plane is x , and the component of the force in the direction of the displacement is ( F cos θ ). The work done is ( F cos θ ) x . The constant force ( F cos θ ) is plotted as a function of x in Figure 2.1b, and it should be noted that the resulting figure is a rectangle. The area of this rectangle (shaded) is equal to the work done, because it is ( F cos θ )( x ). If the force varies so that it is a function of the displacement, it is neces-sary to consider the variation of force with displacement in order to find the work done. Figure 2.1c shows a general plot of force as a function of displacement.
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