Work and energy
Work and energy are fundamental concepts in physics that describe how forces interact with matter to cause motion and changes in energy states. Work is defined as the process of changing the energy of an object or system, which can take various forms, including mechanical, thermal, electrical, and magnetic energy. The amount of work done on an object is contingent upon the direction of the force applied; it is positive when the force aids motion and negative when it opposes it.
Energy is a scalar quantity that represents the capacity for doing work and can be stored and transferred in different forms. The total energy of a system remains constant according to the law of conservation of energy, which states that energy can neither be created nor destroyed, but can change from one form to another. Key forms of energy include potential energy (related to positional factors, like height in a gravitational field) and kinetic energy (associated with the motion of an object).
Power, another essential concept, is the rate at which work is done over time, with various units used to measure it, such as watts and horsepower. Efficiency measures how well a system converts input energy into useful work, highlighting the practical limitations of energy conversion in real-world applications. Understanding the interplay of work and energy is crucial for analyzing mechanical systems, predicting motion, and designing energy-efficient technologies.
Work and energy
Summary: Work is the act of changing the energy of a particle, body, or system. The energy of a mass represents the capacity of the mass to do work.
The energy of a mass represents the capacity of the mass to do work. Such energy can be stored and released. There are many forms that it can take, including mechanical, thermal, electrical, and magnetic. Energy is a positive, scalar quantity, although a change in energy can be either positive or negative. The total energy of a body can be calculated from its mass, m, and the specific energy, U (that is, the energy per unit mass):
E = mU
Typical units of mechanical energy are foot-pounds and joules. A joule is equivalent to the units of N·m and kg·m2/s2. In countries that use traditional English units, the Bristish thermal unit (Btu) is used for thermal energy, whereas the kilocalorie (kcal) is still used in some applications in countries that use the International System of Units (SI units). Joule’s constant, or the Joule equivalent (778.26 ft-lbf/Btu), is used to convert between English mechanical units and thermal energy units.
Energy in Btu = energy in the ft-lbf/J
Law of
The law of conservation of energy says that energy cannot be created or destroyed. However, energy can be converted into different forms. Therefore, the sum of all energy forms is constant.
? E = constant
Work
Work is the act of changing the energy of a particle, body, or system. For a mechanical system, external work is done by an external force, whereas internal work is done by an internal force. Work is a signed, scalar quantity. Typical units are inch-pounds, foot-pounds, and joules. Mechanical work is seldom expressed in British thermal units or kilocalories.
For a mechanical system, work is positive when a force acts in a direction of motion and helps a body move from one location to another. Work is negative when a force acts to oppose motion. Friction, for example, always opposes the direction of motion and can only do negative work. The work done on a body by more than one force can be found by superposition.
From a thermodynamic standpoint, work is positive if a particle or a body does work on its surroundings. Work is negative if the surroundings do work on the object. An example would be inflating a tire, which represents negative work to the tire. This is consistent with the law of conservation of energy, since the sum of the negative work and positive energy increase is zero (that is, there is no net energy change in the system).
of a Mass
Potential energy (gravitational energy) is a form of mechanical energy possessed by a body due to its relative position in a gravitational field. Potential energy is lost when the elevation of a body decreases. The lost potential energy usually is converted to kinetic energy or heat.
Epotential = mgh
Epotential = mgh/gc
In the absence of friction and other nonconservative forces, the change in potential energy of a body is equal to the work required to change the elevation of the body.
W = Epotential
Kinetic Energy of a Mass
Kinetic energy is a form of mechanical energy associated with a moving or rotating body. The kinetic energy of a body moving with instantaneous linear velocity, v, is:
Ekinetic = (½)mv2
Ekinetic = mv2/2gc
The work-energy principle states that the kinetic energy is equal to the work necessary to initially accelerate a stationary body or to bring a moving body to rest:
W = Ekinetic
A body can also have rotational kinetic energy.
Erotational = (½) Iw2
Erotational = Iw2/2gc
Spring Energy
A spring is an energy storage device, since the spring has the ability to perform work. In a perfect spring, the amount of energy stored is equal to the work required to compress the spring initially. The stored spring energy does not depend on the mass of the spring. Given a spring with spring constant (stiffness), k, the spring energy is as follows:
Espring = (½) kx2
Pressure Energy of a Mass
Since work is done in increasing the pressure of a system, mechanical energy can be stored in pressure form. This is known as pressure energy, static energy, flow energy, flow work, and pV work (energy). For a system of pressurized mass, m, the flow energy is as follows:
Eflow = (mp/?) = mpv
Eflow = (mp/gc?) = (mpv/gc)
of a Mass
The total internal energy, usually given the symbol U, of a body increases when the body’s temperature increases. In the absence of any work done on or by the body, the change in internal energy is equal to the heat flow, Q, into the body. Q is positive if the heat flow is into the body and negative otherwise.
U2 - U1 = Q
The property of internal energy is encountered primarily in thermodynamics problems. Typical units are British thermal units, joules, and kilocalories.
Work–Energy Principle
As energy can be neither created nor destroyed, external work performed on a conservative system goes into changing the system’s total energy. This is known as the work-energy principle (or principle of work and energy).
W = E = E2 - E1
The term work-energy principle is limited to use with mechanical energy problems, such as the conversion of work into kinetic or potential energy. When energy is limited to kinetic energy, the work-energy principle introduces some simplifications into many mechanical problems:
• It is not necessary to calculate or know the acceleration of a body to calculate the work performed on it.
• Forces that do not contribute to work—for example, are normal to the direction of motion—are eliminated.
• Only scalar quantities are involved.
• It is not necessary to individually analyze the particles of component parts in a complex system.
Conversion Between Energy Forms
Conversion of one form of energy into another form of energy does not violate the law of conservation of energy. Most problems involving conversion of energy are really just special cases of the work-energy principle. An example is a falling body that is acted upon by a gravitational force. The conversion of potential energy into kinetic energy can be interpreted as equating the work done by the constant gravitational force to the change in kinetic energy.
Power
Power is the amount of work done per unit time. It is a scalar quantity.
P = (W/t)
For a body acted upon by a force or torque, the instantaneous power can be calculated from the velocity.
P = Fv (linear systems)
P = Tw (rotational systems)
Basic units of power are ft-lbf/sec and watts (J/s), although horsepower is also widely used. Some useful power conversion formulas include:
1hp = 550 (ft-lbf/sec) = 33,000 (ft-lbf/min) = 0.7457 kW = 0.7068 (Btu/sec)
1 kW = 737.6 (ft-lbf/sec) = 44,250 (ft-lbf/min) = 1.341 hp = 0.9483 (Btu/sec)
1 (Btu/sec) = 778.26 (ft-lbf/sec) =46,680 (ft-lbf/min) = 1.415 hp
Efficiency
For energy-using systems (such as cars, electrical motors, and televisions), the energy-use efficiency, ?, of a system is the ratio of an ideal property to an actual property. The property used is commonly work, power, or, for thermodynamic problems, heat. When the rate of work is constant, either work or power can be used. Except in rare instances, the numerator and denominator of the ratio must have the same units:
? = (Pideal/Pactual) (Pactual = Pideal)
For energy-producing systems (such as electrical generators, prime movers, and hydroelectric plants), the energy-production efficiency is
? = (Pactual/Pideal) (Pideal = Pactual)
The efficiency of an ideal machine is 1.0 (100 percent). However, all real machines have efficiencies of less than 1.0.
Bibliography
Crowell, Benjamin. Conservation Laws. Fullerton, CA: Light and Matter, 2003.
Ross, John S. “Work, Power, Kinetic Energy.” Project PHYSNET, Michigan State University, April 23, 2002. www.physnet.org/modules/pdf‗modules/m20.pdf.
Serway, Raymond A., and John W. Jewett. Physics for Scientists and Engineers. 8th ed. Belmont, CA: Brooks/Cole Cengage Learning, 2010.
Smil, Vaclav. Energy in Nature and Society: General Energetics of Complex Systems. Cambridge, MA: MIT Press, 2008.
Tipler, Paul. Physics for Scientists and Engineers: Mechanics. 3rd ed. New York: W. H. Freeman, 2008.
Walding, Richard, Greg Rapkins, and Glenn Rossiter. New Century Senior Physics. Melbourne, Australia: Oxford University Press, 1999.
"Work." Energy Education, energyeducation.ca/encyclopedia/Work. Accessed 7 Aug. 2024.