Work, Energy and Power

Definitions:
= Work = From Wikipedia, the free encyclopedia

"Mechanical work" redirects here. For other uses of "Work" in physics, see Work (electrical) and Work (thermodynamics).

In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement).

Work transfers energy from one place to another or one form to another.

According to Jammer[1], the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis[2] as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. According to Dugas[3], it is to Solomon of Caux "that we owe the term work in the sense that it is used in mechanics now".

The SI unit of work is the joule (J).

= Power =

From Wikipedia, the free encyclopedia
==== In physics, power is the rate of doing work, the amount of energy transferred per unit time. Having no direction, it is a scalar quantity. In the International System of Units, the unit of power is the joule per second (J/s), known as the watt in honour of James Watt, the eighteenth-century developer of the steam engine condenser. Another common and traditional measure is horsepower (comparing to the power of a horse). Being the rate of work, the equation for power can be written: ====

==== The integral of power over time defines the work performed. Because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to be path dependent. ====

==== As a physical concept, power requires both a change in the physical universe and a specified time in which the change occurs. This is distinct from the concept of work, which is only measured in terms of a net change in the state of the physical universe. The same amount of work is done when carrying a load up a flight of stairs whether the person carrying it walks or runs, but more power is needed for running because the work is done in a shorter amount of time. ====

==== The output power of an electric motor is the product of the torque that the motor generates and the angular velocity of its output shaft. The power involved in moving a vehicle is the product of the traction force of the wheels and the velocity of the vehicle. The rate at which a light bulb converts electrical energy into light and heat is measured in watts—the higher the wattage, the more power, or equivalently the more electrical energy is used per unit time. ==== The SI unit of power is the watt (W)

= Energy = From Wikipedia, the free encyclopedia

This article is about the scalar physical quantity. For an overview of and topical guide to energy, see Outline of energy. For other uses, see Energy (disambiguation).

"Energetic" redirects here. For other uses, see Energetic (disambiguation).

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In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.[note 1] Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton. =====

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Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature. =====

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Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy (in that frame of reference), and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as an increase in mass, with a sensitive enough scale. =====

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Living organisms require available energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. =====

Equations
The work  done by a constant force of magnitude  on a point that moves a displacement S in a straight line in the direction of the force is the product
 * .W=Fs

For example, if a force of 10 newtons ( F= 10 N) acts along a point that travels 2 meters ( S= 2 m), then it does the work  W= (10 N)(2 m) = 20 N m = 20 J. This is approximately the work done lifting a 1 kg weight from ground level to over a person's head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance.

Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force.

From Newton's second law, it can be shown that work on a free (no fields), rigid (no internal degrees of freedom) body, is equal to the change in kinetic energy KE of the velocity and rotation of that body,

W=Δ KE

The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. Therefore, work on an object that is merely displaced in a conservative force field, without change in velocity or rotation, is equal to minus the change of potential energy  of the object,

W=-Δ PE

These formulas show that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensions, and units, of energy. The work/energy principles discussed here are identical to Electric work/energy principles.

Power, as a function of time, is the rate at which work is done, so can be expressed by this equation:
 * P=dW/dt

where P is power, W is work, and t is time. Because work is a force F applied over a distance r,

W=F*r

for a constant force, power can be rewritten as:

P=dW/dt=d/dt(F*r)=F*(dr/dt)=F*v