**Work power and energy**

**Work**

Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. If the force is constant, work may be computed by multiplying the length of the path by the component of the force acting along the path. To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ. Work done on a body is accomplished not only by a displacement of the body as a whole from one place to another but also, for example, by compressing a gas, by rotating a shaft, and even by causing invisible motions of the particles within a body by an external magnetic force.

No work, as understood in this context, is done unless the object is displaced in some way and there is a component of the force along the path over which the object is moved. Holding a heavy object stationary does not transfer energy to it, because there is no displacement. Holding the end of a rope on which a heavy object is being swung around at constant speed in a circle does not transfer energy to the object, because the force is toward the centre of the circle at a right angle to the displacement. No work is done in either case.

The mathematical expression for work depends upon the particular circumstances. Work done in compressing a gas at constant temperature may be expressed as the product of pressure P times the change in volume dV; that is, W = PdV. Work done by a torque T in rotating a shaft through an angle φ may be expressed as the product of the torque times the angular displacement; that is, W = Tφ.

Work done on a body is equal to the increase in the energy of the body, for work transfers energy to the body. If, however, the applied force is opposite to the motion of the object, the work is considered to be negative, implying that energy is taken from the object. The units in which work is expressed are the same as those for energy, for example, in SI (International System of Units) and the metre-kilogram-second system, joule (newton-metre); in the centimetre-gram-second system, erg (dyne-centimetre); and in the English system, foot-pound.

**Energy**

Energy is the the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are, moreover, heat and work—i.e., energy in the process of transfer from one body to another. After it has been transferred, energy is always designated according to its nature. Hence, heat transferred may become thermal energy, while work done may manifest itself in the form of mechanical energy.

All forms of energy are associated with motion. For example, any given body has kinetic energy if it is in motion. A tensioned device such as a bow or spring, though at rest, has the potential for creating motion; it contains potential energy because of its configuration. Similarly, nuclear energy is potential energy because it results from the configuration of subatomic particles in the nucleus of an atom.

Energy can be neither created nor destroyed but only changed from one form to another. This principle is known as the conservation of energy or the first law of thermodynamics. For example, when a box slides down a hill, the potential energy that the box has from being located high up on the slope is converted to kinetic energy, energy of motion. As the box slows to a stop through friction, the kinetic energy from the box’s motion is converted to thermal energy that heats the box and the slope.

Energy can be converted from one form to another in various other ways. Usable mechanical or electrical energy is, for instance, produced by many kinds of devices, including fuel-burning heat engines, generators, batteries, fuel cells, and magnetohydrodynamic systems.

**Power**

Power, in science and engineering, time rate of doing work or delivering energy, expressible as the amount of work done W, or energy transferred, divided by the time interval t—or W/t. A given amount of work can be done by a low-powered motor in a long time or by a high-powered motor in a short time. Units of power are those of work (or energy) per unit time, such as foot-pounds per minute, joules per second (or watts), and ergs per second. Power is expressible also as the product of the force applied to move an object and the speed of the object in the direction of the force. If the magnitude of the force F is measured in pounds and the speed ν in feet per minute, the power equals Fν foot-pounds per minute. In the International System of Units, power is measured in newton metres per second.

Most machines have rotating shafts, and, in terms of the twisting moment, or magnitude of torque (τ), on a shaft and the angular speed ω of the shaft, the power is given by τω. τ is usually expressed in inch-pounds, ω in radians per second, and power in inch-pounds per second. Another unit of mechanical power is the horsepower (hp), which is equal to 33,000 foot-pounds per minute, or 6,600 inch-pounds per second.

**Relationship between work power and energy**

WORK = W=Fd

Because energy is the capacity to do work , we measure energy and work in the same units (N*m or joules).

POWER (P) is the rate of energy generation (or absorption) over time:P = E/t Power’s SI unit of measurement is the Watt, representing the generation or absorption of energy at the rate of 1 Joule/sec. Power’s unit of measurement in the English system is the horsepower, which is equivalent to 735.7 Watts.

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