Work, Energy and Power

# 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

#### 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).

## 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