![]() ![]() The derivation of the work–energy principle begins with Newton’s second law of motion and the resultant force on a particle.What components of $\vec$. are the speeds of the particle before and after the work is done, and m is its mass. įrom 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 E k corresponding to the linear velocity and angular velocity of that body, If the net work done is negative, then the particle’s kinetic energy decreases by the amount of work. Thus, if the net work is positive, then the particle’s kinetic energy increases by the amount of the work. Each individual particle feels a force of such that, and are internal forces which I pretty much ignore in what follows Id like to show that the work done by is equivalent to the sum of the works done by over all particles. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Suppose we have a system of particles being acted upon by a single external force. 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. The electric field is by definition the force per unit charge, so that multiplying the field times the plate separation gives the work per unit charge. The work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance. This is approximately the work done lifting a 1 kg object from ground level to over a person's head against the force of gravity. The work W done by a constant force of magnitude F on a point that moves a displacement s in a straight line in the direction of the force is the productįor example, if a force of 10 newtons ( F = 10 N) acts along a point that travels 2 metres ( s = 2 m), then W = Fs = (10 N) (2 m) = 20 J. ![]() Due to work having the same physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU and calorie, are used as a measuring unit. Non-SI units of work include the newton-metre, erg, the foot-pound, the foot-poundal, the kilowatt hour, the litre-atmosphere, and the horsepower-hour. Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton-metres is a torque measurement, or a measurement of work. The dimensionally equivalent newton-metre (N⋅m) is sometimes used as the measuring unit for work, but this can be confused with the measurement unit of torque. The SI unit of work is the joule (J), named after the 19th-century English physicist James Prescott Joule, which is defined as the work required to exert a force of one newton through a displacement of one metre. In 1759, John Smeaton described a quantity that he called "power" "to signify the exertion of strength, gravitation, impulse, or pressure, as to produce motion." Smeaton continues that this quantity can be calculated if "the weight raised is multiplied by the height to which it can be raised in a given time," making this definition remarkably similar to Coriolis'. Īlthough work was not formally used until 1826, similar concepts existed before then. According to Rene Dugas, French engineer and historian, it is to Solomon of Caux "that we owe the term work in the sense that it is used in mechanics now". Etymology Īccording to the 1957 physics textbook by Max Jammer, the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis 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. He was the first to explain that simple machines do not create energy, only transform it. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche ( On Mechanics), in which he showed the underlying mathematical similarity of the machines as force amplifiers. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. 8 Work of forces acting on a rigid body.7.5 Coasting down a mountain road (gravity racing).7.4 Moving in a straight line (skid to a stop).7.3 Derivation for a particle in constrained movement.7.2 General derivation of the work–energy principle for a particle. ![]() 7.1 Derivation for a particle moving along a straight line. ![]()
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