User:ThomasDLV/Work (physics)

The general definition of working in calculus is

W = FΔx

W = f(x)Δx

W ${\displaystyle \approx }$ ${\displaystyle \sum _{i=1}^{n}}$f(x)Δx

W = ${\displaystyle \lim _{n\to \infty }\sum _{i=1}^{n}}$f(x)Δx

W = ${\displaystyle \int \limits _{a}^{b}f(x)dx}$

For example, a particle is moved along the x-axis by a force that measures 5x^2 +1 pounds at a point 10 feet from the origin.

W = ${\displaystyle \int \limits _{a}^{b}f(x)dx}$

W = ${\displaystyle \int \limits _{0}^{10}5{x}^{2}}$+1

W = 5030/3 lbft/sec^2

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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.

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. 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.

Another unit for work is the foot-pound, which comes from the English system of measurement. As the unit name suggests, it is the product of pounds for the force and feet for the displacement. One joule is equivalent to 0.07376 ft-lbs.

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. 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.

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 product

For 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. 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 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. Energy shares the same unit of measurement with work (Joules) because the energy from the object doing work is transferred to the other objects it interacts with when work is being done. 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. Thus, if the net work is positive, then the particle's kinetic energy increases by the amount of the work. If the net work done is negative, then the particle's kinetic energy decreases by the amount of work.

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 E_k corresponding to the linear velocity and angular velocity of that body,

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 E_p of the object,

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.

"Work and potential energy." World of Physics, Gale, 2001. Gale In Context: Science

• https://go-gale-com.rcc.idm.oclc.org/ps/i.do?p=SCIC&u=cclc_riverside&id=GALE%7CCV2434500582&v=2.1&it=r&sid=bookmark-SCIC&asid=cd4b4bd7

Calculus: Early Transcendentals, 9th Edition

https://ng.cengage.com/static/nb/ui/evo/index.html?snapshotId=1529049&id=677758950&eISBN=9780357049105