FACTOID # 22: South Dakota has the highest employment ratio in America, but the lowest median earnings of full-time male employees.

 Home Encyclopedia Statistics States A-Z Flags Maps FAQ About

 WHAT'S NEW

SEARCH ALL

Search encyclopedia, statistics and forums:

(* = Graphable)

Encyclopedia > Mechanical work

In physics, mechanical work is the amount of energy transferred by a force. Like energy, it is a scalar quantity, with SI units of joules. The term work was first coined in the 1830s by the French mathematician Gaspard-Gustave Coriolis.[1] A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Force (disambiguation). ... See scalar for an account of the broader concept also used in mathematics and computer science. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The joule (symbol J, also called newton metre, or coulomb volt) is the SI unit of energy and work. ... Gaspard-Gustave de Coriolis or Gustave Coriolis (May 21, 1792â€“September 19, 1843), mathematician, mechanical engineer and scientist born in Paris, France. ...

According to the work-energy theorem if an external force acts upon an object, causing its kinetic energy to change from Ek1 to Ek2, then the mechanical work (W) is given by:[2] The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

$W = Delta E_k = E_{k2} - E_{k1} = frac{1}{2}m Delta (v^2) ,!$

where m is the mass of the object and v is the object's speed. For other uses, see Mass (disambiguation). ... This article does not cite any references or sources. ...

When the force is in the same direction as the displacement, the mechanical work can be calculated from the scalar multiplication of the applied force (F) and the displacement (d) of the object. This is given by: For other uses, see Force (disambiguation). ... Look up displacement in Wiktionary, the free dictionary. ...

$W = F d ,!$

## Contents

A baseball pitcher does positive work on the ball by transferring energy into it. The catcher does negative work on it.

Work can be zero even when there is a force. The centripetal force in uniform circular motion, for example, does zero work because the kinetic energy of the moving object doesn't change. Likewise, when a book sits on a table, the table does no work on the book, because no energy is transferred into or out of the book. The centripetal force is the external force required to make a body follow a circular path at constant speed. ... In physics, circular motion is rotation along a circle: a circular path or a circular orbit. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

Heat conduction is not considered to be a form of work, since there is no macroscopically measurable force, only microscopic forces occurring in atomic collisions. o

## Units

Main article: work (thermodynamics)

The SI unit of work is the joule (J), which is defined as the work done by a force of one newton acting over a distance of one meter. This definition is based on Sadi Carnot's 1824 definition of work as "weight lifted through a height", which is based on the fact that early steam engines were principally used to lift buckets of water, through a gravitational height, out of flooded ore mines. The dimensionally equivalent newton-meter (N·m) is sometimes used instead; however, it is also sometimes reserved for torque to distinguish its units from work or energy. In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. ... The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... For other uses, see Newton (disambiguation). ... The metre, or meter (symbol: m) is the SI base unit of length. ... Sadi Carnot in the dress uniform of a student of the Ã‰cole polytechnique Nicolas LÃ©onard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French physicist and military engineer who gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the... Newton metre is the unit of moment in the SI system. ... For other senses of this word, see torque (disambiguation). ...

Non-SI units of work include the erg, the foot-pound, the foot-poundal, and the liter-atmosphere.r An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, symbol erg. Its name is derived from the Greek word meaning work. The erg is a small unit, equal to a force of one dyne exerted for a distance of one... In physics, a foot-pound (symbol ft·lbf or ft·lbf) is an Imperial and U.S. customary unit of mechanical work, or energy, although in scientific fields one commonly uses the equivalent metric unit of the joule (J). ...

## Mathematical calculation

### Force and displacement

Force and displacement are both vector quantities and they are combined using the dot product to evaluate the mechanical work, a scalar quantity: This article is about vectors that have a particular relation to the spatial coordinates. ... In mathematics, the dot product, also known as the scalar product, is a binary operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. ...

$W = bold{F} cdot bold{d} = F d cosphi$           (1)

where φ is the angle between the force and the displacement vector. k

In order for this formula to be valid, the force and angle must remain constant. The object's path must always remain on a single, straight line, though it may change directions while moving along the line.

In situations where the force changes over time, or the path deviates from a straight line, equation (1) is not generally applicable although it is possible to divide the motion into small steps, such that the force and motion are well approximated as being constant for each step, and then to express the overall work as the sum over these steps. This article is about the concept of time. ...

The general definition of mechanical work is given by the following line integral: This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ...

$W_C := int_{C} bold{F} cdot mathrm{d}bold{s}$             (2)

where:

C is the path or curve traversed by the object;
F is the force vector;
s is the position vector.

The expression δW=F·ds is an inexact differential which means that the calculation of WC is path-dependent and cannot be differentiated to give F·ds. In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... For other uses, see Force (disambiguation). ... A position vector is a vector used to describe the spatial position of a point relative to a reference point called the origin (of the space). ... In physics, an inexact differential, as contrasted with an exact differential, of a function f is denoted: ; as is true of point functions. ... Differentiation can mean the following: In biology: cellular differentiation; evolutionary differentiation; In mathematics: see: derivative In cosmogony: planetary differentiation Differentiation (geology); Differentiation (logic); Differentiation (marketing). ...

Equation (2) explains how a non-zero force can do zero work. The simplest case is where the force is always perpendicular to the direction of motion, making the integrand always zero. This is what happens during circular motion. However, even if the integrand sometimes takes nonzero values, it can still integrate to zero if it is sometimes negative and sometimes positive. This article deals with the concept of an integral in calculus. ...

The possibility of a nonzero force doing zero work illustrates the difference between work and a related quantity, impulse, which is the integral of force over time. Impulse measures change in a body's momentum, a vector quantity sensitive to direction, whereas work considers only the magnitude of the velocity. For instance, as an object in uniform circular motion traverses half of a revolution, its centripetal force does no work, but it transfers a nonzero impulse. For other uses, see Impulse (disambiguation). ... This article is about momentum in physics. ...

### Mechanical energy

Main article: Mechanical energy

The mechanical energy of a body is that part of its total energy which is subject to change by mechanical work. It includes kinetic energy and potential energy. Some notable forms of energy that it does not include are thermal energy (which can be increased by frictional work, but not easily decreased) and rest energy (which is constant as long as the rest mass remains the same). In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... For other uses, see Friction (disambiguation). ... The rest energy of a particle is its energy when it is not moving relative to a given inertial reference frame. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ...

If an external force F acts upon a body, causing its kinetic energy to change from Ek1 to Ek2, then:[3] The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

$W = Delta E_k = E_{k2} - E_{k1} = Delta E_k = frac{1}{2} mv_2 ^2 - frac{1}{2} mv_1 ^2 = frac{1}{2} m Delta (v^2)$

Thus we have derived the result, that the mechanical work done by an external force acting upon a body is proportional to the difference in the squares of the speeds. (It should be observed that the last term in the equation above is Δv2 rather than v)2.)

The principle of conservation of mechanical energy states that, if a system is subject only to conservative forces (e.g. only to a gravitational force), or if the sum of the work of all the other forces is zero, its total mechanical energy remains constant. A conservative force is a force which is path-independent. ... This article covers the physics of gravitation. ...

For instance, if an object with constant mass is in free fall, the total energy of position 1 will equal that of position 2.

$(E_k + E_p)_1 = (E_k + E_p)_2 ,!$

where

The external work will usually be done by the friction force between the system on the motion or the internal-non conservative force in the system or loss of energy due to heat. The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ...

## References

1. ^ Jammer, Max (1957). Concepts of Force. Dover Publications, Inc.. ISBN 0-486-40689-X.
2. ^ See, for example, Tipler (1991), page 138.
3. ^ Zitzewitz,Elliott, Haase, Harper, Herzog, Nelson, Nelson, Schuler, Zorn (2005). Physics: Principles and Problems. McGraw-Hill Glencoe, The McGraw-Hill Companies, Inc.. ISBN 0-07-845813-7.

## Bibliography

• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed., Brooks/Cole. ISBN 0-534-40842-7.
• Tipler, Paul (1991). Physics for Scientists and Engineers: Mechanics, 3rd ed., extended version, W. H. Freeman. ISBN 0-87901-432-6.

Results from FactBites:

 Mechanical work - Wikipedia, the free encyclopedia (1069 words) The SI derived unit of work is the joule (J), which is defined as the work done by a force of one newton acting over a distance of one meter. One mechanism of heat conduction is collisions between fast-moving atoms in a warm body with slow-moving atoms in a cold body. The mechanical energy of a body is that part of its total energy which is subject to change by mechanical work.
More results at FactBites »

Share your thoughts, questions and commentary here