MECHANICAL FORMULAE BY RAMESH

work was first coined in the 1830s by the French mathematician Gaspard-Gustave Coriolis.[1]
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]

where m is the mass of the object and v is the object's speed.
The mechanical work applied to an object can be calculated from the dot product of the applied force (F) and the displacement (d) of the object. This is given by:

Contents[hide]
1 Introduction
2 Units
3 Mathematical calculation
3.1 Force and displacement
3.2 Mechanical energy
4 Frame of reference
5 References
6 Bibliography
7 External links
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[edit] Introduction

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 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 despite exerting a force equivalent to mg upwards, because no energy is transferred into or out of the book.
Heat conduction is not considered to be a form of work, since the energy gets transferred into atomic vibrations rather than a macroscopic displacement.

[edit] 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.
Non-SI units of work include the erg, the foot-pound, the foot-poundal, and the liter-atmosphere.

[edit] Mathematical calculation

[edit] 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:
(1)
where is the angle between the force and the displacement vector.
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.
The general definition of mechanical work is given by the following line integral:
(2)
where: