As W = FS
∴ 1 unit work = 1 unit force × 1 unit distance
Thus, unit work is the amount of work done when a unit force displaces a body through a unit distance in the direction of the force.
Absolute units of work.
Work done is said to be one absolute unit if an absolute unit of force displaces a body through a unit distance in the direction of the force.
(i) Joule:
It is the absolute unit of work in SI, named after British physicist James Prescott Joule (1811 -1869). One joule of work is said to be done when a force of one newton displaces a body through a distance of one metre in its own direction.
1 joule = 1 newton × 1 metre or 1 J = 1 Nm
(ii) Erg:
It is the absolute unit of work in CGS system. One erg of work is said to be done if a force of one dyne displaces a body through a distance of one centimetre in its own direction.
1 erg = 1 dyne × 1 cm
Relation between joule and erg.
1 joule = 1 newton × 1 metre
= 105 dyne× 102 cm =107 dyne cm
or 1 joule = 10 erg
Gravitational units of work
Work is said to be done one gravitational unit if a gravitational unit of force displaces a body through a unit distance in the direction of the force.
(i) Kilogram metre:
It is the gravitational unit of work in SI. One kilogram metre of work is said to be done when a force of one kilogram weight displaces a body through one metre in its own direction.
1 kg m = 1 kg wt × 1m = 9.8N × 1m
or 1 kg m = 9.8 J
(ii) Gram centimetre:
It is gravitational unit of force in CGS system. One gram centimetre of work is said to be done when a force of one gram weight displaces a body through one centimetre in its own direction.
1 g cm = 1 g wt × 1 cm = 980 dyne × 1 cm or 1 g cm = 980 erg