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The same amount of work is done by the object when decelerating from its current speed to a state of rest. [ 2 ] The SI unit of kinetic energy is the joule , while the English unit of kinetic energy is the foot-pound .
The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: = If the force is variable, then work is given by the line integral:
The work per unit of charge is defined as the movement of negligible test charge between two points, and is expressed as the difference in electric potential at those points. The work can be done, for example, by generators, (electrochemical cells) or thermocouples generating an electromotive force.
This is the definition declared in the modern International System of Units in 1960. [13] The definition of the joule as J = kg⋅m 2 ⋅s −2 has remained unchanged since 1946, but the joule as a derived unit has inherited changes in the definitions of the second (in 1960 and 1967), the metre (in 1983) and the kilogram . [14]
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
where r is the distance between the point charges q and Q, and q and Q are the charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.
As an example, mechanical work and heat are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include work, heat and arc length.
If the work for an applied force is independent of the path, then the work done by the force is evaluated from the start to the end of the trajectory of the point of application. This means that there is a function U ( x ), called a "potential", that can be evaluated at the two points x A and x B to obtain the work over any trajectory between ...