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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 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 .
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.
In physics, a conservative force is a force with the property that the total work done by the force in moving a particle between two points is independent of the path taken. [1] Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement ) by a conservative ...
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 ...
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]
This says that the work is equal to the line integral of the force F along a path C; for details see the mechanical work article. Work and thus energy is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball.
The corresponding term in biology, to describe the processes by which animals update their estimates of position or heading, is path integration. Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System , have made simple dead reckoning by humans obsolete ...