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The principle of classical mechanics that E ∝ mv 2 is conserved was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force or vis viva. [4]: 227 Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722. By dropping weights from different heights ...
Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Thus, if the net work is positive, then the particle's kinetic energy increases by the amount of the work. If the net work done is negative, then the particle's kinetic energy decreases by the amount of work. [18]
In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. [133] Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work can be dissipated into heat.
A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system.
In physics and engineering, kinetics is the branch of classical mechanics that is concerned with the relationship between the motion and its causes, specifically, forces and torques. [ 1 ] [ 2 ] [ 3 ] Since the mid-20th century, the term " dynamics " (or " analytical dynamics ") has largely superseded "kinetics" in physics textbooks, [ 4 ...
In a set of curvilinear coordinates ξ = (ξ 1, ξ 2, ξ 3), the law in tensor index notation is the "Lagrangian form" [18] [19] = (+) = (˙), ˙, where F a is the a-th contravariant component of the resultant force acting on the particle, Γ a bc are the Christoffel symbols of the second kind, = is the kinetic energy of the particle, and g bc ...
Therefore, the kinetic energy per kelvin of one mole of monatomic ideal gas (D = 3) is = =, where is the Avogadro constant, and R is the ideal gas constant. Thus, the ratio of the kinetic energy to the absolute temperature of an ideal monatomic gas can be calculated easily:
If the central force is a conservative force, then the magnitude F(r) of a central force can always be expressed as the derivative of a time-independent potential energy function U(r) [3] = Thus, the total energy of the particle—the sum of its kinetic energy and its potential energy U —is a constant; energy is said to be conserved .