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The mathematical by-product of this calculation is the mass–energy equivalence formula, that mass and energy are essentially the same thing: [14]: 51 [15]: 121 = = At a low speed (v ≪ c), the relativistic kinetic energy is approximated well by the classical kinetic energy.
The work done when a force of one newton moves the point of its application a distance of one metre in the direction of the force. [32] = 1 J = 1 m⋅N = 1 kg⋅m 2 /s 2 = 1 C⋅V = 1 W⋅s kilocalorie; large calorie: kcal; Cal ≡ 1000 cal IT = 4.1868 × 10 3 J: kilowatt-hour; Board of Trade Unit: kW⋅h; B.O.T.U. ≡ 1 kW × 1 h = 3.6 × 10 6 J
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Thermodynamic work is one of the principal kinds of process by which a thermodynamic system can interact with and transfer energy to its surroundings. This results in externally measurable macroscopic forces on the system's surroundings, which can cause mechanical work, to lift a weight, for example, [1] or cause changes in electromagnetic, [2] [3] [4] or gravitational [5] variables.
Mechanical work performed on a working fluid causes a change in the mechanical constraints of the system; in other words, for work to occur, the volume must be altered. Hence, volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved.
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F ...
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Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...