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The British imperial units and U.S. customary units for both energy and work include the foot-pound force (1.3558 J), the British thermal unit (BTU) which has various values in the region of 1055 J, the horsepower-hour (2.6845 MJ), and the gasoline gallon equivalent (about 120 MJ).
Systems of measure either define mass and derive a force unit or define a base force and derive a mass unit [1] (cf. poundal, a derived unit of force in a mass-based system). A slug is defined as a mass that is accelerated by 1 ft/s 2 when a net force of one pound (lbf) is exerted on it. [2]
See also kinetic energy per unit mass of projectiles. Potential energy with respect to gravity, close to Earth, per unit mass: gh, where g is the acceleration due to gravity (standardized as ≈9.8 m/s 2) and h is the height above the reference level (giving J/kg when g is in m/s 2 and h is in m).
The foot-pound force (symbol: ft⋅lbf, [1] ft⋅lb f, [2] or ft⋅lb [3]) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI ...
When the pound is used as a unit of mass, the core of the coherent system is similar and functionally equivalent to the corresponding subsets of the International System of Units (SI), using metre, kilogram and second (MKS), and the earlier centimetre–gram–second system of units (CGS).
This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit [11] —the use of Newton's second law, F = m ⋅ a, requires another factor, g c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s 2).
Sometimes the gram is used instead of kilogram for the unit of mass: 1 J⋅g −1 ⋅K −1 = 1000 J⋅kg −1 ⋅K −1. The specific heat capacity of a substance (per unit of mass) has dimension L 2 ⋅Θ −1 ⋅T −2, or (L/T) 2 /Θ. Therefore, the SI unit J⋅kg −1 ⋅K −1 is equivalent to metre squared per second squared per kelvin ...
Quantity (Common Name/s) (Common) Symbol/s Defining Equation SI Units Dimension Relative atomic mass of an element : A r, A, m ram = /The average mass is the average of the T masses m i (X) corresponding the T isotopes of X (i is a dummy index labelling each isotope):