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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 ).
Units for other physical quantities are derived from this set as needed. In English Engineering Units, the pound-mass and the pound-force are distinct base units, and Newton's Second Law of Motion takes the form = where is the acceleration in ft/s 2 and g c = 32.174 lb·ft/(lbf·s 2).
A newton is defined as 1 kg⋅m/s 2 (it is a named derived unit defined in terms of the SI base units). [1]: 137 One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s −2 ...
One slug is a mass equal to 32.17405 lb (14.59390 kg) based on standard gravity, the international foot, and the avoirdupois pound. [3] In other words, at the Earth's surface (in standard gravity), an object with a mass of 1 slug weighs approximately 32.17405 lbf or 143.1173 N. [4] [5]
In unit systems where force is a derived unit, like in SI units, g c is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems , g c may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results. [ 2 ]
1 poundal = force to accelerate 1 pound mass 1 foot/second/second ≈ 0.138 newtons. 1 kip = 1000 lbf ≈ 4.44822 kN; Energy 1 foot-pound ≈ 1.356 J; 1 British thermal unit (Btu) ≈ 1.055 kJ (1,054–1,060 J, depending on which of several definitions of BTU is used)
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).