When we apply this special form of Newton’s second law to a typical application with acceleration due to gravity of approximately 32.2 ft/s 2, we find that 1 lbm produces a force (or weight) of 1 lbf.į = 1 lbm * 32.2 ft/s 2 / (32.2 lbm-ft/lbf-s 2)
Note that the gravitational constant, g c, provides consistency in the units. In this system, mass is given in pounds-mass (lbm), acceleration is given in feet per second-squared (ft/s 2), and force is given in pounds-force (lbf). To see why the gravitational constant is needed, let’s look at the units of the force equation using the EE system:į = (lbm * ft/s 2) / (lbm-ft/lbf-s 2) = lbf In the English Engineering system of units, Newton’s second law is modified to include a gravitational constant, g c, which is equal to 32.2 lbm-ft/lbf-s 2. When we apply this equation in a typical application, where the acceleration due to gravity equals approximately 32.2 ft/s 2, we find that 1 slug produces a force (sometimes referred to as “weight”) of 32.2 lbf. One pound-force (lbf) represents the force required to accelerate 1 slug of mass at 1 ft/s 2. In the British Gravitational (BG) system, mass is measured in slugs, acceleration is measured in feet per second-squared (ft/s 2), and the product of mass and acceleration, force, is measured in pounds-force (lbf). For this discussion, we’ll refer to the British Gravitational and English Engineering systems. (For example, Apothecaries’ units have been mostly replaced, with the exception of the grain.)Ĭurrently, there are three predominant systems of English units: the British Gravitational system (also referred to as the English Gravitational system), the English Absolute system, and the English Engineering system. The English system of units has many variations, most of which have long been discarded with the exception of one or two measurements that are still in use for niche applications. When we apply this equation in a typical application, where the acceleration due to gravity equals approximately 9.81 m/s 2, we find that 1 kg of mass produces a force (sometimes referred to as “weight”) of 9.81 N.į = 9.81 N Image credit: The Physics Classroom Mass and force in English units: lbm, slugs, and lbf One Newton represents the force required to accelerate 1 kg of mass at 1 m/s 2. The typical unit of mass in the metric system is the kilogram (kg), acceleration is defined as meters per second-squared (m/s 2), and the unit of force is the Newton (N), which is equal to 1 kgm/s 2. Regardless of the units of measure, the relationship between mass and force is given in Newton’s second law of motion, which states that force equals mass times acceleration. (For example, Celsius and liters are metric units, but are not included in the SI system.) Note that SI consists only of metric units, but the metric system contains some units that are not included in SI. The SI system is sometimes referred to as the “MKS” system, because it is the only system of units to use meters, kilograms, and seconds as base units for length, mass, and time, respectively.
The most widely-adopted version of the metric system is the International System of units (SI). There are several variations of what we often refer to as the “metric” system of units, in which measurements are based on powers of ten.
NEWTON UNIT OF FORCE EQUAL TO HOW TO
To cut through the confusion and demonstrate how to convert between mass and force, we’ve put together the following formulas to show the relationship between the two - in both metric and English units. (Have you ever purchased 0.1 slug of apples?) One variation of the English system of units specifies mass in terms of slugs, but slugs are hardly a common concept. Using one unit - the pound - for both mass and force is inherently confusing. Part of the difficulty in dealing with mass and force, especially in English units, lies in the fact that we define an object’s weight (force) in pounds. However, mass and force are a different story. One inch is approximately 2.5 centimeters… One meter is approximately thirty-nine inches. If you work in the industrial world, you probably encounter some measurements (such as length) often enough in both English and metric units that you can estimate them with relative ease. But it’s likely there has been (or will be) a time when you need to work in both systems of units, possibly even switching back-and-forth between English units for some components and metric units for others. If you’re lucky, you work primarily in one set of units - either metric or English. Converting between mass and force is a common step in the design and sizing of linear motion systems.
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