Almost everyone has been on a weighing scale; some people check their weight daily for health or athletic purposes, while others make more use of weighing devices at the supermarket, on the job or as part of a comprehensive science education.
Often, weighing scales are accused of being incorrect, and rightly so; these devices are subject to considerable mechanical stress in relation to their size, especially in the case of so-called bathroom or household scales, and it doesn't take a lot to throw the weighing scale parts into disarray even if they are properly constructed and calibrated.
Have you ever pondered how a scale even "knows" how much mass has been added to it? How do these devices, whatever their inner workings, remain accurate over time? And what's with the claim that "weight is not the same mass" when it's clear from a glance at the commercial world that kilograms and pounds are often treated as different units of the very same physical quantity?
Weight and Mass Defined
Mass is a measure of matter per se, the amount of "stuff" present in a sample. One way to conceive of mass is that it has intertia, meaning that if it's not moving, energy must be added to the system to make it move, whereas if it's already moving, energy must be added to slow it down or stop it outright. Intuition tells you that the more massive an object is, the harder it is to either cajole into motion from rest or stop when it's in motion.
Weight is mass multiplied by g, the acceleration produced by gravity. On Earth, the generally used g value is 9.8 meters per second squared (m/s2), whereas on the moon it is considerably less and on Jupiter it is far greater because these bodies have smaller and larger masses than Earth respectively. The upshot is that the same mass will have a different weight when placed in a stronger or weaker gravitational field.
In the SI system of units (the metric, or international, system), the base unit of mass is the kilogram (kg), while the unit of weight, or more broadly force, is the newton (N). Thus a person with a mass of 70 kg (about 154 pounds, or lb; 1 kg = 2.204 lb) will have a weight of (70)(9.8) = 686 N on Earth.
Mass Versus Weight in Everyday Life
The pound is actually a unit of weight, not mass. The root unit of mass in the corresponding imperial, or British, system of units is the slug, which has fallen largely into disuse. Since most humans use their scales on Earth and Americans want to know their "mass" in pounds, gravity in effect is incorporated into weighing scales on Earth.
It is therefore not scientifically correct to say "100 kilograms equals 220.4 pounds," but it is correct to say "A mass of 100 kilograms has a weight of 220.4 pounds on Earth." Bear in mind that most quantities were invented centuries ago, at a time when gravity besides Earth's was not worth accounting for!
A Short History of Weighing Machines
Gottfried Wilhelm Leibniz (1646-1716), who is credited with co-inventing the mathematical field of calculus along with Isaac Newton, is also believed to have conceived the first weighing devices. His construction was much like the astrological sign Libra is usually represented: A vertical post with a horizontal bar fixed to the top of it by a movable joint. From the ends of this horizontal bar were suspended two plates of sufficient relative mass to keep the assembly in balance.
The genius of Leibniz' device, called a center beam balance, is that it could determine relative masses of labeled objects through a series of additions and subtractions of pebbles or the like. From this scheme, it was inevitable that positions would be marked and assigned numerical values, and a whole new system of keeping precise track of quantities was put in play.
In the mid-1750s, the first pendulum scales appeared, and these became more elaborate over time as engineering developments allowed for greater precision in manufacturing. Pendulum scales are still used today in many forms, and many are fitted with electronics that allow for, say, the conversion of a given weight to a given purchase price.
Types of Weighing Scales
The center beam balance, for reasons that are likely already clear, is no more a part of modern science or commerce than is the Pony Express. Without this now-quaint machine, though, none of the scales in modern use would have arisen. A sampling of modern weighing machines:
Analytical balance: This is what you're likely to have seen in the lab. You simply place an object on a plate atop the unit and it returns a mass (or, if the user prefers, a "mass" in imperial units such as ounces or pounds). These are built so that the plate is at rest under the influence of gravity alone, and the machine balances this off by internally determining the force required to keep the plate precisely still.
Bathroom scale: Progressive advances in technology have resulted in models that are no longer anything close to a uniform bathroom scale definition. Most today are digital, but "old-school" analog models persist.
Counting scale: This is used to weigh multiple objects known to have a uniform weight (for example, precision ball bearings) and display a total piece count based on the result.
For example, if you had a large collection of different-colored but otherwise identical rubber balls, you could determine exactly how many are in your collection by loading them onto such a scale and setting the input parameter to the mass of one ball. Thus for a set of rubber balls weighing 0.125 kg apiece and having a total mass of 40 kg, the machine would respond that you have [40 kg/(0.125 kg/ball)] = 320 balls in your collection.
Crane scale: These scales have an expected capacity of 5,000 pounds (2,270 kg) or more, which is 2.5 tons, similar to most everyday motor vehicles. These are designed to weigh loads at the same time they are being suspended above the ground by a crane. This would not be an endeavor for the inattentive!
Microbalance: These can be read to a value of 1 microgram (1µg) or better. A microgram is one billionth of a kilogram, which means that while it's probably not a unit you have intersected with much on a conscious level, it's part of everyday life for chemists, microbiologists, pharmacologists and many other science professionals.
Postal scale: This kind of weighing device is an example of a computing scale, which displays price changes as mass is added or removed to suit customer needs. It is used to determine shipping weight or delivery charges for letters or parcels delivered by the United States Postal Service (USPS) or private shipping companies.
Vehicle scale: These scales are built for weighing large trucks, farm vehicles and other large industrial vehicles. You have probably seen signs that say "Weigh Station Ahead" if you have driven on U.S. interstate highways.
These are used to enforce safety regulations, such as ensuring vehicles using certain roads are not exceeding the posted weight limits of those roads – something, again, most people don't have occasion to peer at closely!
- Bizerba News: History of the Scale Part 3: Scales and Weighing Through the Ages
- Union University Physics: The Science Guys
- Chemistry LibreTexts: Measurements, Quantities, and Unity Factors
- OpenLearn Science, Maths & Technology: Accurate Weighing Balance
- LibreTexts Chemistry: Proper Use of Balances
- Industrial Scale Company: Types of Weighing Scales
About the Author
Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.