Weight Definition in Science

Diagram of mass and weight
The most common definition of weight is mass multiplied by the force acting on it.

Kismalac, Wikimedia Commons

The everyday definition of weight is a measure of how heavy a person or object it. However, the definition is slightly different in science. Weight is the name of the force exerted on an object due to the acceleration of gravity. On Earth, weight is equal to the mass times the acceleration due to gravity (9.8 m/sec2 on Earth).

Key Takeaways: Weight Definition in Science

  • Weight is the product of mass multiplied by acceleration acting on that mass. Usually, it's an object's mass multiplied by the acceleration due to gravity.
  • On Earth, mass and weight have the same value and units. However, weight has a magnitude, like mass, plus a direction. In other words, mass is a scalar quantity while weight is a vector quantity.
  • In the United States, the pound is a unit of mass or weight. The SI unit of weight is the newton. The cgs unit of weight is the dyne.

Units of Weight

In the United States, the units of mass and weight are the same. The most common unit of weight is the pound (lb). However, sometimes the poundal and slug are used. The poundal is the force needed to accelerate a 1-lb mass at 1 ft/s2. The slug is the mass that is accelerated at 1 ft/s2 when 1 pound-force is exerted upon it. One slug is the equivalent of 32.2 pounds.

In the metric system, units of mass and weight are separate. The SI unit of weight is the newton (N), which is 1 kilogram meter per second squared. It is the force required to accelerate a 1-kg mass 1 m/s2. The cgs unit of weight is the dyne. The dyne is the force needed to accelerate a mass of one gram at the rate of one centimeter per second squared. One dyne equals exactly 10-5 newtons.

Mass vs Weight

Mass and weight are easily confused, especially when pounds are used! Mass is a measure of the quantity of matter contained in an object. It is property of matter and does not change. Weight is a measure of the effect of gravity (or other acceleration) upon an object. The same mass can have a different weight depending on the acceleration. For example, a person has the same mass on the Earth and on Mars, yet weighs only about one-third as much on Mars.

Measuring Mass and Weight

Mass is measured on a balance by comparing a known amount of matter (a standard) against an unknown amount of matter.

Two methods may be used to measure weight. A balance may be used to measure weight (in units of mass), however, balances won't work in the absence of gravity. Note a calibrated balance on the Moon would give the same reading as one on Earth. The other method of measuring weight is the spring scale or pneumatic scale. This device accounts for the local force of gravity upon an object, so a spring scale can give a slightly different weight for an object at two locations. For this reason, scales are calibrated to give the weight an object would have at nominal standard gravity. Commercial spring scales must be re-calibrated when they are moved from one location to another.

Weight Variance Across the Earth

Two factors change weight at different locations on the Earth. Increasing altitude decreases weight because it increases the distance between a body and the mass of the Earth. For example, a person who weighs 150 pounds at sea level would weigh about 149.92 pounds at 10,000 feet above sea level.

Weight also varies with latitude. A body weighs slightly more at the poles than at the equator. In part, this is due to the bulge of the Earth near the equator, which puts objects at the surface slightly further from the center of mass. The difference in centrifugal force at the poles compared to the equator also plays a role, where centrifugal force acts perpendicular to the axis of the Earth's rotation.

Sources

  • Bauer, Wolfgang and Westfall, Gary D. (2011). University Physics with Modern Physics. New York: McGraw Hill. p. 103. ISBN 978-0-07-336794-1.
  • Galili, Igal (2001). "Weight versus gravitational force: historical and educational perspectives". International Journal of Science Education. 23: 1073. doi:10.1080/09500690110038585
  • Gat, Uri (1988). "The weight of mass and the mess of weight". In Richard Alan Strehlow (ed.). Standardization of Technical Terminology: Principles and Practice – second volume. ASTM International. pp. 45–48. ISBN 978-0-8031-1183-7.
  • Knight, Randall D. (2004). Physics for Scientists and Engineers: a Strategic Approach. San Francisco, USA: Addison–Wesley. pp. 100–101. ISBN 0-8053-8960-1.
  • Morrison, Richard C. (1999). "Weight and gravity - the need for consistent definitions". The Physics Teacher. 37: 51. doi:10.1119/1.880152