objects are compared in different gravitational fields, such as away from the Earth's surface. For example, on the surface of the Moon, gravity is only about one-sixth as strong as on the surface of the Earth. A one-kilogram mass is still a one-kilogram mass (as mass is an intrinsic property of the object) but the downwards force due to gravity is only one-sixth of what the object would experience on Earth.
- masses are considered in the context of a lever, such as a cantilever structure.
- locating the center of gravity of an object (although if the gravitation field is uniform, the center of gravity will coincide with the center of mass).
Units of weight
Systems of units of weight (force) and mass have a tangled history, partly because the distinction was not properly understood when many of the units first came into use.
SI units
In most modern scientific work, physical quantities are measured in SI units. The SI unit of mass (and hence weight in some everyday senses)[3] is the kilogram. The SI unit of force (and hence weight in the mechanics sense) is the newton (N) – which can also be expressed in SI base units as kg·m/s² (kilograms times metres per second squared).
The gravitational force exerted on an object is proportional to the mass of the object, so it is reasonable to think of the strength of gravity as measured in terms of force per unit mass, that is, newtons per kilogram (N/kg). However, the unit N/kg resolves to m/s²; (metres per second per second), which is the SI unit of acceleration, and in practice gravitational strength is usually quoted as an acceleration.
The pound and other non-SI units
In United States customary units, the pound can be either a unit of force or a unit of mass. Related units used in some distinct, separate subsystems of units include the poundal and the slug. The poundal is defined as the force necessary to accelerate a one-pound object at 1 ft/s², and is equivalent to about 1/32 of a pound (force). The slug is defined as the amount of mass that accelerates at 1 ft/s² when a pound of force is exerted on it, and is equivalent to about 32 pounds (mass).
The kilogram-force is a non-SI unit of force, defined as the force exerted by a one-kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI.
Conversion between weight (force) and mass
To convert between weight (force) and mass we use Newton's second law, F = ma (force = mass × acceleration). Here, F is the force due to gravity, m is the mass of the object in question, and a is the acceleration due to gravity, on Earth approximately 9.8 m/s² or 32.2 ft/s²). In this context the same equation is often written as W = mg, with W standing for weight, and g for the acceleration due to gravity.
Sensation of weight
- See also: apparent weight
The weight force that we actually sense is not the downward force of gravity, but the normal force (an upward contact force) exerted by the surface we stand on, which opposes gravity and prevents us falling to the center of the Earth. This normal force, called the apparent weight, is the one that is measured by a spring scale.
For a body supported in a stationary position, the normal force balances the earth's gravitational force, and so apparent weight has the same magnitude as actual weight. (Technically, things are slightly more complicated. For example, an object immersed in water weighs less, according to a spring scale, than the same object in air; this is due to buoyancy, which opposes the weight force and therefore generates a smaller normal. These and other factors are explained further under apparent weight.)
If there is no contact with any surface to provide such an opposing force then there is no sensation of weight (no apparent weight). This happens in free-fall, as experienced by sky-divers (until they approach terminal velocity) and astronauts in orbit, who feel "weightless" even though their bodies are still subject to the force of gravity: they're just no longer resisting it. The experience of having no apparent weight is also known as microgravity.
A degree of reduction of apparent weight occurs, for example, in elevators. In an elevator, a spring scale will register a decrease in a person's (apparent) weight as the elevator starts to accelerate downwards. This is because the opposing force of the elevator's floor decreases as it accelerates away underneath one's feet.
Measuring weight
- Main article: Weighing scale
Weight is commonly measured using one of two methods. A spring scale or hydraulic or pneumatic scale measures weight force (strictly apparent weight force) directly. If the intention is to measure mass rather than weight, then this force must be converted to mass. As explained above, this calculation depends on the strength of gravity. Household and other low precision scales that are calibrated in units of mass (such as kilograms) assume roughly that standard gravity will apply. However, although nearly constant, the apparent or actual strength of gravity does in fact vary very slightly in different places on the earth (see standard gravity, physical geodesy, gravity anomaly and gravity). This means that same object (the same mass) will exert a slightly different weight force in different places. High precision spring scales intended to measure mass must therefore be calibrated specifically according their location on earth.
Mass may also be measured with a balance, which compares the item in question to others of known mass. This comparison remains valid whatever the local strength of gravity. If weight force, rather than mass, is required, then this can be calculated by multiplying mass by the acceleration due to gravity – either standard gravity (for everyday work) or the precise local gravity (for precision work).
Gross weight is a term that generally is found in commerce or trade applications, and refers to the gross or total weight of a product and its packaging. Conversely, net weight refers to the intrinsic weight of the product itself, discounting the weight of packaging or other materials.
Relative weights on the Earth, other planets and the Moon
The following is a list of the weights of a mass on the surface of some of the bodies in the solar system, relative to its weight on Earth:
References
- ^ a b The National Standard of Canada, CAN/CSA-Z234.1-89 Canadian Metric Practice Guide, January 1989:
5.7.3 Considerable confusion exists in the use of the term "weight." In commercial and everyday use, the term "weight" nearly always means mass. In science and technology, "weight" has primarily meant a force due to gravity. In scientific and technical work, the term "weight" should be replaced by the term "mass" or "force," depending on the application.
5.7.4 The use of the verb "to weigh" meaning "to determine the mass of," e.g., "I weighed this object and determined its mass to be 5 kg," is correct.
- ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 881, section 8.3[1]
- ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 881, section 8.3[2] "Thus the SI unit of the quantity weight used in this sense is the kilogram (kg) and the verb 'to weigh' means 'to determine the mass of' or '"to have a mass of.'"
See also
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