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Concept
Mass versus weight
Summary
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than another with less mass if both are subject to the same gravity (i.e. the same gravitational field strength).
In scientific contexts, mass is the amount of "matter" in an object (though "matter" may be difficult to define), but weight is the force exerted on an object's matter by gravity. At the Earth's surface, an object whose mass is exactly one kilogram weighs approximately 9.81 newtons, the product of its mass and the gravitational field strength there. The object's weight is less on Mars, where gravity is weaker; more on Saturn, where gravity is stronger; and very small in space, far from significant sources of gravity, but it always has the same mass.
Material objects at the surface of the Earth have weight despite such sometimes being difficult to measure. An object floating freely on water, for example, does not appear to have weight since it is buoyed by the water. But its weight can be measured if it is added to water in a container which is entirely supported by and weighed on a scale. Thus, the "weightless object" floating in water actually transfers its weight to the bottom of the container (where the pressure increases). Similarly, a balloon has mass but may appear to have no weight or even negative weight, due to buoyancy in air. However the weight of the balloon and the gas inside it has merely been transferred to a large area of the Earth's surface, making the weight difficult to measure. The weight of a flying airplane is similarly distributed to the ground, but does not disappear. If the airplane is in level flight, the same weight-force is distributed to the surface of the Earth as when the plane was on the runway, but spread over a larger area.
A better scientific definition of mass is its description as being a measure of inertia, which is the tendency of an object to not change its current state of motion (to remain at constant velocity) unless acted on by an external unbalanced force.
Official source
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