Weight is the force of gravity acting on an object. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton [N].

In many real-world situations, the act of weighing may produce a result that differs from the ideal value provided by the definition used. This is usually referred to as the apparent weight of the object. A common example of this is the effect of buoyancy when an object is immersed in a fluid the displacement of the fluid will cause an upward force on the object, making it appear lighter when weighed on a scale.

Specific weight

The weight of a unit volume of a substance is called specific weight (\(\gamma\) also known as the unit weight) and is equal to:

\[\gamma =\rho g=\left[\dfrac{\textrm{N}}{\textrm{m}^3}\right]\]

where \(\rho\) is the density and \(g\) is the gravitational acceleration.

Apparent weight

Apparent weight is a property of objects that correspond to how heavy an object is. The apparent weight of an object will differ from the weight of an object whenever the force of gravity acting on the object is not balanced by an equal but opposite normal force. By definition, the weight of an object is equal to the magnitude of the force of gravity acting on it.

This means that even a “weightless“ astronaut in low Earth orbit, with an apparent weight of zero, has almost the same weight as he would have while standing on the ground; this is due to the force of gravity in low Earth orbit and on the ground being almost the same.

An object that rests on the ground is subject to a normal force exerted by the ground. The normal force acts only on the boundary of the object that is in contact with the ground. This force is transferred into the body; the force of gravity on every part of the body is balanced by stress forces acting on that part. A “weightless“ astronaut feels weightless due to the absence of these stress forces. By defining the apparent weight of an object in terms of normal forces, one can capture this effect of the stress forces. A common definition is “the force the body exerts on whatever it rests on.“

The apparent weight can also differ from weight when an object is “partially or completely immersed in a fluid“, where there is an “upthrust“ from the liquid that is working against the force of gravity. Another example is the weight of an object or person riding in an elevator. When the elevator begins rising, the object begins exerting a force in the downward direction. If a scale was used, it would be seen that the weight of the object is becoming heavier because of the downward force, changing the apparent weight.

The role of apparent weight is also important in fluidization, when dealing with a number of particles, as it is the amount of force that the “upward drag force“ needs to overcome in order for the particles to rise and for fluidization to occur.