Apparent weight
Encyclopedia
The weight in a given frame of reference is a generalized concept of weight
, see the ISO definition of weight.
An object's regular weight is its weight with respect to Earth. An object's weight with respect to, for example, an accelerating elevator
is different: if the elevator accelerates upward, objects feel heavier and seem to fall faster.
In certain contexts the phrase apparent weight may either mean the same, or be affected by external forces other than gravity, for example making it zero in the case of levitation
.
Thus it is the mass of the body times the local acceleration of free fall in the frame of reference
(which is not necessarily an inertial frame of reference
). It is the mass times the acceleration in the frame of reference, minus the non-gravitational forces.
The concept is often applied for the case that there is a nearby floor (or using a more general term: surface) or some other attachment structure that may prevent the object from being separated from it. In this case the structure provides the frame of reference.
In that case we can distinguish between forces exerted by the structure and other non-gravitational forces. Replacing in the definition "free fall" by "fall" we get the apparent weight with respect to the structure; while free fall applies if there is only gravitational force, "fall" refers to the case where no force is exerted by the structure, so there are only gravitational and non-gravitational external forces.
Thus the apparent weight of an object with respect to a structure is the mass of the object times its acceleration with respect to the frame of reference, minus the sum of the forces exerted by the structure (with the important special cases of one of the two being zero). It is equal to the sum of the external forces on the object, minus its mass times the acceleration of the frame of reference.
The forces exerted by the structure are e.g. the normal force
exerted on the object, plus friction
if the object rests on a slope, or tension in a seatbelt, etc.
Thus the apparent weight with respect to a structure is the ordinary weight (weight with respect to a frame of reference that is considered stationary) plus the non-gravitational external forces, minus the mass of the object times the acceleration of the frame of reference. While the last very much resembles weight, the extent to which the other forces resemble weight varies: they may be in various directions, they need not be proportional with mass, and they may vary with the position of the object. Anyway, levitation
is a situation of zero apparent weight in the presence of normal gravity but without acceleration, and hence in the presence of the normal g-force of 1g.
Inside a spherical capsule without windows and without anything fixed to or painted on the inside wall the only experienced concept of "downward direction" would be the direction of the apparent weight. If there are no other external forces than gravity this is the direction of the gravitational field strength minus the acceleration of the capsule, and there would be no way to know the direction of each separately. However, (non-gravitational) external forces which are not proportional to mass could give objects inside the capsule apparent weights in differing directions, making the concept "downward" ambiguous.
The apparent weight is equal to the object's weight in an inertial frame of reference if there are no other forces than gravity and the forces exerted by the structure, and the structure is at rest or moving with a constant velocity.
Thus an object's apparent weight is equal to its weight in an inertial frame of reference, unless:
Buoyancy
can be considered to reduce the apparent weight, since a scale shows a lower value. However, buoyancy can also be considered a spread-out normal force. See also below.
is the sum of all forces except gravity, so the apparent weight with respect to a structure is the sum of external non-gravitational forces, plus the mass of the object times the acceleration with respect to the structure minus the g-force. In many cases there are no such other forces; in those cases the apparent weight per unit mass is the acceleration with respect to the structure, minus the g-force. For example, in an elevator the apparent weight per unit mass of an object manifests itself as the negative of the g-force when it rests on the floor, and as the acceleration with respect to the elevator when it is falling (with the g-force being zero).
If the object rests on a surface of the structure (the g-force points out of the surface) then the total compressive force in the object near the surface is equal to the apparent weight. If the object hangs from the support structure then the total tensile force in the object near the points of support is equal to the apparent weight. A combination is also possible. The compressive or tensile force at any cross-section is the apparent weight of the free end of the object (resting on or hanging from the cross-section).
The weight per unit mass of an object in a particular frame of reference is the acceleration in the frame of reference, minus the non-gravitational forces per unit mass. In particular, it is the acceleration in the frame of reference when the object is in free fall.
The weight per unit mass of an object with respect to a structure is its acceleration with respect to the structure, minus the sum of the forces per unit mass exerted by the structure. In particular, it is the negative of the sum of the forces per unit mass exerted by the structure when the object is stationary with respect to the structure. This can be measured with a spring scale
.
It is equal to the gravitational field strength (which is the weight per unit mass in an inertial frame of reference) minus the acceleration of the structure.
The weight per unit mass with respect to the structure is the acceleration minus the g-force. For example, the weight per unit mass of an object with respect to an elevator cabin manifests itself as the negative of the g-force when it rests on the floor of the elevator cabin, and as the acceleration with respect to the elevator cabin when the object is falling.
s and is standing stationary on the floor. Gravity is pulling her downward with a force of:
where m is mass
and g is the acceleration due to gravity
. By definition,
Fgrav, the downward force of gravity, is Alice's actual weight. (Note that the force of gravity varies slightly over the surface of the earth, and 9.81 m/s2 is only an approximate value. See standard gravity
, Physical geodesy
, Gravity anomaly
and Gravity for further information.)
However, since Alice is at rest, the net force acting on her must be zero (otherwise Alice would be accelerating, according to Newton's second law). Since the net force is zero, the upward force exerted by the floor must exactly balance the downward force of gravity, meaning that Alice's actual weight and apparent weight are the same. (Here we are ignoring some minor effects such as buoyancy and centrifugal force, discussed later.)
It is the reaction force transmitted through the floor, not gravity pulling on her, that makes Alice feel heavy (the g-force is 1g). The crucial difference is that gravity is a long-range force that acts uniformly throughout an object, while reaction forces are short-range forces that act only on the surfaces of an object. Reaction forces are transferred throughout the body, causing it to deform slightly and allowing stresses to build up. Gravity, because it acts uniformly, does not cause such stresses.
It is essential to be clear about the signs of these forces and accelerations. Let us take downward forces and accelerations to be positive and upward forces and accelerations to be negative. This means that Fgravity is positive, Fnormal is negative, and Alice's acceleration is positive.
We know that Alice is accelerating at +3 ms−2, and we know that her mass is 65 kg. Applying an equation we get from Newton's second law, we have that
However, this net force is the sum of the force due to gravity and the normal force. Thus,
We already know from the earlier example that Fgravity = 637 N. Therefore
so
Thus the normal force is 442 N (upwards), so Alice's apparent weight is 442 N, and it feels to Alice as if her weight has decreased by about 30% (the g-force is 0.7g) — even though her actual weight (the force exerted on her by gravity) remains unchanged. If Alice were standing on a weighing scale then the weight registered would also be 442 N. This is because a scale does not measure an object's actual weight, but rather measures the force that it exerts on the scale.
The workings above consolidate into the neat formula
We can now more easily examine what happens when a takes a range of different values. The formula shows that when a = 0 we have Fnormal = −mg, which is, as expected, just the formula for Alice's actual weight (with the negative sign reflecting the fact that the normal force is upwards).
For increasingly positive a (increasing downward acceleration), the absolute magnitude of Fnormal (the magnitude ignoring the sign) steadily decreases, meaning that Alice's apparent weight steadily decreases (the g-force also). Conversely, for increasingly negative a (increasing upward acceleration), Alice's apparent weight steadily increases.
It is important to understand that it is acceleration, not velocity, that causes changes in apparent weight. In a lift travelling upwards or downards at any constant speed – however great – Alice's apparent weight will be the same as if the lift were at rest.
. During free-fall Alice experiences weightlessness
.
Free-fall also occurs, of course, if Alice is falling freely through the air (in the absence of any containing lift). Ignoring air resistance there is again no supporting force, and no sensation of weight. Objects in orbit
are also in free-fall; the mechanics are explained at Orbit
.
notation.
The apparent weight for an object under the influence of two arbitrary forces
, and 
, in the most general case can be calculated by the addition of vectors:
For the specific case mentioned above where
is the force of gravity with the choice of coordinate system such that the force of gravity is in the positive-y direction, and with 
is the force caused by the acceleration of a racing car equal to 
in the positive-x direction, the previous equations become:
In the most general case, an object under the influence of n accelerations has an apparent weight of:
, which occurs when an object is immersed in a fluid (a liquid or a gas). For example, an object immersed in water seems to weigh less, according to a spring scale, than the same object in air. The apparent weight of any floating object is zero. To make a precise definition of apparent weight involving buoyancy, apparent weight is equal to the tension force as a spring scale would measure when the object is hung downward from the scale in a body of fluid, and for positive apparent weight (of a negatively buoyant "sinkable" object), the scale is pulling the object upward. A negative apparent weight (of a positively buoyant "float-able" object) would need to be measured by having the spring scale pull the object downward instead.
This effect is quite different from the accelerating lift examples. A floating or immersed object is not accelerating upwards or downwards, so there can be no net force. In fact, buoyancy provides a supporting force exactly as the solid floor does. Because this force is diffuse and dispersed over the surface of the body, a feeling of "pseudo-weightlessness" arises when one is floating. A human can still tell the difference between weightlessness due to buoyancy and true weightlessness, because people can feel buoyancy forces due to their fluid pressure.
Objects also experience some buoyancy in air, so even in air, the normal force (apparent weight) is slightly less than the normal force which would be experienced in an evacuated chamber. The density of air
at sea level pressure
and room temperature
is about 1.2 kg/m3. Most objects are much denser than air and so this force is usually small. For an object with the same density
as water – about 1000 kg/m3 – the relative effect is about 0.12%. However, for objects of very low density the relative effect can be large. In fact, an object that is lighter than air, such as a helium balloon, has a negative apparent weight (as does an object lighter than water when it is forcibly pulled below the surface).
Variations in air pressure cause variations in air density and hence variations in apparent weight. Over a typical range of sea-level pressures this may amount to about a 0.01% change in apparent weight for an object of the same density as water (less for denser objects, more for less dense objects). Extremely accurate measurements must take this into account.
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...
, see the ISO definition of weight.
An object's regular weight is its weight with respect to Earth. An object's weight with respect to, for example, an accelerating elevator
Elevator
An elevator is a type of vertical transport equipment that efficiently moves people or goods between floors of a building, vessel or other structures...
is different: if the elevator accelerates upward, objects feel heavier and seem to fall faster.
In certain contexts the phrase apparent weight may either mean the same, or be affected by external forces other than gravity, for example making it zero in the case of levitation
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...
.
Definition
The ISO standard ISO 80000-4 (2006) defines weight as followsThus it is the mass of the body times the local acceleration of free fall in the frame of reference
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
(which is not necessarily an inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
). It is the mass times the acceleration in the frame of reference, minus the non-gravitational forces.
The concept is often applied for the case that there is a nearby floor (or using a more general term: surface) or some other attachment structure that may prevent the object from being separated from it. In this case the structure provides the frame of reference.
In that case we can distinguish between forces exerted by the structure and other non-gravitational forces. Replacing in the definition "free fall" by "fall" we get the apparent weight with respect to the structure; while free fall applies if there is only gravitational force, "fall" refers to the case where no force is exerted by the structure, so there are only gravitational and non-gravitational external forces.
Thus the apparent weight of an object with respect to a structure is the mass of the object times its acceleration with respect to the frame of reference, minus the sum of the forces exerted by the structure (with the important special cases of one of the two being zero). It is equal to the sum of the external forces on the object, minus its mass times the acceleration of the frame of reference.
The forces exerted by the structure are e.g. the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...
exerted on the object, plus friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
if the object rests on a slope, or tension in a seatbelt, etc.
Thus the apparent weight with respect to a structure is the ordinary weight (weight with respect to a frame of reference that is considered stationary) plus the non-gravitational external forces, minus the mass of the object times the acceleration of the frame of reference. While the last very much resembles weight, the extent to which the other forces resemble weight varies: they may be in various directions, they need not be proportional with mass, and they may vary with the position of the object. Anyway, levitation
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...
is a situation of zero apparent weight in the presence of normal gravity but without acceleration, and hence in the presence of the normal g-force of 1g.
Inside a spherical capsule without windows and without anything fixed to or painted on the inside wall the only experienced concept of "downward direction" would be the direction of the apparent weight. If there are no other external forces than gravity this is the direction of the gravitational field strength minus the acceleration of the capsule, and there would be no way to know the direction of each separately. However, (non-gravitational) external forces which are not proportional to mass could give objects inside the capsule apparent weights in differing directions, making the concept "downward" ambiguous.
The apparent weight is equal to the object's weight in an inertial frame of reference if there are no other forces than gravity and the forces exerted by the structure, and the structure is at rest or moving with a constant velocity.
Thus an object's apparent weight is equal to its weight in an inertial frame of reference, unless:
- The immediate environment has an acceleration, as in an elevator, a rocket, or a roller coaster. This includes also the case of centripetal acceleration, as when making a turn in a car, and also when being subjected to the rotation of EarthEarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
: in the non-polar regions his makes the apparent weight less than the actual weight, or in other words, it makes Earth's effective gravitational field slightly less than its true gravitational fieldNewton's law of universal gravitationNewton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...
. - Some force other than gravity and the associated normal force is acting on the object. This may, for example, be a magnetic force (strong magnetic fields have even been used to levitate frogs ).
Buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
can be considered to reduce the apparent weight, since a scale shows a lower value. However, buoyancy can also be considered a spread-out normal force. See also below.
Relation with g-force and mechanical resistive forces
The mass of an object times the g-forceG-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...
is the sum of all forces except gravity, so the apparent weight with respect to a structure is the sum of external non-gravitational forces, plus the mass of the object times the acceleration with respect to the structure minus the g-force. In many cases there are no such other forces; in those cases the apparent weight per unit mass is the acceleration with respect to the structure, minus the g-force. For example, in an elevator the apparent weight per unit mass of an object manifests itself as the negative of the g-force when it rests on the floor, and as the acceleration with respect to the elevator when it is falling (with the g-force being zero).
If the object rests on a surface of the structure (the g-force points out of the surface) then the total compressive force in the object near the surface is equal to the apparent weight. If the object hangs from the support structure then the total tensile force in the object near the points of support is equal to the apparent weight. A combination is also possible. The compressive or tensile force at any cross-section is the apparent weight of the free end of the object (resting on or hanging from the cross-section).
Case without non-gravitational external forces
- Summary for the important special case without non-gravitational external forces:
The weight per unit mass of an object in a particular frame of reference is the acceleration in the frame of reference, minus the non-gravitational forces per unit mass. In particular, it is the acceleration in the frame of reference when the object is in free fall.
The weight per unit mass of an object with respect to a structure is its acceleration with respect to the structure, minus the sum of the forces per unit mass exerted by the structure. In particular, it is the negative of the sum of the forces per unit mass exerted by the structure when the object is stationary with respect to the structure. This can be measured with a spring scale
Spring scale
The spring scale apparatus is simply a spring fixed at one end with a hook to attach an object at the other. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position...
.
It is equal to the gravitational field strength (which is the weight per unit mass in an inertial frame of reference) minus the acceleration of the structure.
The weight per unit mass with respect to the structure is the acceleration minus the g-force. For example, the weight per unit mass of an object with respect to an elevator cabin manifests itself as the negative of the g-force when it rests on the floor of the elevator cabin, and as the acceleration with respect to the elevator cabin when the object is falling.
Objects at rest
Suppose that Alice has a mass of 65 kilogramKilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...
s and is standing stationary on the floor. Gravity is pulling her downward with a force of:
| Fgrav | = mg |
| = 65 kg × 9.81 m/s2 | |
| = 637.65 N (newtons) |
where m is mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and g is the acceleration due to gravity
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...
. By definition,
Fgrav, the downward force of gravity, is Alice's actual weight. (Note that the force of gravity varies slightly over the surface of the earth, and 9.81 m/s2 is only an approximate value. See standard gravity
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...
, Physical geodesy
Physical geodesy
Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy.-Measurement procedure:...
, Gravity anomaly
Gravity anomaly
A gravity anomaly is the difference between the observed acceleration of Earth's gravity and a value predicted from a model.-Geodesy and geophysics:...
and Gravity for further information.)
However, since Alice is at rest, the net force acting on her must be zero (otherwise Alice would be accelerating, according to Newton's second law). Since the net force is zero, the upward force exerted by the floor must exactly balance the downward force of gravity, meaning that Alice's actual weight and apparent weight are the same. (Here we are ignoring some minor effects such as buoyancy and centrifugal force, discussed later.)
It is the reaction force transmitted through the floor, not gravity pulling on her, that makes Alice feel heavy (the g-force is 1g). The crucial difference is that gravity is a long-range force that acts uniformly throughout an object, while reaction forces are short-range forces that act only on the surfaces of an object. Reaction forces are transferred throughout the body, causing it to deform slightly and allowing stresses to build up. Gravity, because it acts uniformly, does not cause such stresses.
Objects accelerating vertically
If an object is accelerating upwards or downwards then its apparent weight respectively increases or decreases. Consider Alice again, but now in a lift accelerating downwards at 3 ms-2 (metres per second per second). Let Fgravity be the downwards force on Alice due to gravity, Fnormal be the normal (upwards) force exerted by the floor of the lift, and Fnet be the net force on Alice.It is essential to be clear about the signs of these forces and accelerations. Let us take downward forces and accelerations to be positive and upward forces and accelerations to be negative. This means that Fgravity is positive, Fnormal is negative, and Alice's acceleration is positive.
We know that Alice is accelerating at +3 ms−2, and we know that her mass is 65 kg. Applying an equation we get from Newton's second law, we have that
| Fnet | = ma |
| = 65 kg × 3 ms−2 | |
| = 195 N |
However, this net force is the sum of the force due to gravity and the normal force. Thus,
| Fgravity + Fnormal | = Fnet |
| = 195 N |
We already know from the earlier example that Fgravity = 637 N. Therefore
- 637 N + Fnormal = 195 N
so
- Fnormal = −442 N
Thus the normal force is 442 N (upwards), so Alice's apparent weight is 442 N, and it feels to Alice as if her weight has decreased by about 30% (the g-force is 0.7g) — even though her actual weight (the force exerted on her by gravity) remains unchanged. If Alice were standing on a weighing scale then the weight registered would also be 442 N. This is because a scale does not measure an object's actual weight, but rather measures the force that it exerts on the scale.
The workings above consolidate into the neat formula
- Fnormal = m(a − g)
We can now more easily examine what happens when a takes a range of different values. The formula shows that when a = 0 we have Fnormal = −mg, which is, as expected, just the formula for Alice's actual weight (with the negative sign reflecting the fact that the normal force is upwards).
For increasingly positive a (increasing downward acceleration), the absolute magnitude of Fnormal (the magnitude ignoring the sign) steadily decreases, meaning that Alice's apparent weight steadily decreases (the g-force also). Conversely, for increasingly negative a (increasing upward acceleration), Alice's apparent weight steadily increases.
It is important to understand that it is acceleration, not velocity, that causes changes in apparent weight. In a lift travelling upwards or downards at any constant speed – however great – Alice's apparent weight will be the same as if the lift were at rest.
Free-fall
Apparent weight decreases with increasing downward acceleration until eventually a reaches g (the acceleration due to gravity, 9.81 ms2), when the formula shows that Alice's apparent weight is zero (the g-force also). At this point the floor of the lift no longer provides any supporting force at all, the only force acting on her is gravity, and Alice is in free-fallFree-fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...
. During free-fall Alice experiences weightlessness
Weightlessness
Weightlessness is the condition that exists for an object or person when they experience little or no acceleration except the acceleration that defines their inertial trajectory, or the trajectory of pure free-fall...
.
Free-fall also occurs, of course, if Alice is falling freely through the air (in the absence of any containing lift). Ignoring air resistance there is again no supporting force, and no sensation of weight. Objects in orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
are also in free-fall; the mechanics are explained at Orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
.
"Beyond" free-fall
If a increases beyond g then the apparent weight becomes upward, so Alice "falls" to the ceiling of the lift, which she now experiences as a floor, and which now provides a "supporting" force.Objects accelerating in arbitrary direction
In general, an object's apparent weight is its mass multiplied by the vector difference between the gravitational acceleration and the acceleration of the object. This definition means that apparent weight is a vector that can act in any direction, not just vertically. For example, in a racing car accelerating horizontally at 1 g, apparent weight acts at an angle of 45 degrees downwards. For the calculation of apparent weight in cases where the two accelerations do not fall on a line it is often essential to utilize vectorCoordinate vector
In linear algebra, a coordinate vector is an explicit representation of a vector in an abstract vector space as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn....
notation.
The apparent weight for an object under the influence of two arbitrary forces
, and , in the most general case can be calculated by the addition of vectors:| F1 | =[F1x, F1y, F1z] |
| F2 | =[F2x, F2y, F2z] |
| Fnet | =F1 + F2 |
| =[F1x + F2x, F1y + F2y, F1z + F2z] | |
For the specific case mentioned above where
is the force of gravity with the choice of coordinate system such that the force of gravity is in the positive-y direction, and with is the force caused by the acceleration of a racing car equal to in the positive-x direction, the previous equations become:| Fgravity | =[0, mg, 0] |
| Fcar | =[m*ac, 0, 0] |
| Fnet | =Fgravity + Fcar |
| =[m*ac, mg, 0] | |
In the most general case, an object under the influence of n accelerations has an apparent weight of:
| Fnet | = |
= |
|
Buoyancy
Apparent weight is lessened by buoyancyBuoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
, which occurs when an object is immersed in a fluid (a liquid or a gas). For example, an object immersed in water seems to weigh less, according to a spring scale, than the same object in air. The apparent weight of any floating object is zero. To make a precise definition of apparent weight involving buoyancy, apparent weight is equal to the tension force as a spring scale would measure when the object is hung downward from the scale in a body of fluid, and for positive apparent weight (of a negatively buoyant "sinkable" object), the scale is pulling the object upward. A negative apparent weight (of a positively buoyant "float-able" object) would need to be measured by having the spring scale pull the object downward instead.
This effect is quite different from the accelerating lift examples. A floating or immersed object is not accelerating upwards or downwards, so there can be no net force. In fact, buoyancy provides a supporting force exactly as the solid floor does. Because this force is diffuse and dispersed over the surface of the body, a feeling of "pseudo-weightlessness" arises when one is floating. A human can still tell the difference between weightlessness due to buoyancy and true weightlessness, because people can feel buoyancy forces due to their fluid pressure.
Objects also experience some buoyancy in air, so even in air, the normal force (apparent weight) is slightly less than the normal force which would be experienced in an evacuated chamber. The density of air
Density of air
The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity...
at sea level pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...
and room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...
is about 1.2 kg/m3. Most objects are much denser than air and so this force is usually small. For an object with the same density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
as water – about 1000 kg/m3 – the relative effect is about 0.12%. However, for objects of very low density the relative effect can be large. In fact, an object that is lighter than air, such as a helium balloon, has a negative apparent weight (as does an object lighter than water when it is forcibly pulled below the surface).
Variations in air pressure cause variations in air density and hence variations in apparent weight. Over a typical range of sea-level pressures this may amount to about a 0.01% change in apparent weight for an object of the same density as water (less for denser objects, more for less dense objects). Extremely accurate measurements must take this into account.
Other factors
In general, any force (other than the normal force) that opposes or augments the downwards force of gravity will have an effect on apparent weight. Some examples are:- Centrifugal effect. Because the earth is a rotating reference frame, objects on the Earth's surface experience a small centrifugal effect, which increases at lower latitudes (nearer to the equator). This reduces the force of gravity, and a corresponding small decrease in the normal forceNormal forceIn mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...
opposing force. Note that this is a centrifugal effect or a centrifugal pseudoforce (not a forceForceIn physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
) that is used here because it is convenient to view objects in a reference frame rotating around the Earth, rather than referring to the center of Earth reference frame to understand that these bodies are actually accelerating. It is intentionally not referred to as centripetal forceCentripetal forceCentripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...
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- The gravitational influence of the Sun and the Moon. This varies slightly across the Earth because different locations lie at slightly different distances from these bodies. This alters the net gravitational force on objects at the Earth's surface by a small amount, depending on their location on the Earth and the relative positions of the Sun, Earth and Moon. The effect of other astronomical bodies is vanishingly small.