Apparent weight is the sum of all the forces acting on an object, including its own weight. Apparent weight, F_A=SigmaF_iFA=ΣFi, is defined the same way in the cases of lift and buoyant force.
Explanation:
The apparent weight, F_AFA, of an object can be thought of as the net force acting on an object where the object’s weight is included as one of the forces.
In the case of an object experiencing lift, the apparent weight is
F_A=SigmaF_i=F_W+F_LFA=ΣFi=FW+FL,
where F_WFW is the weight of the object and F_LFL is the force providing lift. **
In the case of an object floating in a fluid, the apparent weight is
F_A=SigmaF_i=F_W+F_BFA=ΣFi=FW+FB,
where F_WFW is the weight of the object and F_BFB is the buoyant force acting on the object.
In the case of a person standing on a moving elevator.
F_A=SigmaF_i=F_W+ma_"E"FA=ΣFi=FW+maE where F_WFW is the weight of the person, m is the mass of the person and a_"E"aE the acceleration of the elevator. a_"E"aE is positive when the elevator accelerates upward and negative when the elevator accelerates downward (e.g. under the acceleration of gravity).
So with that said, your next thought might be the case where the apparent weight F_A=0FA=0. What’s that mean and what does it look like?
Well since F_W=mgFW=mg, when the elevator or let’s say an airplane is accelerating downward at a_"E"=-gaE=−g (in other words falling in a nose dive), F_A=F_W+ma_"E"=mg-mg=0FA=FW+maE=mg−mg=0. Under this condition where F_A=0FA=0 you feel weightless and here’s what it looks like!
* Zero-g, Parabolic Flight.* **
Hope that helps. Good luck!
**Each F_iFi represents a different force, ii allows us to denote and distinguish them. ii typically takes on integer values (e.g. i=0,1,2,3i=0,1,2,3) , but in this case there are only two forces F_W+F_LFW+FL, so i takes on the values i=Wi=W and i=Li=L.
