How do you calculate the force needed to lift an object?
Do you mean in theory, or in practice?
In theory, you just write down all the forces and calculate the nett force. In the simplest case, you only need to counter gravity, so you will need a force F = m g. If you include for example air friction, the same principle works although the calculations quickly get tedious.
In practice, there are usually many effects which are hard to completely describe, so you may make an approximation and do the theoretical calculation, or you can simply make a measurement (by lifting the object with a force meter for example, which is basically a spring with a scale).
Depends on how you want to lift the cup. Do you want to put your hands under the cup, or do you use the 'ear' on the cup (if that's how you call that thing in English ;) ). If it's the latter, one would need to know the horizontal distance between the center of mass and the place on which the force is exerted.i mean in practice. For instance i need to lift up a coffee cup from a table, how much force is needed to do it? or how much force do i need to apply on my fingers to lift the cup?