How do astronauts in zero gravity know if something is heavier than something else, and can they like use a hammer against a nail to drive it through a wooden board?
There is a difference between the weight (the pull
of gravity on an object) and its inertia. The weight of the object is what makes it difficult to
pick up heavy things on the earth but in orbit the spacecraft, hammer and astronaut are all in
free fall – that means they are weightless. You can hold heavy objects above the floor of the
spacecraft with no force.
However if you try to move them then it is the inertia of the
object that it is important. This has to do with how difficult they are to move and is connected
with the mass of the object and not its weight. Your mass is the same everywhere in the
universe but your weight changes depending in the gravitational field acting on you wherever
you are.
An object with a large mass will also have a large weight on the
Earth.
Objects with a large inertia are difficult to move and so although you can hold
up a heavy object in the spacecraft it may take a large force to move it across the
spacecraft.
You can hammer in the spacecraft but it will be just as difficult as it is on
Earth, the lack of effective gravity there has no effect on the inertia of the hammer or the nail
or on the resistance of the wooden board.