How weight become zero during free fall?

Answer 1

First off it is important to realize that weight is not the same as mass. (Some people make that mistake, so I thought it best to clear that one immediately). The mass of an object is unaffected by free fall.

Now for the question, weight is the force that stops you from free fall. In this regard it is automatically zero in free fall since there is no force opposing you. However, it is instructive to consider this somewhat further.

How do you measure weight? Well, here on Earth you might simply stand on a weight meter and read off what it says (even though it usually gives its answer in kilograms, you can convert these into Newtons using the gravitational constant). How does this device measure your weight? Usually it contains a spring of some sort that provides a force stopping you from crushing it. This force is what is measured, and this force is what stops you from falling through the meter. It is sometimes referred to as the normal force. This is your weight.

Now imagine doing the same in free fall. Say you jump out of spaceship above Earth (to neglect air resistance), in a spacesuit (to neglect you dying from lack of said air), and a weight meter. How would you proceed to use it?

You can put it under your feet, but the meter is accelerated towards Earth in the same manner as you (barring any tidal effects), so the spring is not needed to stop you from crushing it. As a result the meter shows you are weightless. You move towards the meter due to gravity, but the meter moves away just as quickly due to the same gravity. The overall point then is that you are weightless because your acceleration towards Earth exactly cancels the gravitational acceleration in a way.

This is because an object's resistance to acceleration is its mass, and the strength of the gravitational force is also depending on its mass and these quantities drop out of the equation and everything falls with the same speed.