# B Can one feel negative weight?

1. Aug 17, 2016

### Prem1998

I have read that the apparent weight of a person in a lift accelerating with acceleration 'a' downwards is given by:
W = m(g-a) where 'm' is his mass
so if a>g, then one feels negative apparent weight.
But, it is also true that one becomes conscious of his weight only when he gets a reaction force from the surface. So, weight is actually the reaction force we receive. But, the minimum reaction force we can receive is 0, so we can't receive negative reaction force, so doesn't that mean that the minimum weight possible is zero. Then what about the equation when a>g?

2. Aug 17, 2016

### Staff: Mentor

In your lift example, it would mean that the ceiling is pushing down on you, or that you are glued to the floor, and the glue is in tension.

3. Aug 17, 2016

### Orodruin

Staff Emeritus
If you are strapped to the floor of the accelerating elevator with a > g, it will be like hanging upside down in the roof. If you are not, you will accelerate to the other end of the elevator and once you reach it you will have the reaction force from there, making it seem like it is your floor. Only when g = a will you seem weightless in the elevator. If a > g you will think that down (the down direction before you started accelerating) is up.

You can experience similar things in acceleration perpendicular to gravity as well. If you try to move forward in an accelerating train, it will be equivalent to climbing a slope in a slightly stronger gravitational field. When the train decelerates, moving forward will be like going downhill.

4. Aug 17, 2016

### Prem1998

Thanks for the very helpful reply. Can you tell me which of these describes weightlessness correctly?:
1 Is it the state in which our body receives no reaction force and there is a sense of direction? Or
2 Is it the state in which our body receives no reaction and no directions seems more preferable to the other as upwards or downwards and a body does not seem to accelerate in any preferable direction when suspended freely without any support?
It seems to me that in case of a person freely falling, the first definition seems to suit because in that case the body receives no reaction and it is feels to be weightless while free falling as described in my book. In this case, the second definition does not apply because there is a sense of direction that we are going downwards and we are actually accelerating downwards.
BUT in case of weightlessness of a person in a spacecraft orbiting the Earth, the second definition seems to suit because in that case we are not accelerating in any particular direction and all directions seem alike.
So, both the cases of free falling and being in a spacecraft are described as weightlessness but in one case one is accelerating downwards and in other case no direction seems preferable?

5. Aug 17, 2016

### Orodruin

Staff Emeritus
You need to get rid of the background in your thinking about weightlessness. 2 would be more accurate - there is no way for an observer in free fall to determine a preferred direction based on the forces acting on it. In the observer frame, there is no gravitational force (or if you prefer, it is exactly canceled by an equivalent pseudo force).

6. Aug 18, 2016

### CWatters

Here are two different situations...

1) man free falling in a gravitational field
2) man in deep space far from any planets where there is no significant gravitational field.

These two men both feel weightless and cannot tell which situation they are in from the forces acting on them.

Although I think they could if there was a significant gravitational gradient, such as near a black hole.

7. Aug 18, 2016

### CWatters

And yes you can feel negative weight as any aerobatic pilot will confirm.