# Work done by gravity

1. Jun 20, 2013

### alingy1

Let's say a ball falls from a height of 20m from the ground. g=9,8m/s^2. m=3kg.
Consider resistance of air in a qualitative way.

What's the formula for the work done by gravity?

So, I just thought about this question. I wonder if W=F*s should be applied. Does gravity still do 588J of work? Or should we take into account that F is smaller because of air friction? All this concept of work is very new to me and I googled for similar questions but couldn't find any web page alluding to my problem.

2. Jun 20, 2013

### Kitnoforlife

If considering air resistance, then the net work is not the same as the work done by gravity, which is the same regardless of air resistance.

Your notion of W=F*S works if you treat gravity as an approximately constant force, but that approximation becomes poor as S gets larger. This all comes from the fact that the gravitational force on Earth or any other planet is actually given by Newton's Laws of Gravitation, which creates a more difficult work calculation.

You should also note that work is not simply F*S.

See: https://en.wikipedia.org/wiki/Work_(physics [Broken])

Last edited by a moderator: May 6, 2017
3. Jun 20, 2013

### PeterO

The force due to gravity is the same, the distance fallen is the same, so the Work done by gravity should still be the same.
HOWEVER: the resistance of air will be doing some work too.

4. Jun 20, 2013

### alingy1

Okay, so, the total work done (not only by g) will be smaller than the work that should have been done without air. The air does negative work and g, the same work.

5. Jun 20, 2013

### Kitnoforlife

Correct. It is similar to pushing a box with friction opposing the push. You do work with your own force F_p as you move the block, while the ground also does work in the OTHER direction (different signs) with the frictional force F_f doing work as the block moves.