# Significance of negative work done

Suppose,

I am lifting a ball of mass $$m$$ very slowly from the ground to a height $$h$$. That is,for the whole time,approximately, $$F_{me}=-F_g$$

I am doing a work of $$+mgh$$, which is transferred to the body. Gravity is doing a work of $$-mgh$$.

What is the significance of the negative work done by gravity? What does it do?

I am thinking: If gravity didn't exist,my whole work done $$+mgh$$ would be present as the kinetic energy in the body at the height $$h$$. The negative work done $$-mgh$$ by gravity makes sure it is stored as the potential energy, rather than the kinetic energy.

Is this correct? I'd love to hear some more insights.

When something does negative work it takes energy away from something. In your example gravity takes away the energy you transferred to the object and stores it as gravitational potential energy of the Earth-object system.

Hope this helps.

Indeed the value/necessity of taking negative work into account is that it balances the books.

Here is a case where only one force is acting: orbital motion.
To make it a vivid example I take a case of orbital motion with a very high eccentricity: Halley's comet.

We start at aphelion, the point where the comet is at its farthest from the Sun. All the way from that outer point to the inside of the Solar the gravitational attraction from the Sun is doing work, increasing the kinetic energy of the comet. The comet then whips around the Sun.

The motion of the comet after passing its perihelion mirrors the inward motion. After passing the perihelion: the comet has so much velocity that the radial distance to the Sun starts increasing again.

From perihelion to all the way out to aphelion: kinetic energy is converted to potential energy.

So, as the comet goes through loop after loop of its orbit:
From aphelion to perihelion the gravitational attraction from the Sun is doing work.
From perihelion to aphelion the gravitational attraction from the Sun is doing negative work.

In the case of orbital motion the only entity that is doing work is the gravitational attraction from the Sun. So we describe that as cycling between doing work and doing negative work.