# What the physical interpretation of negative work done in case of attractive force? Also how negative potential energy is related with negative work?

I want to ask why potential energy becomes negative in attractive forces along with the work done. As the meaning of potential energy according to my knowledge is the amount of energy required to keep a body at a particular position against a particular force in a particular field and if this definition is correct then the work done should be positive to provide energy in an attractive field instead of being negative and viceversa.

• Attractive forces are considered to be of negative magnitude since they're opposite in direction to $\vec{r}$. Does this answer your question? Dec 23, 2023 at 14:28

What the physical interpretation of negative work done in case of attractive force?

Negative work typically means that the work is being done by the object on the actor, rather than the other way around.

For example, how much work do I do pushing a 5 kg bowling ball down a 10 m hill very slowly? If I calculated it using $$W = mgh$$ I get roughly -500 J (taking $$h$$ as negative because I'm pushing downhill). That means that rather than doing 500 J of work on the ball, the ball has done 500 J of work on me as I push backwards to keep it moving slowly rather than picking up kinetic energy as it rolls down the hill.

Also how negative potential energy is related with negative work?

There's really no relationship at all. Negative potential energy just means we've chosen our reference level for the potential at a place where it's still possible to obtain a lower potential.

For example if I roll the ball to the bottom of the hill I might say it now has zero gravitational potential energy. But if I dig a hole in the ground and roll it there it can still reach an even lower potential energy. Since this potential energy is lower than zero, it is negative.

But as for the work done on the ball, it only depends on the difference in height between the start and finish of any given movement. If it starts at the bottom of the hole and I raise it partly toward ground level I can do positive work even though it remains at a negative potential energy. If I start it at the top of the hill and roll it partway down I can do negative work on it even though it remains at a positive potential energy.

In spaceflight calculations we might even prefer to make the reference level be infinitely high above the Earth where the Earth's gravity no longer affects a space craft or satellite. Then we will always have a negative potential energy for any object in orbit around the Earth.