Saying that work done is +ve or -ve is a mathematical convention used for calculating energy transfers. It is +ve when it is done by us on the system, and -ve when it is done by the system on us.
Positive work is done in pushing against a force to reach a configuration - eg pushing a car uphill. Negative work is done if a force pulls in the direction we want to go - eg lowering a car downhill. In keeping the car from accelerating out of control, we can extract useful work, store it, and perhaps use it to push the car back uphill to where it started from. When we get there, the car has the same GPE as when it started, so the net work done on it is zero. We have done +ve work pushing it back uphill, so we must have done -ve work on it (it has done +ve work on us, or for us) when we lowered it downhill.
If the force were not there (eg if the hill were not there) we would have to do no work at all to move the car from one place to another.
When talking about the gravitational attraction between two objects, by convention their mutual GPE is zero when there is no interaction between them - ie when the separation is infinite. Moving one from infinity towards the other is like rolling the car downhill. The force of attraction does work for or on us. When we have got them to the required separation, we have to do +ve work to separate them again. If the mutual GPE is zero again after doing +ve work, we must have done -ve work in moving them closer.
manpreet![Tuteehub forum best answer]()
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2 years ago
An outcome of my high school syllabus is to "define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field: −GMm/r−GMm/r".
It makes sense that GPE is always negative since a positive force against gravity and hence positive work must be done to move an object very far away, where it has 0 GPE since the field is not present at all.
But I don't understand why moving an object from an infinite distance to a point in the field is negative work. The object would experience a net negative force, and be moved a negative displacement. Won't W=FsW=Fs then be positive? What does negative work even mean?
Thank you very much for helping.