Quick Q About W equally the negative change in potential energy

[Fusilli_Jerry89]

We all know work equals the negative change in potential energy where there is no change in kinetic energy, but can someone explain to me how this works in the following example?

Say there is an object 100 metres away from the earth. We move this object to 2000 metres away from earth. Given that potential energy is 0 at infinity, potential energy change would be -GMm/2000 + Gmm/100 = 19GMm/2000. This is a positive number, yet the work would also be positive to move this object. How does this make sense?

Thx

 

[Tedjn]

The way I understand it is as follows:

We assume the object is at rest at 100 m before the move and at rest at 2000 m after the move. Its change in kinetic energy is therefore 0 J, and by the work-kinetic energy theorem, we know that net work must also be 0 J. How is this possible if we clearly needed to do positive work against the pull of gravity to move up our object?

While we do positive work, gravity is doing negative work. It is a weird concept, but it makes sense if you imagine that we need to put in effort to first speed up the object, but when it stops at 2000 m, gravity is stopping it, so whatever we do, gravity opposes against the direction of motion. This is only because change in kinetic energy is 0 J and the object needs to slow down after it first sped up.

Since potential energy can be taken to mean the amount of work gravity can do on an object at a certain height, the negative work gravity did when we moved our object upwards is "stored" as potential energy--positive work that gravity can do if we release our object.

Certainly, we have expended positive work to move our object to its higher height. This energy came from chemical processes within our body. In essence, we are using up the potential energy stored in the food we eat to do this positive work, and our overall potential energy decreases.

Thus, there is no contradiction.