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.

 

[Moetasim]

In this example, the work done to move the object from 100m to 2000m away from the earth is positive because the object is moving in the direction of the gravitational force. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, there is no change in kinetic energy because the object is not moving faster or slower. However, there is a change in potential energy because the object has moved to a different distance from the earth. The equation you provided for potential energy change takes into account the distance and masses of the object and the earth, and it is a positive number because the object has moved to a greater distance. Overall, the work done is positive because the object has gained potential energy, even though there is no change in kinetic energy.