Negative Work or Positive Work? and gravitational potential energy

Tommy1995

Hi!

So, when we're calculating the potential energy of a mass in space we make it negative because we assign infinity as the reference point.
Now, to find the potential energy of something I understand that we find the work that is done to it to move it from the reference point to another point in space.
And I also understand that positive work is when the displacement and force are in the same direction.

Now here's the bit I don't get! When we find the potential energy of an object in space the potential energy is negative. Thus the work that is needed to move the object from a point at infinity to a point "X" in space will be negative.
But when we move an object from this infinity point to a point "X" in space wouldn't work be positive because the force and displacement of the object are in the same direction???
Please help, I'm seriously confused right now...

Btw I'm just a 12th grade highschool physics student so go easy on me with the maths LOL

Doc Al

Imagine you have a planet and a rock out in space. Let's call the gravitational potential energy zero when they are infinitely far apart. If they were some finite distance X apart, it should make sense that you must do positive work to separate them further: The force you must exert on the rock is in the same direction as the displacement.

But when you bring the rock towards the planet (slowly, so as not to give them any kinetic energy) the force you exert on the rock is still outwards while the displacement is inwards. Thus the work you do is negative.

Make sense?

Tommy1995

Sorry Doc Al but I don't understand, how can you apply an outwards force on the rock and yet have the rock move inwards...?

please explain further, it would be greatly appreciated.

MrWarlock616

Lol i didn't get that too..

Doc Al

Sure.

Imagine you are slowly lifting a heavy rock from the ground to put it on a shelf. What's the direction of the force you must exert on the rock as you lift it?

Now imagine you are slowly lowering that rock from the shelf to gently place it back on the ground. What's the direction of the force you must exert on the rock as you lower it?

Tommy1995

I totally get it now! Thanks doc your a legend!! :d

DocZaius

When you think about work, the first thing you must think of is "Work done by what?". In Doc Al's examples, there are two forces in question: gravity, and you.

When you are lowering the rock, gravity is doing positive work on it (the force on the rock by gravity is in the same direction as its displacement) and you are doing negative work on it (the force on the rock by you is opposite the direction of its displacement).

jtbell

Also, if the work that you do has the same magnitude as the work that gravity does, then the net work is zero because one is negative and the other is positive. This means the final KE of the object is the same as the initial KE, as for example when you lower the object with constant speed.

Tommy1995

Thank you guys heeeeaps, very nice responses helped so much xD