Energy Conservation and Escape Velocity

[Gilgalad]

If a particle is launched with kinetic energy as it gets further from the mass (eg a planet) the kinetic energy decreases. However Potential Energy GMm/r also decreases the further you get from the mass. Where does all this energy go?

Granted, the calculation U + K = 0 does give an answer that I have seen all over the place for escape velocity but I always thought energy is conserved and we have initial kinetic and potential energy but no final energy. I was wondering if energy is a vector quantity and there is no resultant energy.

 

[arildno]

It is negative potential energy that decreases in the escape velocity example, whereas kinetic energy is always a non-negative quantity.
Hence, in the escape velocity example, potential energy increases up to zero level as kinetic energy decreases to zero level.

 

[Gilgalad]

I unterstand that potential energy is negative but I thought that was just convention. The size of the number is decreasing as you move away from a planet. So is the energy still not getting less as you move away?

 

[Janus]

I unterstand that potential energy is negative but I thought that was just convention. The size of the number is decreasing as you move away from a planet. So is the energy still not getting less as you move away?

Try thinking about it in terms of a debt. As the magnitude of your debt decreases, it is the same as gaining money.

 

[Gilgalad]

I think I get it now. Newton only put it negatively inversely proportional to the radius (squared in force equation) because that is the rate it increases at. So if you plot -1/r (for symplicity) for PE as well as a 1/r for KE and translate PE up by an infinite amount so both graphs are in the top right quadrant except for when PE goes off to infinity down the y-axis the total of both energies at any certain radius is constant.

Also where the two graphs cross is that the the distance you need to get to to have enough KE to overcome the PE?

 

[arildno]

What do you mean by that KE is to overcome PE?
I'm not sure I understand..