Energy Conservation and Escape Velocity

AI Thread Summary
When a particle is launched away from a mass, its kinetic energy decreases while its potential energy, which is negative, also decreases in magnitude. The conservation of energy principle applies, indicating that the total energy remains constant, but the kinetic and potential energies convert into one another. As the particle moves away, potential energy approaches zero, while kinetic energy diminishes correspondingly. The analogy of debt illustrates that as potential energy becomes less negative, it equates to a gain in energy. The discussion emphasizes understanding energy conservation in terms of energy transformations rather than absolute values.
Gilgalad
Messages
7
Reaction score
0
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? :confused:

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.
 
Last edited:
Physics news on Phys.org
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.
 
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?
 
Gilgalad said:
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.
 
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 infinate 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?
 
What do you mean by that KE is to overcome PE?
I'm not sure I understand..
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top