Conservation of momentum/energy

[dougy]

Hello,

Inside a theoretical perfectly isolated system, momentum and energy are conserved. But is it possible to imagine a system gaining/losing energy while its momentum remains the same, or a system gaining/losing momentum while its energy remains the same? Or does one necessarily imply the other?

The way I see it, if the system consists of one macroscopic body, then its momentum is equal to the vectorial sum of the momentums of all its atoms. So if this body was to gain energy in the form of heat, then its atoms would vibrate more rigorously, thus if on average all these atoms "pushed" equally more in all directions then wouldn't this body be an example of a system gaining energy while keeping the same momentum?

 

[Fightfish]

So if this body was to gain energy in the form of heat

Then this body alone does not constitute an isolated system. You would have to include the heat source in the system for it to be considered isolated.

But is it possible to imagine a system gaining/losing energy while its momentum remains the same, or a system gaining/losing momentum while its energy remains the same?

Why not? The total energy of a system in general is the sum of its potential and kinetic energies. The momentum of the system is related only to the kinetic energy of the system via $p = \sqrt{2mK}$, and is independent of the potential energy.

 

[dougy]

Then this body alone does not constitute an isolated system. You would have to include the heat source in the system for it to be considered isolated.

Yes of course, I was there referring to a hypothetical non-isolated system gaining energy and not momentum.

Why not? The total energy of a system in general is the sum of its potential and kinetic energies. The momentum of the system is related only to the kinetic energy of the system via $p = \sqrt{2mK}$, and is independent of the potential energy.

Is it obvious that kinetic and potential energies are independent? Do you have an example where the variation of the potential energy of a system is not accompanied with a variation of its kinetic energy?

 

[Fightfish]

Do you have an example where the variation of the potential energy of a system is not accompanied with a variation of its kinetic energy?

Sure, consider any object present in a potential field. As long as I apply a force on the object such that the net force on the object is zero, I can change its position (and hence its potential energy) without changing the velocity of the object.

 

[dougy]

Sure, consider any object present in a potential field. As long as I apply a force on the object such that the net force on the object is zero, I can change its position (and hence its potential energy) without changing the velocity of the object.

All good, thank you!

 

[conquest]

Sure, consider any object present in a potential field. As long as I apply a force on the object such that the net force on the object is zero, I can change its position (and hence its potential energy) without changing the velocity of the object.

To give a real world example just consider picking up something of mass m form the ground and holding it over your head. Since the potential energy is mgh and the object went from standing still to standing still again it has just gained mg times your height in potential energy.