Question

Can a particle have momentum without energy?

Answer 1

No. Conceptually, if it is moving, then it must have some energy, right? If it is moving, it must have some momentum. Mathematically this is shown by momentum and kinetic energy equations; \[momentum = mass \times velocity\] and \[kinetic energy = 1/2 mass \times velocity^2\]. If velocity (motion) is non-zero, then the particle must have kinetic energy.

Answer 2

No it's not possible !!!
This question looks familiar and if you have watched Dr. Walter Lewin's lecture on the topic, he asks this question at the end. He explains the situation as following


Consider a elastic collision between a tennis ball and a rigid wall. In this case the initial momentum of the tennis ball will be mv while its final momentum will be -mv. This means that change in the magnitude of its momentum is 2mv. Initial and final momentum of wall of-course will remain 0.

Now think, this additional momentum (mv) must be imparted by the wall to the ball. This means the wall had this momentum despite of having zero velocity (because it's not moving) and zero KE

Answer 3

This is practically/approximately true because mass of wall is >> mass of tennis ball so we don't observe it moving but in fact is does moves a bit and hence does has a minute KE

Answer 4

I disagree with you Abhisar. The wall (which is connected to the Earth so it is really the wall-earth object) will experience a change in momentum equal and opposite that of the ball (-2mv). The wall is able to exert a force on the ball due to its mass (inertia). Additionally, you do not impart momentum from one object to another, you transfer energy, right. I know it is dancing on the head of a pin but I'm learning and trying to get my language down solid. I'm not trying to be a jerk. Im gonna go watch Lewing though, I'm intrigued and he is awesome. Too bad he is a perv and lost his Emeritus status and videos removed by MIT.

Answer 5

Haha, i didn't see that second post :)

Answer 6

abhisar ,thanks for answer but i'm not completely satisfied .............u said 'this additional momentum (mv) must be imparted by the wall to the ball. This means the wall had this momentum despite of having zero velocity (because it's not moving) and zero KE'
the additional momentum is given to ball not to the wall if wall has zero k .e. it has also zero momentum ...i asked about a particle having some momentum but have zero energy not zero k.e. but it is total energy ................. not 2 different objects!

Answer 7

squoe44oz thanks for reply but i asked about total mechanical energy not kinetic energy

Answer 8

You did not specify what type of energy, and the question can be answered regardless. It is true that you cannot have momentum and have zero energy. If you have momentum, then you have kinetic energy; therefore you have energy. A particle can have zero momentum and have potential energy. That is different than what you asked. Moreover, an object can have internal energy (energy thermal or chemical) without having potential or kinetic energy.

Answer 9

ohk sry ..my fault ............so can can particle exist without energy ( means without mechanical energy ,without chemical enegy ,without internal energy ,without any kind of energy ) can a particle exist with total zero energy

Answer 10

I would say no. This would occur at absolute zero which, as far as we know, cannot be achieved. NASA currently working on an extreme cold lab on the International Space Station to investigate this. Quantum mechanics dictates what happens at this level. I think the theory is that matter becomes purely wave-like and can even be superimposed. That is way way beyond my pay grade.

Answer 11

thanks

Answer 12

squoe44oz u plz help me a little more ?

Answer 13

why divergence of electric field due to a point charge is zero ?
mathematically we can prove but what is the physical significance of zero divergence in this case?

Answer 14

I cannot help but here is a link to a forum discussing the same question:

https://www.physicsforums.com/threads/zero-divergence-in-an-enclosed-point-charge.165292/