How can a system of particles with kinetic energy have no momentum?

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Homework Help Overview

The discussion revolves around the relationship between kinetic energy and momentum in a system of particles. Participants explore how it is possible for a system to possess kinetic energy while having a total momentum of zero.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the fundamental definitions of kinetic energy and momentum, considering how a system can have particles moving in opposite directions, leading to a net momentum of zero while still having kinetic energy. Examples of particle systems are discussed to illustrate this point.

Discussion Status

Some participants have provided insights into the vector nature of momentum versus the scalar nature of kinetic energy. There is acknowledgment of the possibility of particles with equal and opposite momentum canceling each other out, while still contributing to the system's kinetic energy. The conversation appears to be productive, with participants building on each other's ideas.

Contextual Notes

There is an implicit assumption that the participants are familiar with the basic principles of physics regarding kinetic energy and momentum, as well as the vector nature of momentum.

Lo.Lee.Ta.
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I thought objects with kinetic energy have to be moving...

And moving objects have momentum...

So how is it that something with kinetic energy can have no momentum?

Could you give me specific examples of such cases?

Thank you so much! :)
 
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If you mean the sum of the momentum of all the particles, it could be half of them going one way and half the opposite way so the total is zero.
 
The momentum is vector, the KE is scalar.

A system of two particles, each of mas m and one with velocity v, the other with velocity -v, has momentum mv-mv=0 and kinetic energy mv2/2+m(-v)2/2=mv2.

ehild
 
Oh! I didn't even think of that! Okay, so there can be particles with negative momentum and others with positive momentum of equal magnitude, and they can cancel each other out?
 
Lo.Lee.Ta. said:
Oh! I didn't even think of that! Okay, so there can be particles with negative momentum and others with positive momentum of equal magnitude, and they can cancel each other out?

In general, the momentum can be of any direction, and their vector sum can cancel, but the KE is positive for all particles.

ehild
 
Oh, okay! Thank you ehild and Delphi51! :)
 

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