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

In summary, objects with kinetic energy do not necessarily have momentum, as the momentum is a vector quantity while kinetic energy is scalar. This can occur when there are particles with equal and opposite momenta, resulting in a total momentum of zero. However, the kinetic energy for each particle remains positive. Specific examples include a system of two particles with equal masses and opposite velocities, resulting in a total momentum of zero but non-zero kinetic energy for each particle.
  • #1
Lo.Lee.Ta.
217
0
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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  • #2
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.
 
  • #3
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
 
  • #4
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?
 
  • #5
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
 
  • #6
Oh, okay! Thank you ehild and Delphi51! :)
 

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

1. How can a system of particles have kinetic energy but no momentum?

This may seem counterintuitive, but it is possible for a system of particles to have kinetic energy without any momentum. This can occur when the particles have equal and opposite velocities, canceling out their individual momentums.

2. Can the total momentum of a system of particles be zero even if some particles are moving?

Yes, the total momentum of a system can still be zero even if individual particles are moving. As long as the momentums cancel out each other, the net momentum of the system will be zero.

3. Is it possible for a system of particles with kinetic energy to have negative momentum?

No, momentum is a vector quantity and cannot be negative. If the particles in a system have opposite velocities, their momentums will have different directions but will still sum up to zero.

4. How does the mass of particles affect the relationship between kinetic energy and momentum?

The mass of particles affects the relationship between kinetic energy and momentum by directly influencing the magnitude of both quantities. A system with particles of larger mass will have a higher momentum and kinetic energy compared to a system with particles of smaller mass.

5. What is the difference between kinetic energy and momentum in a system of particles?

Kinetic energy is the energy that a system possesses due to its motion, while momentum is the measure of the system's motion. Kinetic energy depends on the mass and velocity of the particles, while momentum only depends on the mass and velocity of the particles in the direction of motion.

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