Can kinetic energy be conserved without momentum conservation?

[Vasco]

I got a conceptual doubt:Momentum(linear) conservation doesn't depend on conservation of kinetic energy.But,is the opposite true?Can kinetic energy be conserved without the conservation of momentum?

Thanks!

 

[arildno]

I got a conceptual doubt:Momentum(linear) conservation doesn't depend on conservation of kinetic energy.But,is the opposite true?Can kinetic energy be conserved without the conservation of momentum?

Thanks!

Yes, the typical example is a particle which only experiences CENTRIPETAL acceleration from some force (with centripetal acceleration, I mean that the acceleration is orthogonal to the velocity at all times) .
The vector quantity momentum changes continually, yet the particle's SPEED, and hence, its kinetic energy remains conseved.

 

[thepatientmental]

Hi there,

I'm happy to help with your conceptual doubt about energy and momentum conservation.

To answer your question, yes, it is possible for kinetic energy to be conserved without the conservation of momentum. This can happen in situations where there is an external force acting on the system and changing the momentum, but the kinetic energy remains constant.

For example, imagine a ball rolling down a frictionless hill. The ball has both momentum and kinetic energy as it moves down the hill. However, when it reaches the bottom of the hill, it hits a wall and comes to a stop. The momentum of the ball has changed, but the kinetic energy remains the same.

On the other hand, momentum conservation does not necessarily depend on the conservation of kinetic energy. This is because momentum takes into account both the mass and velocity of an object, while kinetic energy only considers the velocity. So, even if the kinetic energy changes, the momentum can still be conserved if the mass and velocity also change in a specific way.

I hope this helps to clarify your doubt. Remember, conservation of energy and momentum are fundamental principles in physics, and they both play important roles in understanding the behavior of particles and systems. Keep practicing and exploring these concepts, and you'll continue to gain a deeper understanding. Good luck!