Sure, whenever we have a case where the Lagrangian of a system isn't independent of time, while being independent of translation, i.e., not invariant with respect to time but invariant with respect to space.

Usually, the Lagrangian in any classical mechanics system is invariant with respect to time, i.e., doing an experiment now will produce the same results as "yesterday" or "tomorrow", but as the universe evolves, not necessarily over great spans of time.

Note: This reply was given before the question was modified to "conservation of kinetic energy". In that case, wow, there's lots of places where that "before" kinetic energy could get squirreled away into many other forms of energy "afterwards". Meanwhile, if the entire system is isolated, then its center of mass remains in uniform motion and thus "linear momentum" is conserved.
–
Michael Mendrin
·
1 year, 4 months ago

Log in to reply

@Michael Mendrin
–
How do you have so much loads of information? You are the "Wikipedia of Brilliant" :P
–
Nihar Mahajan
·
1 year, 4 months ago

Log in to reply

@Nihar Mahajan
–
If you're going to go around saying I'm the Wikipedia of Brilliant, then I am going to have to add a caveat to this matter of conservation of kinetic energy. Given any closed system, with a fixed total mass and uniform center of mass motion, then the kinetic energy of the total mass as defined by the motion of its center of mass is always conserved. We complicate the issue by introducing other forms of energy such as heat or electric fields, so that the total energy of the closed system could be greater than the kinetic energy defined as above---and then we involve external influences (like the planet Earth!) so that it's not truly a closed system.

When doing physics, we need to pay particular attention to whether a dynamic system is truly closed or open. A lot of laws of physics depend on such a distinction.
–
Michael Mendrin
·
1 year, 4 months ago

Log in to reply

Nihar stating that energy conservation is violated is not the correct way of saying what you probably wanted to.You should rephrase it so that what you intend is clear and more importantly an incorrect idea is not conveyed.
–
Sudeep Salgia
·
1 year, 4 months ago

Is the law of conservation energy really violated i mean the enegy is still converted into a non recoverable form it is still energy. Being one of the 3 most fundamental conservation primciples i dont expect it to get violated.
–
Satvik Choudhary
·
1 year, 4 months ago

Suppose a stationary (relative to some frame of reference ) box explodes into two pieces in the vacuum of space. The net momentum of the system of particles before and after is zero, but the kinetic energy, being scalar, goes from zero to a posotive quantity, hence kinetic energy isn't conserved.
–
Paul Denham
·
1 year, 4 months ago

Log in to reply

Fluid flow over a fix plate and other plate is movable..
–
Rajan Sah
·
1 year, 4 months ago

Log in to reply

Catching a ball
–
Naila Aftab
·
1 year, 4 months ago

Log in to reply

Inelastic collision,the loss in kinetic energy becomes a form of internal elastic of the system or lost as heat !
–
Sriram Jbl
·
1 year, 4 months ago

Log in to reply

In an inelastic collision the K.E is not conserved but momentum is . (some energy goes in deformation due to in elasticity)
–
Kush Pandya
·
1 year, 4 months ago

An example is Inelastic collision.
–
Surya Prakash
·
1 year, 4 months ago

Log in to reply

Decay. In the rest frame, initially there's an unstable particle with 0 kinetic energy and 0 momentum. After its decay into multiple particles, there still must be 0 momentum, but the particles each carry some kinetic energy.
–
Grant Larsen
·
1 year, 4 months ago

Log in to reply

Inelastic collision such as a car crash
–
Jesus Serrano
·
1 year, 4 months ago

Log in to reply

A vertical elastic collision would also work. Kinetic energy is converted into potential energy.
–
Raj Magesh
·
1 year, 4 months ago

Log in to reply

@Raj Magesh
–
That would work only if you include Earth itself as part of the dynamic system with a center of gravity in uniform motion.
–
Michael Mendrin
·
1 year, 4 months ago

Log in to reply

I hope it may inelastic be collision
–
Mukthesh Mahadev
·
1 year, 4 months ago

Log in to reply

Inelastic and perfectly inelastic collision
–
Jahnvi Verma
·
1 year, 4 months ago

It is better to say that mechanical energy is changed. It is in case of Inelastic and some oblique collisions.
–
Pranjal Prashant
·
1 year, 4 months ago

Log in to reply

I hope it may be inelastic collision
–
Mukthesh Mahadev
·
1 year, 4 months ago

Log in to reply

An inelastic collision between two bodies? Energy is lost as heat/used to deform the body but linear momentum is still conserved.
–
Raj Magesh
·
1 year, 4 months ago

Log in to reply

think this scenario violates the law of conservation of energy: A ball is rolling twards a fan, witch provides a constant force on the ball, with some amount of kinetic energy. As the ball gets closer to the fan, its kinetic energy is converted to "fan potential energy". Then, when the ball's kinetic energy is copletly converted to potential energy, the fan turns off. An instantanious force is then applied on the ball, and the ball rolls away from the fan. Now, the energy of the ball is smaller than the energy it had at first, because its kinetic energy is essentially zero and its fan potential energy is constantly decreasing. Where does the energy go? oh, also, the surface the ball is on has no friction

## Comments

Sort by:

TopNewestSure, whenever we have a case where the Lagrangian of a system isn't independent of time, while being independent of translation, i.e., not invariant with respect to time but invariant with respect to space.

Usually, the Lagrangian in any classical mechanics system is invariant with respect to time, i.e., doing an experiment now will produce the same results as "yesterday" or "tomorrow", but as the universe evolves, not necessarily over great spans of time.

Note: This reply was given before the question was modified to "conservation of kinetic energy". In that case, wow, there's lots of places where that "before" kinetic energy could get squirreled away into many other forms of energy "afterwards". Meanwhile, if the entire system is isolated, then its center of mass remains in uniform motion and thus "linear momentum" is conserved. – Michael Mendrin · 1 year, 4 months ago

Log in to reply

– Nihar Mahajan · 1 year, 4 months ago

How do you have so much loads of information? You are the "Wikipedia of Brilliant" :PLog in to reply

haveto add a caveat to this matter of conservation of kinetic energy. Given any closed system, with a fixed total mass and uniform center of mass motion, then the kinetic energy of the total mass as defined by the motion of its center of mass is always conserved. We complicate the issue by introducing other forms of energy such as heat or electric fields, so that the total energy of the closed system could be greater than the kinetic energy defined as above---and then we involve external influences (like the planet Earth!) so that it's not truly a closed system.When doing physics, we need to pay particular attention to whether a dynamic system is truly closed or open. A lot of laws of physics depend on such a distinction. – Michael Mendrin · 1 year, 4 months ago

Log in to reply

Nihar stating that energy conservation is violated is not the correct way of saying what you probably wanted to.You should rephrase it so that what you intend is clear and more importantly an incorrect idea is not conveyed. – Sudeep Salgia · 1 year, 4 months ago

Log in to reply

– Nihar Mahajan · 1 year, 4 months ago

Thanks. Edited.Log in to reply

Is the law of conservation energy really violated i mean the enegy is still converted into a non recoverable form it is still energy. Being one of the 3 most fundamental conservation primciples i dont expect it to get violated. – Satvik Choudhary · 1 year, 4 months ago

Log in to reply

– Aditya Chauhan · 1 year, 4 months ago

I think he means Kinetic Energy. I answered according to thatLog in to reply

– Nihar Mahajan · 1 year, 4 months ago

Thanks. Edited.Log in to reply

A spring block system. ...... – Suraj Soni · 1 year, 3 months ago

Log in to reply

Any example of Inelastic collision is true. – Aditya Chauhan · 1 year, 4 months ago

Log in to reply

– Nihar Mahajan · 1 year, 4 months ago

Yes , correct. Can you think of more examples?Log in to reply

Perfectly inelastic collision – Shreenidhi Bodas · 1 year, 3 months ago

Log in to reply

Inelastic collision – Debasish Som · 1 year, 3 months ago

Log in to reply

Inelastic collisions... – Tanishq Wadhwani · 1 year, 3 months ago

Log in to reply

Inelastic collision – Brad Baker · 1 year, 3 months ago

Log in to reply

Suppose a stationary (relative to some frame of reference ) box explodes into two pieces in the vacuum of space. The net momentum of the system of particles before and after is zero, but the kinetic energy, being scalar, goes from zero to a posotive quantity, hence kinetic energy isn't conserved. – Paul Denham · 1 year, 4 months ago

Log in to reply

Fluid flow over a fix plate and other plate is movable.. – Rajan Sah · 1 year, 4 months ago

Log in to reply

Catching a ball – Naila Aftab · 1 year, 4 months ago

Log in to reply

Inelastic collision,the loss in kinetic energy becomes a form of internal elastic of the system or lost as heat ! – Sriram Jbl · 1 year, 4 months ago

Log in to reply

In an inelastic collision the K.E is not conserved but momentum is . (some energy goes in deformation due to in elasticity) – Kush Pandya · 1 year, 4 months ago

Log in to reply

Inelastic collision – Anmol Srivastava · 1 year, 4 months ago

Log in to reply

An example is Inelastic collision. – Surya Prakash · 1 year, 4 months ago

Log in to reply

Decay. In the rest frame, initially there's an unstable particle with 0 kinetic energy and 0 momentum. After its decay into multiple particles, there still must be 0 momentum, but the particles each carry some kinetic energy. – Grant Larsen · 1 year, 4 months ago

Log in to reply

Inelastic collision such as a car crash – Jesus Serrano · 1 year, 4 months ago

Log in to reply

A vertical elastic collision would also work. Kinetic energy is converted into potential energy. – Raj Magesh · 1 year, 4 months ago

Log in to reply

– Michael Mendrin · 1 year, 4 months ago

That would work only if you include Earth itself as part of the dynamic system with a center of gravity in uniform motion.Log in to reply

I hope it may inelastic be collision – Mukthesh Mahadev · 1 year, 4 months ago

Log in to reply

Inelastic and perfectly inelastic collision – Jahnvi Verma · 1 year, 4 months ago

Log in to reply

Was weds – Ty Patrick · 1 year, 4 months ago

Log in to reply

It is better to say that mechanical energy is changed. It is in case of Inelastic and some oblique collisions. – Pranjal Prashant · 1 year, 4 months ago

Log in to reply

I hope it may be inelastic collision – Mukthesh Mahadev · 1 year, 4 months ago

Log in to reply

An inelastic collision between two bodies? Energy is lost as heat/used to deform the body but linear momentum is still conserved. – Raj Magesh · 1 year, 4 months ago

Log in to reply

think this scenario violates the law of conservation of energy: A ball is rolling twards a fan, witch provides a constant force on the ball, with some amount of kinetic energy. As the ball gets closer to the fan, its kinetic energy is converted to "fan potential energy". Then, when the ball's kinetic energy is copletly converted to potential energy, the fan turns off. An instantanious force is then applied on the ball, and the ball rolls away from the fan. Now, the energy of the ball is smaller than the energy it had at first, because its kinetic energy is essentially zero and its fan potential energy is constantly decreasing. Where does the energy go? oh, also, the surface the ball is on has no friction

Reference https://www.physicsforums.com/threads/does-this-situation-violate-conservation-of-energy.346004/ – Harshul Mehta · 1 year, 4 months ago

Log in to reply