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.
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Michael Mendrin
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1 year, 1 month ago

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

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@Nihar Mahajan
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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.
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Michael Mendrin
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1 year, 1 month ago

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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.
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Sudeep Salgia
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1 year, 1 month 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.
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Satvik Choudhary
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1 year, 1 month 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.
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Paul Denham
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1 year, 1 month ago

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Fluid flow over a fix plate and other plate is movable..
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Rajan Sah
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1 year, 1 month ago

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

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

An example is Inelastic collision.
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Surya Prakash
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1 year, 1 month ago

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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.
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Grant Larsen
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1 year, 1 month ago

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Inelastic collision such as a car crash
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Jesus Serrano
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1 year, 1 month ago

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

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

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I hope it may inelastic be collision
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Mukthesh Mahadev
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1 year, 1 month ago

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Inelastic and perfectly inelastic collision
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Jahnvi Verma
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1 year, 1 month ago

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

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I hope it may be inelastic collision
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Mukthesh Mahadev
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1 year, 1 month ago

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

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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

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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, 1 month ago

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– Nihar Mahajan · 1 year, 1 month 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, 1 month ago

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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, 1 month ago

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– Nihar Mahajan · 1 year, 1 month 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, 1 month ago

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– Aditya Chauhan · 1 year, 1 month ago

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

– Nihar Mahajan · 1 year, 1 month ago

Thanks. Edited.Log in to reply

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

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

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– Nihar Mahajan · 1 year, 1 month ago

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

Perfectly inelastic collision – Shreenidhi Bodas · 1 year ago

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Inelastic collision – Debasish Som · 1 year ago

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Inelastic collisions... – Tanishq Wadhwani · 1 year ago

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Inelastic collision – Brad Baker · 1 year, 1 month ago

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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, 1 month ago

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

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Catching a ball – Naila Aftab · 1 year, 1 month ago

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

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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, 1 month ago

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Inelastic collision – Anmol Srivastava · 1 year, 1 month ago

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

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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, 1 month ago

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

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

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– Michael Mendrin · 1 year, 1 month 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, 1 month ago

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

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Was weds – Ty Patrick · 1 year, 1 month ago

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

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

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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, 1 month ago

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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, 1 month ago

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