Linear momentum but quadratic kinetic energy?

[Rick28]

Homework Statement

Conservation of momentum and cinetic energy : I don't understand why the total kinetic energy seems to increase (or decrease) when we apply the conservation of momentum

Example with 100 kg ball at 5 m/s that go to 0 m/s when hitting a 10 kg ball.
The 10 kg ball should be at 50 m/s now, but the kinetic energy will be increased in comparision to the 100 kg ball that was previously at 5 m/s.
12.5 kJ for the 10 kg ball at 50 m/s vs 1.25 kJ for the 100 kg ball at 5 m/s

How is this possible ?
thanks

Relevant Equations

P = m.v
E = (m.v^2 ) . 1/2

no clues

 

[haruspex]

Example with 100 kg ball at 5 m/s that go to 0 m/s when hitting a 10 kg ball.

That cannot happen. If you start with a false premiss you can deduce anything.

Edit: Challenge for you: what is the minimum final speed of the 100kg ball, and in which direction?

 

[Philip Koeck]

Homework Statement: Conservation of momentum and cinetic energy : I don't understand why the total kinetic energy seems to increase (or decrease) when we apply the conservation of momentum

Example with 100 kg ball at 5 m/s that go to 0 m/s when hitting a 10 kg ball.
The 10 kg ball should be at 50 m/s now, but the kinetic energy will be increased in comparision to the 100 kg ball that was previously at 5 m/s.
12.5 kJ for the 10 kg ball at 50 m/s vs 1.25 kJ for the 100 kg ball at 5 m/s

How is this possible ?
thanks
Relevant Equations: P = m.v
E = (m.v^2 ) . 1/2

no clues

That's not possible.
In an inelastic collision momentum is conserved and some of the kinetic energy is transformed to heat, so the macroscopic kinetic energy decreases.
The opposite is not possible since it would mean that heat is completely transformed to work.

 

[jbriggs444]

How is this possible ?

As you have computed, the kinetic energy increases in this scenario. The smaller ball bounces away from the larger more rapidly than it arrived.

In an ordinary passive encounter between two balls we expect them to slow down relative to each other as the result of an impact. We know this to be the case. It happens every time. It has to do with "entropy". Total mechanical energy tends to decrease as it is dissipated into thermal energy.

If we observe a violation of this behavior then we know that something unexpected is going on. Perhaps someone had painted the larger ball with some contact explosive so that there was a pop and a puff of smoke along with the collision. The increase in mechanical energy was balanced by a decrease in chemical potential energy.

Or perhaps this was an unfair encounter between a 100 kg spinning Beyblade [yikes!] and a 5 kg Beyblade. Linear kinetic enegy increased at the expense of the rotational kinetic energy of the objects.

 

[haruspex]

As you have computed, the kinetic energy increases in this scenario. The smaller ball bounces away from the larger more rapidly than it arrived.

In an ordinary passive encounter between two balls we expect them to slow down relative to each other as the result of an impact. We know this to be the case. It happens every time. It has to do with "entropy". Total mechanical energy tends to decrease as it is dissipated into thermal energy.

If we observe a violation of this behavior then we know that something unexpected is going on. Perhaps someone had painted the larger ball with some contact explosive so that there was a pop and a puff of smoke along with the collision. The increase in mechanical energy was balanced by a decrease in chemical potential energy.

Or perhaps this was an unfair encounter between a 100 kg spinning Beyblade [yikes!] and a 5 kg Beyblade. Linear kinetic enegy increased at the expense of the rotational kinetic energy of the objects.

Seems to me the OP has made up the scenario, not realising it might violate reality.