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.