Do kinetic energy changes always cause momentum changes?

[grayb]

Hi, I'm learning about momentum and kinetic energy and I wanted to know if the following relationships are true. I think they are true, but I am not sure:

1. If kinetic energy goes down and mass stays constant, momentum goes down
2. If kinetic energy stays constant and mass goes down, momentum goes down
3. If kinetic energy goes up and mass stays constant, then momentum goes up
4. If kinetic energy is constant and mass goes up, momentum goes up

Are they true? Thank you.

 

[Drakkith]

Have you done the math? If so, what does the math say? Remember, the math won't lie.

 

[jacket]

All true.

KE = p$^{2}$/(2m)

Now, for constant mass:
KE $\propto$ p$^{2}$

For constant kinetic energy:
m $\propto$ p$^{2}$