Basic question about kinetic energy and momentum

1. Aug 28, 2013

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.

2. Aug 28, 2013

Drakkith

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

3. Sep 15, 2013

jacket

All true.

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

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

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