- #1

Mr.V.

- 9

- 1

For instance let's take this problem.

Say I have a gun that fires two different bullets.

The first bullet travels at say 100m/s and has a mass of 0.1kg.

Therefore it's momentum is [tex]100m/s*0.1kg = 10 kg*m/s [/tex]

and it's energy is [tex]1/2*0.1kg*(100m/s)^2 = 500J [/tex] (at least I think that's right)

The second bullet travels at say 50m/s and has a mass of 0.3kg.

Therefore it's momentum is [tex] 50m/s*0.3kg = 15 kg*m/s [/tex]

and it's energy is [tex]1/2*0.3kg*(50m/s)^2 = 375J [/tex]

This is the part I don't get. The first bullet has

**more energy**than the second but

**less momentum**.

What does that mean to, say, the moose or bear or cute baby seal that get's hit by the bullet. Let's assume the bullet hits the target and goes into it but doesn't come out the side and therefore all the energy is transferred to the target. Is the momentum what determines the damage or knockdown or is it the energy?

Let's say the target is a moose that isn't moving anywhere and is 100kg.

From the conservation of momentum formula and given that this would be an inelastic collision you would expect that the first bullet would be

[tex]10kg*m/s=(100kg+0.1kg)*V_2 [/tex] you could calculate that the moose+bullet1 would end up traveling ~0.10m/s in the direction of the bullet

bullet two would be [tex]15kg*m/s=(100kg+0.3kg)*V_2[/tex] you could calculate that the moose+bullet two would end up traveling 0.15m/s.

But if we say that the bullet transfers its energy (hits the moose and transfers the kinetic energy) we can see that the moose in the first bullet instance gains 500J of kinetic energy and therefore [tex] 500J=1/2*(100kg+0.1kg)*V^2 [/tex] and solving for V we get V=3.16m/s

and in bullet2's case we get [tex] 375J=1/2*(100kg+0.3kg)*V^2 [/tex] and solving for V we get V=2.73m/s.

So now I have two problems. Using the conservation of momentum equation I see that a bullet with LESS energy but MORE momentum can cause the moose to move more

But using kinetic energy I see that the bullet with MORE energy but LESS momentum causes the moose to move more.

And the HUGE problem that the velocities don't add up.

I'm clearly doing something wrong and I also don't understand the difference between momentum and energy.

Any help would be appreciated. Sorry for the drawn out example. I thought creating a scenario would be more helpful than just asking a bunch of questions.

Thanks!

Vik