# Do I use kinetic energy or momentum to figure out the final velocity? [duplicate]

Let's say hypothetically that a gun fires a bullet which has a mass of 1 gram and a $V_\mathrm{initial}$ of 10 m/s, which becomes lodged in a wooden block that has a mass of 9 grams and is initially at rest. The impact causes the block (with the lodged bullet) to travel at a velocity $V_\mathrm{final}$. What is $V_\mathrm{final}$?

I'm confused. I don't know whether I should use momentum or kinetic energy to figure out the $V_\mathrm{final}$. I plugged in the numbers to both equations, and the resulting values of $V_\mathrm{final}$ didn't agree.

## marked as duplicate by David Z♦Nov 22 '16 at 7:52

Okay, lets start this off with a simple answer, you can solve it many ways using fundamental algebra, that includes work energy, kinematic-dynamic and Impulse momentum theorem. I personally check myself with both. We can go into more detail later if we need so.

I personally use Work-energy-kinematic ways. However, we can start however by using Impulse-momentum theorem, just to make this short

Fnet * t = m * (change in) Velocity.

now, we can just say that the impulse that will produced on impact is 0.01 Ns the impact will result in mass combined of 0.01kg's, thus 0.01Ns/0.01kg is 1 m/s resultant velocity.

We however, can use energy to find velocity after v=(square root) 2(KE)/mass

• How do you account for the energy dissipated in heat, sound of impact, tearing of wood/lead? – DJohnM Nov 22 '16 at 3:28

You can think of the problem this way: You can just divide the velocity by mf/mi or (9+1)/1, or 10/1, which is the same as multiplying the initial velocity by 1/10, which is the amount of mass that the motion energy is changing to apply to, which gives 1 m/s final velocity.

• How does this address the OP question? You don't talk about any conservation principle. – Bill N Nov 22 '16 at 3:03
• But was I wrong? The final velocity is scaled by the initial velocity and the ratio of the initial mass to the final mass, because the momentum is velocity times mass, so vf = vi*(mi/mf) or as I originally put it vf=vi/(mf/mi). Therefore, the final velocity is 1 m/s. – Aaron Franke Nov 16 '18 at 9:18
• OP did not ask about conservation. Boy, I sure love getting downvoted for posting a correct answer, gotta love StackExchange. – Aaron Franke Nov 16 '18 at 9:20