Finding recoil velocity of a gun after firing a bullet

[Woopy]

Homework Statement

http://hypertextbook.com/physics/mechanics/momentum-energy/problems.shtml

It's numerical #1, filling out the table, the part I am stuck on is recoil velocity. I have figured out the bullet momentum and bullet energy, however.

Homework Equations

(m₁+m₂)v=m₁v₁'+m₂v₂'

The Attempt at a Solution

The part that I don't understand is what is m₂? M₁ would be the mass of the bullet, but is the mass of the gun suppose to be m₂?

 

[turin]

... is the mass of the gun suppose to be m₂?

Most likely.

 

[Woopy]

there's 3 different velocities, and I don't see how there can be. V is recoil velocity what I am solving for, v1 would be the muzzle velocity, and v2 as the velocity of the gun (0 m/s?)

 

[turin]

You have your velocity assignments backwards. Treat this like an "inverse inelastic collision". That means that you begin with the two objects combined (like you have in your equation). So, if v is the velocity of the combined object (bullet inside gun before it is fired), then what do you think should be v? Hint: it isn't recoil.

 

[Woopy]

(.0097kg + 4.4kg)(0 m/s) = (.0097kg)(890m/s)+ (4.4kg)(v2') ?

-4.4kg(v2') = 8.633 kgm/s
v2' = -1.96 m/s (since its a recoil, it'd go backwards so negative.

 

[LowlyPion]

there's 3 different velocities, and I don't see how there can be. V is recoil velocity what I am solving for, v1 would be the muzzle velocity, and v2 as the velocity of the gun (0 m/s?)

Your table has three different bullets fired from 3 different guns with different barrel lengths and total masses.

Filling out the table is really observing Newton's Third Law of Action/Reaction for each bullet/gun combination.

Whatever momentum the bullet leaves the gun with will be equal to the momentum of the gun in the opposite direction.

MV_bullet = - MV_gun

 

[turin]

I didn't check your numerical calculation this time, but your approach looks good.