Velocity of .30 Cal Rifle After Firing a Bullet

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The discussion focuses on calculating the velocity of a .30 caliber rifle after firing a bullet, using the principle of conservation of momentum. It is established that the rifle and the cart it is mounted on can be treated as a single rigid body, and the assumption of a massless cart simplifies the calculations. The momentum before firing equals the momentum after firing, allowing for the determination of the rifle's velocity based on the known mass and velocity of the bullet. Additionally, the conversation touches on the inelastic collision between the bullet and a block of wood, emphasizing the need to solve for the combined velocity of the bullet and wood after impact. Overall, the participants confirm their understanding of the problem and the necessary calculations.
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Imagine I were to shoots a .30 caliber rifle at a 0.56 kg block of wood. The rifle and wood are mounted on separate carts that sit atop an air track (like a linear air hockey table--ie. frictionless). The 6.4 kg rifle fires a 33 gram bullet at 219 m/s in the positive direction. What would be the velocity of the rifle after the bullet is fired?
 
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It seems like you need to apply conservation of momentum. In order to do that you would need to know the mass of the cart to which the rifle is attatched. Can it be assumed to be massless?
 
Since the air track is frictionless, and every force has an equal and opposite force, the momentum of the rifle should equal the momentum of the bullet, yes?

PL
 
But if the rifle is attached to the cart, much of the rifle's momentum will be transferred to it. They are being treated as one rigid body, I think.
 
Yes, conservation of momentum would be the easiest, and from the information i think you would have to assume the cart is massless, otherwise the question is incomplete. Also the fact that it was shot at a block of wood seems irrelevant, unless there is a part B...
 
The first part:
momentum before is equal to momentum after.
Mass of rifle x velocity of rifle = mass of bullet x velocity of bullet

I know the mass of the rifle and bullet and the velocity of the bullet,
so no I have to find the mass of the rifle.

The second part: (this is an inelastic collision-hit or 'stick collision'.)
Mass of bullet x velocity of bullet = total mass of block and bullet x
velocity of bullet and wood together.

I would have to solve for the velocity of the bullet and wood together.
 
Okay, so do you understand how to do both parts now? You have all the information you need. Solve for the velocity of the rifle in the first one (as it seems the cart is massless), and solve for the velocity of the bullet and wood in the second one.
 
Yes I got it. Thanks all!
 

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