How Does Holding an Air Rifle Affect Recoil Speed?

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The discussion focuses on calculating the recoil speed of an air rifle when fired, considering the conservation of momentum. The initial scenario involves a 2.0 kg air rifle firing a 1.0 g bullet at 150 m/s, prompting questions about the correct mass to use for calculations. Participants clarify that the total mass for recoil calculations should include the girl's mass, the rifle, and the bullet. They discuss the need for an additional term in the momentum equation to account for the backward movement of the girl after firing. The conversation concludes with a consensus on the approach to solving the problem, emphasizing the importance of momentum conservation.
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Kim holds a 2.0 kg air rifle loosely and fires a bullet of mass 1.0 g. The muzzle velocity of the bullet is 150 m/s. What is the recoil spped of the rifle? The next shot the girl holds the rifle tightly against her body. Calculate the new recoil speed assuming the girl has a mass of 48kg.

I'm really not sure how to do this problem, any help would be appreciated.
Thanks
 
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Well you know that momentum will play a part in this question, so will momentum be conserved as the bullet leaves the gun?
 
Yes so is this the right way to set up the equation for the second part:
(50)(v)=(.001)(150)
v=-.003 m/s - v is negative because moving backwards

I'm not sure if 50 kg is the right mass though. I took it as the girl and the gun becoming one system so their masses are added.
 
dlilpyro said:
Yes so is this the right way to set up the equation for the second part:
(50)(v)=(.001)(150)
v=-.003 m/s - v is negative because moving backwards

I'm not sure if 50 kg is the right mass though. I took it as the girl and the gun becoming one system so their masses are added.


Her initial mass would be 48+2+0.001 since she is holding the gun with the bullet in it. However, what is her initial velocity if she is not moving?

After the bullet is fired, you are right with the 0.001(150) but remember she will move backwards with some velocity. So you need to have an additional term on the right side.
 
I'm not sure what the additional term is because we didn't have time to get the equation during class today. But if the initial velocity is zero how can you solve for v final on the left side?
 
dlilpyro said:
I'm not sure what the additional term is because we didn't have time to get the equation during class today. But if the initial velocity is zero how can you solve for v final on the left side?

The v on the left side will be zero since the girl is not moving.

There will be a different V on the right side since the bullet will move forward and she will move backward due to the recoil.

on the right side you will need the moment of bullet (which you have already) + momentum of girl (which will have the V to solve).
 
Alright I think I have it now. Thanks for all the help.
 

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