Physics-Momentum

[Piccokuh]

Alright, I can do most of my other problems, but I'm having some trouble figuring out how to even set this one up, so here goes...

A 500 g gun sliding on ice at a speed of 4 m/s accidentally fires a 5 g bullet in the same direction as the motion of the gun. If the bullet travels at 300 m/s, what is the velocity of the gun after the shot?

[Fiz]

I think I can be of assistance here.

Momentum is equal to mass times velocity (p = mv).

You want to find the recoil velocity of the gun after it fires the bullet. First, draw a free-body diagram of the entire scenario:

Before:

Gun ------->
v = 4 m/s
m = 500 g

After:

<--- Gun ---------> Bullet
v = ?....................v = 300 m/s
m = 500 g............m = 5 g

You know that the gun already has a forward momentum:

p(before) = m*v
p(before) = (0.5 kg)(300 m/s)
p(before) = 150 kg*m/s

This is the momentum of the gun before the bullet is fired.

From here, you can use the conservation of momentum to solve for the velocity of the gun after the bullet leaves. You can calculate the momentum of the bullet, and from there you can calculate the momentum of the gun after, or the recoil of the gun.

If you need more help, feel free to ask! I'll let you see if you can figure it out from here.

EDIT: Oh, and I don't know how detailed your teacher wants you to be, but unless he states otherwise, the momentum of the gun before could also include the mass of the bullet, so in essence, the mass of the gun would be 505 g. That might be a little overboard though. ;)

[Diamond187]

Well, 5g could make a difference, and I think it would actually be that the gun would weigh 495g after it fires.

[Fiz]

That would make more sense Diamond...I agree...but I'm guessing he doesn't have to worry about it in that much detail.

[Diamond187]

Iunno, I hope not, but some people can be real sticklers about that kind of thing.

[Vagrant]

THen there's always the gunpowder lost, but let's not get too technical ;-)

[Fiz]

And air resistance, which would just be a frictional force...lol

[theundeclinable]

and cant forget that ice isnt actually frictionless :)

[cheesecake]

And gravity. When the bullet is fired form the gun, gravity will try to pull them back together. I swear..I am talking about the most minute of forces here lol........Ehem, back on topic.

Anyway the weigght of the gun is 500g. The bullet is 5g. I dont know how many bullets are in the gun, but I am assuming that original weight will be 505g, then will separate into 500g and 5g. Don't get caught out on these, although you probably won't be asked this question in a test, as it is very brief and doesnt explain things well.

[Fiz]

Actually, to be truthful, in academic physics questions, the golden rule is that you should always only work with the information you're given. Don't assume things. In this case, in an academic problem solving scenario, unless you're given explicit information that the net weight before is 505 g, don't assume it is. Although it makes sense that it should be, your answer will not change by much. In an academic sense, the methods are not more important than the reasoning, but its usually the method of solving that's given precedence.

To be safe, I always write little notes like "Assume the mass of the gun always 500 g". Or, I'll write something to show my understanding, like "I assumed that the bullet was part of the original weight, which was 500 g in total".

Richie, can you explain how gravity will try to pull the gun and the bullet back together? I'm not saying you're wrong, I just want to hear your reasoning to see if its similar to what I thought when I read it. :) The great thing about physics is that if you can prove your reasoning, you can prove that you're right even when people don't follow your initial statement.

[Diamond187]

LOL, how's this for far out: if we assume that the bullet is made of some type of steel, then the huge velocity it's given so suddenly will likely induce a ferromagnetic moment in the bullet, which creates a magnetic field which is then accelerated down the barrel of the gun, which will act as solenoid, and have a charge induced through it. So how badly is the shooter shocked? LOL

[Fiz]

:roll: Hehehe...