Linear momentum: a bullet and the earth

[quasar987]

If I shoot a bullet in the soft ground (meaning it doesn't bounce back), how is the momentum conserved? In that the entire Earth starts moving?

 

[Phymath]

do u ever notice when bullets hit the ground a bunch of dirt flies into the air? Watch any action movie and you can see this. momentum goes into moving the individual particles and a little into the planet but its so small it doesn't do anything, just my idea

 

[krab]

If I shoot a bullet in the soft ground (meaning it doesn't bounce back), how is the momentum conserved? In that the entire Earth starts moving?

That's right.

 

[Integral]

Actually it stops the motion of the Earth that started when you fired the bullet.

 

[quasar987]

Could you explain? I have the feeling only the gun starts moving when the bullet is shot.

 

[krab]

Eventually, the gun stops moving with respect to the earth. Integral is right. The Earth is a system, and anything done there cannot change the trajectory of its centre of mass. So if you fire a gun, even straight up into the air, the bullet travels one way and the Earth the other. Eventually, it turns around and falls back down and similarly, the perturbation to the Earth reverses as well and the Earth moves (too slightly to be measured, but that's beside the point) toward the bullet. Now if your gun was powerful enough that the bullet had escape velocity, it would not come back, and every time you fire it into space, you change the Earth's velocity. Fire it often and in succession, and you are accelerating the earth. In a way, your gun is acting like a rocket engine for rocketship earth.

 

[DaveC426913]

"Actually it stops the motion of the Earth that started when you fired the bullet."

"I have the feeling only the gun starts moving when the bullet is shot."

quasar is correct. The gun is being fired downward, towards the ground. The gun, and the person it's attached to is lifted.

But that doesn't change the end result. The bullet's friction with the air and its impact on the Earth both accelerate the Earth very slightly. OK, well, they would if the Earth were a perfectly rigid object.

 

[omin]

If I shoot a bullet in the soft ground (meaning it doesn't bounce back), how is the momentum conserved? In that the entire Earth starts moving?

There are two categories of collisions that show conservation of momentum: sticky collisions and rebound collisions.

When the bullet hits the soft ground, it would be categorized as a sticky collision, because both objects tend toward a rest state relative to each other after the collision.

If it were to bounce of a rock of the earth, it would be a rebounding collision, because both objects tend to show a state of motion relative to each other after the collision.

The conservation of momentum is implied by Newtons Second Law. Your question is a sticky one. So, Newtons Second law must be used in a sticky sense.

A gnat finds itself on a busy intestate. He doesn't have time to move out of the way of an oncomming semi wind shield. He has a sticky collsion with the semi wind sheild. This is similar to a small bullet colliding with the huge mass of the earth. One is very large compared to the other and when they collide, they stick to each other.

Momentum is mass times velocity.

Mass is consistent throughout the collision. The mass of the bullet and the gnat does not change during the collision. The gnat and bullet may be splattered or deformed some, but they still have the same quantity of mass.

Velocity is consistent throughout the collision. The velocity of the bullet and gnat seems to go to zero, but not really. They change the velocity of the semi and Earth ever so slightly.

Therefore, momentum is conserved.