Conservation of momentum scenario

[Sidney]

if a nice fuzzy block is stationary on a frictionless surface and is hit by a high velocity bullet in such a way that the bullet cleanly penetrates and exits the box leaving the box stationary but the velocity of the bullet slightly changed, what can one say about the conservation of momentum of the system..? how can it be shown mathematically that the momentum is conserved

 

[Dale]

leaving the box stationary but the velocity of the bullet slightly changed,

This is not possible.

If the velocity of the bullet changed then there was a force on the bullet. If there was a force on the bullet then there was an equal and opposite force on the block. If there was a force on the block then its velocity changed.

 

[Sidney]

ok, new scenario, describe the momentum changes when the impacted object is stationary by all means (maybe it's even mounted) and is impacted by a high velocity object and the collision is completely inelastic

 

[AlephNumbers]

ok describe the momentum changes when the impacted object is stationary by all means (maybe it's even mounted) and is impacted by a high velocity object and the collision is completely inelastic

I suppose that momentum would not be conserved. There are external forces acting on the impacted object.

 

[Sidney]

what does that mean, momentum is not conserved?? is it not a law that it always is..?

 

[Sidney]

can the problem not be split up in some way as to mathematically describe the changes in momentum like the ballistic pendulum for example..

 

[phyzguy]

Momentum is always conserved. In your scenario where the impacted object is mounted firmly to some larger object (the Earth for example), then the momentum of the impacted object plus the Earth changes by an amount equal and opposite to the momentum change of the bullet. But since the mass of the Earth is so large, the momentum change of the block plus the Earth is immeasurably small.

 

[AlephNumbers]

what does that mean, momentum is not conserved?? is it not a law that it always is..?

Anyone that told you that momentum is always conserved was doing you a disservice.

The momentum of a closed, isolated system is constant. However, in your example there are external forces acting on the system. Namely, whatever is holding the impacted object in place.

 

[ZapperZ]

what does that mean, momentum is not conserved?? is it not a law that it always is..?

Having read your posts here, the problem you are having is not realizing what the "entire system" is that is involved in the conservation law.

Note that in an ISOLATED SYSTEM, meaning no external forces acting on it, then the momentum of the ENTIRE SYSTEM is conserved.

When you fixed something or attach it to something (like the earth), then the entire system now includes the earth! This is because by fixing it to the earth, whatever you do to that object, the Earth will provide the counter force to it. So the bullet-block system is not an isolated system. Your isolated system is now bullet-block-earth. The conservation of momentum only applies to that system, not to bullet-block.

Zz.

 

[Dale]

ok, new scenario, describe the momentum changes when the impacted object is stationary by all means (maybe it's even mounted) and is impacted by a high velocity object and the collision is completely inelastic

As was mentioned by others, momentum is only conserved for an isolated system, meaning no external force. This system (bullet + block) is not isolated as the mounting provides an external force. Therefore the momentum of this system is not conserved.

If you wish to analyze the system using conservation of momentum then you need to expand the system to include the object providing the force which keeps the block stationary.