Conservation of Momentum in Moving Buckets of Water

[Gear2d]

Homework Statement

a) A bucket full of water is slid across a sheet of ice (no friction). As bucket fills (as it moving), what happens to its velocity and momentum?

b) Now instead of filling the bucket with more water, say it has a leak as it moves, what happens to its velocity and momentum?

Homework Equations

p=mv

The Attempt at a Solution

a)The velocity decreases, but momentum is constant. I

I do not see why this is the case. Is this because m = p/v, so if my mass is increasing v has to decrease. Momentum remain constant because pi = pf?

b) Velocity constant, but momentum decreases.

Here v = p/m. But I don't see the math behind why velocity is constant if you are losing mass (loss of mass means momentum decreases, since momentum is a factor of inertia).

 

[C. Hollmann]

You are on the right track. However, what happens to water "leaking" in a frictionless environment? Each unit of water (molecule?) will have the same velocity as the bucket. You are not adding any outside decelerating force, which means the bucket will move at the same rate. If you had a midget (sorry, I meant "little person") riding in the bucket throwing water out of the bucket opposite to the direction of movement, the bucket would slow down due to opposing force of the expelled water. Since velocity remains constant, and mass is decreased, the momentum of the bucket will decrease.

I also have an issue with the original premise:
A bucket being filled as it is moving would only slow down if it was filled with water coming from a motionless reference frame. If you were standing still, and adding water with zero velocity to a moving bucket the bucket would indeed slow down. In reality this would be hard to achieve. If you take the easy way out and pour water from a second moving bucket (moving at the same velocity as the one to be filled) you will not see any change in velocity as the bucket fills ...but since mass is increased, momentum will also increase.

This applet may help you visualize this using a brick ...not water which has a nasty habit of sloshing around and messing up your observations.
http://www.ngsir.netfirms.com/englishhtm/DropABrick.htm"

Hope I didn't over complicate things too much!

CH

 

[Defennder]

Thanks for the animation. It looks rather neat!

 

[Gear2d]

Thank You C. Hollmann. That helped.