Carts gaining and losing mass: What happens to velocity?

[Jormungandr]

Homework Statement

There are 2 versions of the problem that I've heard:

A bucket on wheels is moving at a constant velocity on a frictionless surface. It's raining out so the bucket is gaining mass. Will it slow down, speed up, or remain at that velocity as it gains mass?

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:
A. Constant, forwards
B. Constant, backwards
C. Variable, forwards
D. Variable, backwards
E. Zero

The Attempt at a Solution

The answer to the first one is that it will slow down because it gains mass. The answer to the second one, however, is E, that it does not decelerate and will keep its initial velocity. So what gives? What's the difference between these answers?

 

[ehild]

Supposedly, the rain drops fall vertically so they have zero horizontal velocity. They have to speed up to the velocity of the bucket, have to gain momentum - from where?

In the second case, the sand particles move with the same velocity as the bucket. They just fall out across the hole. They carry their own momentum and mass. If M is the initial mass of the bucket + sand, and v is the velocity, and m mass falls out, the momentum of the bucket+sand decreased by mv, and the mass decreased by m. What are the remaining momentum and mass? What is the new velocity?

ehild

 

[Nathanael]

The answer to the first one is that it will slow down because it gains mass. The answer to the second one, however, is E, that it does not decelerate and will keep its initial velocity. So what gives? What's the difference between these answers?

"Because it gains mass" is not a valid explanation. Ehild covered it pretty well; it's all about momentum.