Rolling in the Rain?

Question

Suppose an open railroad car is rolling without friction in a vertically-falling downpour and an appreciable amount of rain falls into the car and accumulates there. Consider the effect of the accumulating rain on the speed, momentum, and kinetic energy of the car.

Question #1

The speed of the car will

a) increase
b) decrease
c) not change

Question #2

The momentum of the car will

a) increase
b) decrease
c) not change

Question #3

And the kinetic energy of the car will

a) increase
b) decrease
c) not change

The answer to the first question is B; the second C; and the third, B. The rolling car has momentum only in the horizontal direction. The rain falls straight downward and has no horizontal momentum to add to the car. So the momentum of the car doesn't change. The mass of the car however, does change -- it's increased by the mass of accumulated rain. A mass increase while momentum is constant results in a decrease in velocity. So the car slows down as rain accumulates, This situation is almost a repeat of y question SMUSH AGAIN. Speed and kinetic energy are cut while momentum is uneffected. What happens to the lost kinetic energy? it goes into heat -- the water in the car is a bit warmer than the rain.

We have reasoned so far with only the conservation rules for momentum and energy. Answers to many questions are provided by these powerful rules that completely bypass often very messy forces. But let's think about force anyway to better understand our conclusions.

Answer 1

Since the accumulating rainwater needs to be accelerated to stay in the car, its speed will decrease. It will lose as much momentum due to reduced speed as it gains in increased mass, so the momentum will stay the same. But since kinetic energy is proportional to the square of velocity, it will decrease.

So b), c), and b)

I think - but then, it's pretty late, and I could be doing the last two backwards.

Answer 2

Let us sit on the car. If the rain pouring is vertically down, then we will see it, inclined at some angle, from the car. An angle that is in the third quadrant in the cross wire of our frame. So it can be said that the rain would try to push us 'behind' ( in the direction negative to our motion with respect to the ground .) With respect to the ground we are moving forward. so an addition in velocity in the opposite direction would imply that our speed decreases.
Therefore,
Answer #1 :b) decrease
Answer #2,3 : can't say

Answer 3

If the car is moving perpendicular to the rain, naught will happen.

If the car is on a slant, things will add.

Think of this as a vector problem.

Answer 4

And I will say...B~C~B