Rolling Drain?

Question

The rain has stopped (refer to prior question ROLLING IN THE RAIN). A drain plug is opened in the bottom of the rolling (without friction) open railroad car allowing the accumulated water to run out. Consider the effects of the draining water on the speed, momentum, and kinetic energy of the rolling car.

The speed of the car will

a) increase
b) decrease
c) not change

The momentum of the car will

a) increase
b) decrease
c) not change

And the kinetic energy of the car will

a) increase
b) decrease
c) not change

The answer to the first question is C; the second B; and the third B. If you simply let go of something you are holding, it does not exert any force on you and you do not exert any force on it. As the water is released from the car it exerts no force on the car so the speed of the car is not changed. The water just drops away with the same horizontal velocity it had while in the car -- like some clod dropping a beer can out of the window of a moving car. Of course the departing water akes its momemtum and kinetic energy with it when it goes. So the car is left with less momentum and less kinetic energy.

Answer 1

This one is a little more straightforward. Since the water is already moving with the same horizontal velocity as the rail car, and will remain so as it takes its mass away, no horizontal acceleration will be imparted by it draining out.

As such, the car's speed will not change. But it will lose mass, so both its momentum and kinetic energy will decrease.

That's C), B), B)