A railroad car rolling along by itself is passing by a grain elevator, which is dumping grain into it at a constant rate. (a) Does momentum conservation imply that the railroad car should be slowing down as it passes the grain elevator? Assume that the track is frictionless and perfectly level and that the grain is falling vertically. (b) If the car is slowing down, this situation implies that there is some external force acting on the car to slow it down. Where does this force come from? (c) After passing the elevator, the railroad car springs a leak, and grain starts leaking out of a vertical hole in its floor at a constant rate. Should the car speed up as it loses mass?

Question

A railroad car rolling along by itself is passing by a grain elevator, which is dumping grain into it at a constant rate. (a) Does momentum conservation imply that the railroad car should be slowing down as it passes the grain elevator? Assume that the track is frictionless and perfectly level and that the grain is falling vertically. (b) If the car is slowing down, this situation implies that there is some external force acting on the car to slow it down. Where does this force come from? (c) After passing the elevator, the railroad car springs a leak, and grain starts leaking out of a vertical hole in its floor at a constant rate. Should the car speed up as it loses mass?

Answer 1

I will be happy to critique your thinking on this.

Answer 2

I am unable to visualize a rolling railroad car passing by a grain elevator

Answer 3

(a) According to the principle of momentum conservation, the total momentum before and after an interaction remains constant if no external forces act on the system. In this case, the system can be considered as the railroad car and the grain elevator.

When the grain is being dumped into the railroad car, it adds mass to the system, thus increasing the total momentum. However, since momentum is the product of mass and velocity, and the velocity of the incoming grain is essentially zero (falling vertically), the change in momentum due to the added mass is negligible. Therefore, the momentum conservation principle alone does not imply that the railroad car should be slowing down as it passes the grain elevator in this frictionless and level scenario.

(b) If the railroad car is slowing down in this situation, it implies that there is an external force acting on the car. In the absence of friction or other obvious forces, we need to consider the force exerted by the grain as it falls into the car. This force arises from the change in momentum of the grain, as it goes from a static position to downward motion. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the reaction forces of the grain falling into the car exert an upward force on the car. This force slows down the car's forward motion.

(c) After the railroad car passes the elevator, and it starts leaking grain through a vertical hole, it will indeed experience a change in speed due to the loss of mass. According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act on it. Since the grain is leaking out of the car with a constant velocity, the momentum carried by the leaking grain will be equal and opposite to the momentum of the car with respect to the grain. As the car loses mass, the conservation of momentum implies that the car's speed will increase to offset the loss of momentum from the leaking grain.