Download A railroad car is passing underneath a grain elevator that is dumping

A railroad car is passing underneath a grain elevator that is dumping grain at a constant rate. Assume
perfectly level and frictionless railroad tracks.<br />
a) Why does momentum conservation imply that the railroad car should be slowing down as it
passes the elevator? .<br />
b) If the car slows down, this implies that some external force is acting upon the car to slow it
down. What is the origin of this force? .<br />
c) If at some later time, grain were to start leaking out of a vertical hole in the bottom of the
railroad car at a constant rate, would the railroad car speed up?
The system consists of the grain and the railroad car. Since the only horizontal momentum in the
system prior to collision is that of the car, then the final momentum in that direction must be the same.
Since the mass moving horizontally has increased, the horizontal velocity of that mass has decreased.
The grain is not moving in the horizontal direction before it collides with the car, so the forward
acceleration of the grain during the collision is matched by a ‘backward’ acceleration on the car. Thus,
the car experiences a net force opposite the direction of motion and must slow down. Ultimately, it is a
frictional force that halts the grain’s motion relative to the car, so that is the force that slows the car.
The answer to the last bit is contained in the answer to the precious question. If the grain falls out
perfectly vertically, then there is no interaction with the car as it exits. That is to say that the grain does
not experience a change in its horizontal velocity. As such, there is no action-reaction force pair to
consider and the car does not accelerate in the horizontal direction.
Alternatively you could say that the grain-car system still has the same horizontal momentum as before
the grain fell out - -the grain and car are separated, but still traveling horizontally in the same direction
so the speed of the car shouldn’t change.
In other words, there are no external forces acting on the center of mass in the horizontal direction, so
its velocity cannot change.