Solving a Railroad Car Sand Filling Problem

[nlightner]

Here it is, I cannot seem to start (b) so hopefully someone can help.

An open top railroad car (initially empty and of mass M.) rolls with negigible friction along a straight horizontal track and passes under the sprout of a sand conveyor. When the car is under the conveyor, sand is dispensed from the conveyer in a narrow stream at a steady rate delta-M/delta-t=C and falss vertically from an average height h above the florr of the railroad car. The car has an initial speed v. and sand is filling it from time t = 0 to t = T. Express your answers to the following in terms of the given quatities and g.

a) Determine the mass M of the car plus the sand that it catches as a function of time t for 0 < t < T.

b) Determine the speed v of the car as a function of time t for for 0 < t < T.

c) i.) Determine the initial kinetic energy of the empty car.
ii.) Determine the final kinetic energy K final of the car and its load
iii.) Is kinetic energy conserved? Explain.

d.) Determine the expressions for the normal force exerted on the car by the tracks at the following times
i.) before t=0
ii.) for for 0 < t < T.
iii.) after t=T

 

[nlightner]

help

come on somebody must be able to answer just b.), the rest are easy, but dependent on b. I believe you can use related rates, but?

 

[Doc Al]

Hint: as the sand fills the car, what quantity is conserved?

 

[nlightner]

I figured it out, it was a lot easier than I thought. No need to use related rates.

 

[PrudensOptimus]

Originally posted by Doc Al
Hint: as the sand fills the car, what quantity is conserved?

Mass, right?

 

[Doc Al]

Originally posted by PrudensOptimus
Mass, right?

Considering the car and the sand inside it as the "system":
Mass is certainly not conserved---it's filling with sand!