(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(Kleppner & Kolenkow - Introduction to Mechanics - 3.12)

A sand-spraying locomotive sprays sand horizontally into a freight car situated ahead of it. The locomotive and freight car are not attached. The engineer in the locomotive maintains his speed so that the distance to the freight car is constant. The sand is transferred at a rate dm/dt = 10 kg/s with a velocity of 5 m/s relative to the locomotive. The car starts from rest with an initial mass of 2000 kg. Find its speed after 100 s.

2. Relevant equations

Momentum equation

3. The attempt at a solution

Let the mass of the freight car be m'. At some time t, the momentum of the car is given by:

[itex]P(t)=(m'+ t \frac{dm}{dt})u [/itex]

where u is the velocity at that time.

At a time t+dt, the momentum would be:

[itex]P(t+dt)=(m'+ (t+dt)\frac{dm}{dt})(u+du) [/itex]

The momentum change:

[itex]dP=P(t+dt)-P(t)=(m'+t\frac{dm}{dt})u+udm+(m'+t\frac{dm}{dt})du [/itex]

Basically I'm trying to make a differential equation for u. I'm not sure if the above is correct or not, and I also need some other expression for dP to equate this to. I'm assuming that will use the fact that the sand moves at 5 m/s relative to the locomotive and car setup (since they maintain a constant distance). How should I proceed?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Momentum problem with mass transfer

**Physics Forums | Science Articles, Homework Help, Discussion**