# Conservation of Momentum Set-Up

1. Jun 22, 2009

### alexander_i

1. The problem statement, all variables and given/known data

An empty freight car of mass M starts moving from rest with a constant applied force F0. At the same time, coal runs into the car at steady rate b from a hopper above the car at rest along the track. Calculate the velocity of the car as a function of time.

GIVEN: M = 1400 kg; F0 = 42000 N; b = 150 kg/s; t = 6.5 s.

2. Relevant equations

I have a problem setting up conservation of momentum problems; I was wondering if there are some basic steps or factors to always look at, and help me understand the anatomy of them.

3. The attempt at a solution

I tried treating this like a rocket ship problem-

Fexternal = F0 = d(mv)/dt

F0*dt = d(mv) -->

F0 = v*dM/dt + M*dv/dt = v*b + M*dv/dt

to differentiate--> F0 - v*b = M*dv/dt
--> (1/m)dt = (1/b)(1/F0/b - v)*dv

V(t) = [F0/b]*[1-e-b*t/m]

And plugging in I get 140.45 m/s which is not correct.

will someone help me understand the anatomy of the conservation of momentum, any helpful links are also appreciated. Thanks!

Last edited: Jun 22, 2009
2. Jun 22, 2009

### SonyAlmeida

Your problem is that you forgot that m(t) = M + bt, so when you separated variables, your LHS should have been (1/(M+bt))dt

Think that should fix it.

I got: << solution edited out by berkeman >>

Last edited by a moderator: Jun 22, 2009
3. Jun 22, 2009

### alexander_i

YEAH! Thank you for your help!