Conservation of Momentum Set-Up

[alexander_i]

Homework Statement

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.

Homework 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.

The Attempt at a Solution

I tried treating this like a rocket ship problem-

F_external = 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!

 

[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 >>

 

[alexander_i]

YEAH! Thank you for your help!