- #1

oddjobmj

- 306

- 0

## 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.

Data: M = 1900 kg; F0 = 47000 N; b = 190 kg/s; t = 6.8 s.

## Homework Equations

F=m*a

V(t)=v

_{0}+a*t

## The Attempt at a Solution

M(t)=M+bt

F=ma=M[itex]\frac{dv}{dt}[/itex]

F dt=M dv

dv=[itex]\frac{F}{M}[/itex]dt=[itex]\frac{F}{M=bt}[/itex]dt

Integrating both sides I get:

v=[itex]\frac{F*ln((bt/M)+1)}{b}[/itex]

Plugging in my known values I find that v(6.8)=128.33 m/s which is incorrect. Any suggestions?

Thank you!