- #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)=v0+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!