# Momentum of variable mass system - train & rain

1. Jun 25, 2012

### Beelzebro

1. The problem statement, all variables and given/known data
An open-topped railway wagon of mass M is rolling freely along straight level frictionless track at a constant velocity v0. At time t=0 the wagon enters a heavy rain shower and starts to collect rainwater. The rain falls vertically. As a consequence the wagons mass increases at a rate of μ per second

A. Show that the velocity v(t) at time t after entering the shower is v(t) = [Mv(0)]/[M+μt]

B. If the wagon had been fitted with a drain hole to prevent rainwater accumulating, find its velocity at time t, assuming that the water leaves the wagon at zero relative velocity.

C. Compute the momentum of the system (the system being the wagon plus water in A, and wagon in B) as a function of time, and explain the qualitative difference between cases A and B.

2. Relevant equations
Newtons 2nd law
P=mv

3. The attempt at a solution
http://img171.imageshack.us/img171/5905/dsc01142nk.jpg [Broken]
http://img341.imageshack.us/img341/6921/dsc01143y.jpg [Broken]
http://img16.imageshack.us/img16/3945/dsc01144g.jpg [Broken]

Basically I don't need a huge amount of help as I think I grasp the physics of the problem. But I'm a bit unsure about C. I know that for system B the momentum should be decreasing, because the system is gaining μt rainwater with velocity zero and losing μt rainwater with velocity v(t). But looking at the equation it seems to me that the momentum increases with time, until μt = M at which point it asymptotes. This definitely doesn't seem right.

Thanks in advance for any help.

Also apologies if the images are too big, I'm not sure how to resize them :(

Last edited by a moderator: May 6, 2017
2. Jun 25, 2012

### Beelzebro

Woooooaahhh ok the images were huge. I've spoiler tagged them but they're still massive. Can someone tell me how to resize please? (sorry this is my first thread I'm a noob)

EDIT: ok well spoiler tags achieved nothing. What use are spoiler tags when they don't hide whatever you put in them??