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# Variable Mass Problem watch

1. Variable Mass Problem ...

Only minutes old ...
I have not even written the solution yet.
2. (Original post by TeeEm)
Variable Mass Problem ...

Only minutes old ...
I have not even written the solution yet.
I get 1/k * ln 2 but I haven't checked just yet.
3. (Original post by A Slice of Pi)
I get 1/k * ln 2 but I haven't checked just yet.
one of the two answers is
4. (Original post by TeeEm)
one of the two answers is
Didn't see the last bit aha, I'll work it out now
Edit: I get
5. (Original post by A Slice of Pi)
I get 1/k * ln 2 but I haven't checked just yet.
Bloody hell, how are you so good at mechanics?!
6. (Original post by Zacken)
Bloody hell, how are you so good at mechanics?!
I was thinking the same thing..
7. (Original post by TeeEm)
one of the two answers is
I get as well, but I don't see where another answer is going to come from, so maybe I've just fluked it. I derived the eqns of motion from scratch though, so perhaps I screwed up. Roughly, for the raindrop, assuming infinitesimal changes of mass and velocity over time :

But

Thereafter it's just integration and initial conditions so I'm not sure what I've missed.
8. (Original post by atsruser)
I get as well, but I don't see where another answer is going to come from, so maybe I've just fluked it. I derived the eqns of motion from scratch though, so perhaps I screwed up. Roughly, for the raindrop, assuming infinitesimal changes of mass and velocity over time :

But

Thereafter it's just integration and initial conditions so I'm not sure what I've missed.
clearly too tired

the same equation
2 solutions

one as
a = dv/dt
the other
a = v dv/dx
9. (Original post by TeeEm)
clearly too tired

the same equation
2 solutions

one as
a = dv/dt
the other
a = v dv/dx
OK, perhaps I'm being really dense but I have no idea what you are saying here. We can only get one time from that equation, AFAICS.

[edit: eff it. There's another question - sorry didn't see it]
10. (Original post by atsruser)
OK, perhaps I'm being really dense but I have no idea what you are saying here. We can only get one time from that equation, AFAICS.
the equation of motion should be after simplification

dv/dt = g - kv

you can also solve the same ODE as

v dv/dx = g - kv

to get v as a function of x
11. (Original post by A Slice of Pi)
Didn't see the last bit aha, I'll work it out now
Edit: I get
yes that is the other solution
12. (Original post by TeeEm)
the equation of motion should be after simplification

dv/dt = g - kv

you can also solve the same ODE as

v dv/dx = g - kv

to get v as a function of x
Yes - see my edited answer above. You hid the second question too well. This is a pretty standard variable mass question though. Got any harder ones?
13. (Original post by Zacken)
Bloody hell, how are you so good at mechanics?!
(Original post by Student403)
I was thinking the same thing..
he is the governor !!!
14. (Original post by atsruser)
Yes - see my edited answer above. You hid the second question too well. This is a pretty standard variable mass question though. Got any harder ones?
Yes very standard ... good practice for the students here

I have written 3 more, 2 slightly harder, the other very hard.

I have written the solutions but they need typing
15. Solution
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