Math Is Fun Forum

zetafunc.

Guest

Variable Mass

I'm a bit stuck on a variable mass question... I've done the first part but can't do the second bit.

A spaceship is moving in deep space with no external forces acting on it. At time t the spaceship has total mass m and is moving with velocity v. The spaceship reduces its speed by ejecting fuel from its front end with a speed c relative to itself and in the same direction as its own motion.

Show that

To do that bit, I used the principle that

Change in momentum = Impulse of external force

Since there are no external forces, we can say that the change in momentum is zero. Now to get the change in momentum:

The second part is as follows;

Initially the spaceship is moving with speed V and has total mass M. Its speed is reduced to 0.5V. Find the mass of fuel ejected.

I am guessing I'm supposed to use the differential equation I just found and integrate, but I don't know where that gets me afterwards. Help would be appreciated.

zetafunc.

Guest

Re: Variable Mass

Sorry, I meant that we can say that the impulse of external forces is 0 (no external forces), not the change in momentum. But the change in momentum does equate to 0.

zetafunc.

Guest

Re: Variable Mass

So I integrated dv between V and 0.5V, and integrated (c/m)dm between M and m. This got me an answer of:

But the textbook is saying the answer is

...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Variable Mass

hi zetafunc

Nice work!  And nothing wrong at all except read the question.

Find the mass of fuel ejected.

Your 'm' is the mass remaining so subtract it from the initial mass,  M.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc.

Guest

Re: Variable Mass

Ah, I see... thanks!