21here : F = d(mv)/dt= m(dv/dt) + v(dm/dt)
m will be minst. rite, ie (M - μt + m) and dV/dt = a; dM/dt = μ
thn i guess we'll hav to integrate frm ini. vel V to final inst vel 0
can anyone explain me how to solve problems involving variable mass systems.. except rocket propulsion... please..?
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35 Answers
106nishant bhaiyya:
can u solve that question so that atleast i can get some hint how to do them... i cant get head or tail of this one...
211hi.....asish....
Q) Acart moves in horizontal dirn due to a cost. focre F in same dirn. In the process sand spills thru a hole in the bottom with a const. vel m kg/sec. Find accn and vel of the cart at any time instant t.(initial mass of cart+sand=M and vel = 0)
1waise i will give a simple problem.
A trolley has a small hole on one side, from which sand falls in the forward direction at a rate of μ kg/ hr at a velocity of v relative to the trolley!
total mass of the sand on trolley is M
mass of trolley is m
initial velocity is V
find the time after which it stops.
doubt it ever stop ?
for that we will get a term ln0 .. which is undefined..
1net force on the trolley = mdv/dt = -v μ/(3600)
=> V∫V'dv/v = -μ0∫tdt/(3600m)
=> ln(V/V') = μt/(3600m)
to find out t when V' =0 is impossible.
we can find out t for some particular value of V.
106@kumar.. i was doing irodov yesterday and saw that prob... but i cudnt solve it.. anyone mind helping out??
1#22.)
let at time t, mass of the trolley = m = [mo-μt]
and its velocity be v.
afetr time Δt, mass =m-Δm [Δm=μΔt]
v ---> v+Δv
by momentum conservation:
(m-Δm)(v+Δv) + Δm(v-u) = mv [u=velocity of the sand wrt trolley]
=> (m-Δm)Δv = Δm.u
=> Δv = Δm.u/(m-Δm) = μΔt.u/(m-μΔt)
=> Δv/Δt = μ.u/m-μΔt
[since Δm --->0 as delt-->0]
so, dv/dt = μu/m = μu/(mo-μt)
=> 0∫vdv = 0∫tμu/(mo-μt) dt.
=> v = u ln[mo/(mo-μt)]
now u =Ft/m. = F/(m/t) = F/μ = velocity of sand wrt trolley.
put this value in place of u..........
21haan!!!
par mene socha ki Pink wink kuch nahi hai to shayad rong hoga isliye dekha hi nahi tha, abhi DEKHA
[78]
1[3]
woh... bhaiya sat-sunday very busy...
isiliye i wont disturb him by doing jhagra for pink [3]
24I believed this one was in syllabus...but today again 3 people told me this topic is not in syllabus.....
what do tiitians say ??
62ye typing error tha... solved got replaced by loved (:)
nothing like that in my mind :P
waise i will give a simple problem.
A trolley has a small hole on one side, from which sand falls in the forward direction at a rate of μ kg/ hr at a velocity of v relative to the trolley!
total mass of the sand on trolley is M
mass of trolley is m
initial velocity is V
find the time after which it stops.
242)Impulse method
Δp=J
=>pf-pi=F.t
(here both initial and final momentum will contain variable mass term.....)
Write correct initial and final momentum taking rocket +fuel as system or any other thing like truck with sand......[1][1]
106eureka can u explain using sum example...
suppose.. there is a heap of rope on a table...of mass M and length L .... what will be the valocity of te rope when the rope has slid down by a dist x??
24that can be done using energy method......it wont require all this.......
btw i have to go now,,,,wil reply later
11@asish
THIS IS NOT IN SYLLABUS
SO I RECOMMEND NOT TO WASTE TIME ON IT
106yes eureka.. sry for such a late reply..kyonki net ka wire kho gayaa tha
can u solve the question i had given.. and how it wud have been different. if the chain was not heaped but was laid on the table on a single line.... wud it have been different?
62Variable mass is solved by momentum conservation in a small time...
If there is an external force you just have to consider that too..
In theory it is very simple. .but a lot of people and sometimes the books themselves will make you believe that it is very difficult!
The most basic thing to do is F=d(mv)/dt
106Variable mass is loved by momentum conservation in a small time... [7]
abd bhaiyya can u plz div me some problems so that i can try...
24One is which involves log (common method) and other one does not involve log but will involve correct selection of system
1)Instantaneous mass=Force other than impulses + Thrust due to impulses
=>m.dv/dt=Fext+vrelativedm/dt
24@ asish should i do this question for u.. or do u want to try???????[7]