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kuktryne
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This problem sounds like a homework problem but its not and it is really hard.
Consider a rail tank wagon filled with liquid, say water.
Suppose that at some moment t=0 there opens a nozzle at left side of the tank at the bottom. The water jet from the nozzle is directed vertikally down.
Question:
How will the wagon's movement be while the water is running out?
What is the final velocity of the rail tank wagon after emptying?Simplifications and assumptions:
Rail tracks lie horizontally, there is no rolling(air) friction, the speed of the water jet from the nozzle is subject to the Torricelli's law, alternately one can assume constant rate of r litre/sec, the horizontal cross-section of the tank is a constant, the water surface inside the tank remains horizontal.Data given:
M(mass of the wagon without water)
m(initial mass of the water)
S(horizontal cross-section of the tank)
S>>s(cross sectional area of the nozzle)
ρ(density of the water)
l(horizontal distance from the nozzle to the centre of the mass of the wagon with water)
g(gravitational acceleration)One thing is obvious: If l=0 then the wagon will not move at all.
For an inconclusive discussion see here:
http://physics.stackexchange.com/questions/1683/mechanics-around-a-rail-tank-wagon
Consider a rail tank wagon filled with liquid, say water.
Suppose that at some moment t=0 there opens a nozzle at left side of the tank at the bottom. The water jet from the nozzle is directed vertikally down.
Question:
How will the wagon's movement be while the water is running out?
What is the final velocity of the rail tank wagon after emptying?Simplifications and assumptions:
Rail tracks lie horizontally, there is no rolling(air) friction, the speed of the water jet from the nozzle is subject to the Torricelli's law, alternately one can assume constant rate of r litre/sec, the horizontal cross-section of the tank is a constant, the water surface inside the tank remains horizontal.Data given:
M(mass of the wagon without water)
m(initial mass of the water)
S(horizontal cross-section of the tank)
S>>s(cross sectional area of the nozzle)
ρ(density of the water)
l(horizontal distance from the nozzle to the centre of the mass of the wagon with water)
g(gravitational acceleration)One thing is obvious: If l=0 then the wagon will not move at all.
For an inconclusive discussion see here:
http://physics.stackexchange.com/questions/1683/mechanics-around-a-rail-tank-wagon