1Is it a Straight Line with negative slope? [7]
above is a rod having a perpendicular extension MN which has a container permanently fixed to it ..
the container contains water full to its top..
the rod was rotated in such a way that water comes out of the hole of container in a constant rate ..
draw the graph of the tension in the MN with time?
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5 Answers
11COMPLETE ANALYSIS OF THE SYSTEM.
if we sit on the rotating rod assumed to be rotating with constant ω
Then the box will experience a force ∫dmω2x where x is its distance from the axis.
The volume dQ is changing at constant rate
∫dQ=-∫kdt
Q=-kt
∫dm=∫ÏdQ
m=Ïkt
f=Ïktω2x
The water comming out will have some velocity v=xω n thus momentum change per second will give the force with which it will come out.
it will also experience a normal force perpendicular to surface.
Now since box is stationary applyΣf=0 n calculat the normal force being experienced by the rod.
THE rod is in circular motion and has ar nat
NOW tension can be calculated
IF say normal force is N the taking torque about joint
NL/2=Icmα
due to this α the ω is not constant n is changing
At any t time ω'=ω+αt
now consider any infinitesimal element dx with mass dm
At instant of t
dm=σdx
∫dT=∫dmω2 x
∫σω2xdx=Mω'2L/2
I think from the above analysis the graph should be parabola.
(although i am not very sure )