Vertical circular motion with accelerating centre

AI Thread Summary
In vertical circular motion with an accelerating center, the problem can be approached by applying pseudo forces due to the non-inertial frame of reference. The initial steps involve calculating the velocity at the top position assuming zero tension, followed by using mechanical energy conservation between the top and bottom positions. When the center is accelerating, incorporating pseudo forces simplifies the analysis. It is confirmed that applying pseudo forces and following the established steps is the correct method. This approach effectively addresses the complexities introduced by the accelerating center.
subhradeep mahata
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Homework Statement
Suppose, a ball of mass m has to just complete the vertical circular motion when its point of suspension is accelerating vertically upwards with an acceleration g/3. We have to find that particular minimum speed at the extreme bottom that must be given to it so that it just completes the vertical circle.
Relevant Equations
General laws of motion and energy conservation
I can do the problem if the centre is fixed. The steps are:
1) Assuming tension in the string is zero at the top most position, we calculate the velocity at top most position by mv2/R = mg
2)Now, we simply apply mechanical energy conservation when the ball is at the top and bottom positions respectively and find out the required speed.
But, now as the centre is accelerating, I am confused. Do I have to apply pseudo force and proceed in the same way?
Please explain it to me.
Thanks.
 
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subhradeep mahata said:
Do I have to apply pseudo force and proceed in the same way?
The use of non inertial frames (and hence pseudo forces) is certainly an option, and probably the easier way here.
 
So, I should apply pseudo force and follow the two steps, isn't it?
 
subhradeep mahata said:
So, I should apply pseudo force and follow the two steps, isn't it?
Yes.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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