- #1
songoku
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- Homework Statement
- Please see below
- Relevant Equations
- Equilibrium
Thanks
AI Thread Summary
The discussion centers on understanding the correct vector diagram of forces acting on a hinge in static equilibrium. The force on the hinge has both horizontal and vertical components, with the horizontal component directed to the right to balance tension. The vertical component can be either upward or downward, but clarification is sought on why it should be downward in this scenario. The importance of considering resultant torque at different pivot points is emphasized for accurate analysis. The conversation also touches on the implications of replacing the hinge with a slider, which would require an external downward force to maintain equilibrium.
Thanks
- #2
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Hint: What are the conditions for static equilibrium of such an object?
- #3
songoku
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I get the hint. I need to consider resultant torque at different pivot.robphy said:
Thank you very much for the help robphy
- #4
Lnewqban
Homework Helper
Gold Member
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If you replace that hinge with a slider, which is free to move up and down that wall, an external down force would be needed to counteract the moment that W induces about the point of connection of the cable to the trapdoor.
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
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}...
I was told forces are vectors so they can be divided into x and y components, but what about the normal force or the force of static friction? do you divide those into x and y components if say you had a block that was lying on an angled surface?
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