Solve Equilibrium Problem: Two Uniform Beams, Hinge & Chain

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The discussion centers on solving an equilibrium problem involving two uniform beams connected by a hinge and a chain on a frictionless surface. Participants analyze the forces and torques acting on the system, using equations for static equilibrium. The tension in the chain is derived from the balance of forces, with initial attempts yielding different expressions for tension. There is some confusion regarding the correct formulation of the equations, particularly in relating the forces and angles involved. The conversation highlights the need for clarity in applying torque and force balance principles to arrive at the correct solutions for the tension, hinge forces, and ground reaction forces.
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Homework Statement


[PLAIN]http://img820.imageshack.us/img820/3505/23625990.jpg

Two uniform beams, each of mass M and length L, are connected by a hinge at the top and by a chain of negligible mass attached between their centers. The system will stand upright on a frictionless surface as shown in the figure. Determine (a) the tension in the chain, (b) the force on the hinge by each plank, (c) the force of the ground on each plank, as a function of the length of the chain, l.

Homework Equations



My force diagram.

[PLAIN]http://img440.imageshack.us/img440/2272/98244983.jpg

Sum of F = 0
Sum of Torque = 0

Torque = (-T sinθ L ) + (-W cos θ L) + (Fx sin θ L) = 0

FxsinθL - WsinθL / sin θL = Tension is this right?

if this is right I will attempt part b.

The Attempt at a Solution

Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
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FxsinθL - WcosθL / sin θL = Tension

edit: FxsinθL - WsinθL / sin θL = Tension

then it will simplfy as ,

T = Fx-W = Tension... now it doesn't even seem right
 
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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