Calculating Tension in a Rope Supporting a Mass

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The discussion focuses on calculating the tension in a rope supporting a hinged rod with a mass of 1.4 kg and an angle of 34 degrees between the rope and the rod. Key equations include the balance of forces in the x and y directions, as well as the net torque acting on the rod. Clarification is sought regarding the rod's orientation and the attachment point of the rope. The torque calculations are emphasized, particularly using the hinged end as the pivot point. Understanding these factors is crucial for accurately determining the tension in the rope.
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Homework Statement



Consider an example that will make use of a hinged rod supported by a rope. The rod has a mass of 1.4 kg, a length r, and there is an angle of 34 degrees between the rope and the rod. What is the tension the rope


Homework Equations




The Attempt at a Solution



Fx = 0 = Hx-Tcos34
Fy = 0 = Hy - Tsin34 - mg
Net Torque = Tcos34(r) - Tsin34...?

please help
 
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Is the rod horizontal? Is the rope attached at the end of the rod?

If so, using the hinged end as the pivot, what torques act on the rod?
 
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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