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khemist
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Homework Statement
Two sticks are connected, with hinges, to each other and to a wall. The
bottom stick is horizontal and has length L, and the sticks make an angle
of θ with each other, as shown in Fig. 2.38. If both sticks have the same
mass per unit length, ρ, find the horizontal and vertical components
of the force that the wall exerts on the top hinge, and show that the
magnitude goes to infinity for both θ → 0 and θ → π/2
Homework Equations
F=ma
T=RF
The Attempt at a Solution
I drew my FBD as follows. The wall and two sticks form a right triangle. Stick 1 (at the angle) has mg pointing down, a force at the top hinge at some angle (F1x, F1y), and a force at the bottom hinge (F2x, F2y), where the two sticks meet, again at some angle. The bottom stick (horizontal, stick 2) has the normal force from the wall (N), pointing parallel to the stick, and the force of mg pointing down.
I attempted to write down the sum of the forces for each stick. For stick 1,
Fx = F1x + F2x = 0
Fy = F1y + F2y = 0
Stick 2:
Fx = N = 0
Fy = mg + F2x
To find the torque, I picked the hinge where the two sticks meet as my rotation origin, and my positive rotation is in the counter clockwise direction.
T = \frac{cos\phi}{L}(\frac{L}{2}m_{2}g + sin\phi m_{1}g\frac{L}{2cos\phi} - F_{1}(\frac{L}{cos\phi}))
This is as far as I have gotten. I am pretty sure that my forces are not labeled correctly. Can anyone point me in the right direction? Thanks!