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bfusco
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Homework Statement
A uniform beam of mass M and length L is mounted on a hinge at a wall as shown in the figure. It is held in a horizontal position by a wire making an angle (theta) as shown. A mass m is placed on the beam a distance from the wall, and this distance can be varied.
http://session.masteringphysics.com/problemAsset/1058226/6/GIANCOLI.ch12.p84.jpg
a)Determine, as a function of x, the tension in the wire.
Express your answer in terms of the variables m, M, L, x, θ, and appropriate constants.
b)Determine, as a function of x, the horizontal component of the force exerted by the hinge on the beam. Assume that the positive x and y axes are directed to the right and upward, respectively.
c)Determine, as a function of x, the vertical component of the force exerted by the hinge on the beam.
The Attempt at a Solution
a)first i realized that the force from the hinge and force due to tension had components.
choosing the hinge for the torque axis of rotation, i used the equation ƩFx=0, Fhx-Tx=0, Fhx=Tx. Then i used ƩFy=0, Fhy+Ty-mg-Mg=0 (here i didn't know what to solve for) and finally i used the equation Ʃτ=0, LT-xmg-(L/2)Mg=0, T=(xmg+(L/2)Mg)/L and it is at this point i don't see how i have yet to solve for anything useful to simplify any of the other equations.