A 12.0 m uniform beam is hinged to a vertical wall and held horizontally by a 5.

Question

A 12.0 m uniform beam is hinged to a vertical wall and held horizontally by a 5.00 m cable attached to the wall 4.00 m above the hinge, as shown in the figure below (Figure 1). The metal of this cable has a test strength of 1.10 kN, which means that it will break if the tension in it exceeds that amount. What is the heaviest beam that the cable can support with the given configuration? Part B Find the horizontal component of the force the hinge exerts on the beam. Part C Find the vertical component of the force the hinge exerts on the beam.

Explanation / Answer

the cable is attached at x = sqrt(r^2-y^2) = sqrt(5^2-4^2) = 3 m

In equilibrium net torque about the hinge = 0

T*x*y/r = M*g*L/2

1.1*10^3*3*5/4 = M*9.8*12/2

M = 70.15 kg <<-------answer

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part B

along horizantal

Fx - Tx = 0

Fx = T*x/r = 0

Fx = 1.1*10^3*3/5

Fx = 660 N <<-----answeer

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along vertical

Fy + Ty - Mg = 0

Fy + T*y/r - Mg = 0

Fy + (1.1*10^3*(3/5)) - (70.15*9.8)=0

Fy = 27.47 N <<<-------answer

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