A horizontal beam 4m long is attached to a vertical wall witha hinge at one endm

Question

A horizontal beam 4m long is attached to a vertical wall witha hinge at one endm and a body of weight 500 N hangs from the outerend. The beam is supported by a guy wire from its outer endto the wall directly above the beam. Figure below. A) If the tension in the wire is not to exceed 1000N, what isthe minimum height (h) above the beam at which it may be fastenedto the wall? B) If the wire were now to be fastened at distance 0.5 belowthis point in Part A, with the beam reamaining horizontal, whatwould be the new tension in the wire be? Ignore the weight of thebeam. A horizontal beam 4m long is attached to a vertical wall witha hinge at one endm and a body of weight 500 N hangs from the outerend. The beam is supported by a guy wire from its outer endto the wall directly above the beam. Figure below. A) If the tension in the wire is not to exceed 1000N, what isthe minimum height (h) above the beam at which it may be fastenedto the wall? B) If the wire were now to be fastened at distance 0.5 belowthis point in Part A, with the beam reamaining horizontal, whatwould be the new tension in the wire be? Ignore the weight of thebeam.

Explanation / Answer

A)the net torqe acting on the beam is zero therefore weget T * h + w * L = 0 or h = -(w * L/T) w = 500 N,L = 4 m and T = 1000 N or h = -(500 * 4/1000) = 2 m B)let the new tension in the wire be T1 thereforewe get T1 * h1 + w * L = 0 or T1 = (w * L/h1) h1 = (2 - 0.5) m = 1.5 m or T1 = (500 * 4/1.5) = 1333.3 N

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