A horizontal beam 4m long is attached to a vertical wall with a hinge at one end

Question

A horizontal beam 4m long is attached to a vertical wall with a hinge at one end, and a body of weight 500N hangs from the outer end. The beam is supported by a guy wire from its outer end to the wall directly above the beam.

a/ If the tension in the wire is not to exceed 1000N, what is the minimum height (h) above the beam at which it may be fastened to the wall?

b/ If the wire were now to be fastened at distance of 0.5m below this point in part A, with the beam remaining horizontal, what would the new tension in the wire be? Ignore the weight of the beam.

Explanation / Answer

(A) Let (theta) be the angle between the guide wire and the end of the beam. T- Tension in guide wire We have T sin(theta) = 500 Newtons T = 1000N Solving we get (theta) = 30 degrees Now tan(theta) = h/4 So h=2.3m (B) h_1=2.3-0.5=1.8m Thus tan(theta_1)=1.8/4.0 (theta_1)=24.35 degrees So the new Tension is T_1 sin(24.35) = 500 So T_1 = 1213 Newtons

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