Question

Problem #2: 25 points A 24m long, horizontal beam is attached to a wall by a hinge. A support cable, 26 m long, is attached to the other end of the beam and attached to the wall 10m above the hinge, forming a 5, 12, 13 right triangle (HINT: leave sin and cos as a simple ratio of integers). The load hanging from the very end of the beam is 1000 Kg and the beam has a mass of 300Kg. Assume that the hinge applies a force to the beam with both x and y components. State the requirements for static equilibrium, write out the equilibrium equations for this problem. Solve for the tension in the cable and the components of the force supplied by the hinge onto the beam. HINT: Use the beam as the item in equilibrium, the hinge as the axis-of- rotation, and remember that Torque =rxF.

Answer 1

ster-t Given ISMO ze Mobi 1000 kg mbeam= 300kg coso = 123 sino e Boge Wat T (OSD - +20- - 12 ng 3000 1000ts Efx20 - Nx= Toso Efro 10000 +3000 - Tsino. Z 0 0 – 3000 x12 + 10 3000 x12 + 10000x 24 = Tsin ox24 23000 = 2Tsmo To 23000X13 299OON. 2x8 Tension in the cable = 29900 N from o Nx = 7 COSO = 29900 x 12 = 27600 N ur : 2800 from egn (11) 13000 = Tsino they Ny - 13000 - 11500 = 1500 N. Nx = 27600 N [ My = 1500 N