A uniform steel beam of length 5.3 m has a mass of 530 kg. One end of the beam i

Question

A uniform steel beam of length 5.3 m has a mass of 530 kg. One end of the beam is bolted to a vertical wall. The beam is held in a horizontal position by a cable attached between the other end of the beam and a point on the wall. The cable makes an angle of 25 degrees above the horizontal. A load whose mass is 200 kg is hung from the beam at a point that is 3.5 m from the wall. Find the magnitude of the tension in the supporting cable.


Find the magnitude of the force R exerted on the end of the beam by the bolt that attaches it to the wall.

Explanation / Answer

Let Rx = force exerted by wall to the beam along x axis

      Ry = force exerted by wall to the beam along y axis

Fx = 0                                             Fy = 0

Rx - T cos 25o = 0                              Ry + T sin 25o - W1 - W1 = 0

Rx = T cos 25 ....(1)                          Ry = W1 + W1 - T sin 25o

                                                       Ry = 530(9.8) + 200(9.8) - T sin 25o

                                                       Ry = 7154 - T sin 25o

= 0

T( 5.3 sin 25o ) - 530.9.8(2.65) - 200.9.8(3.5) = 0

T = 9207.69 N

subsitute T into eq (1) get Rx = 8345 N

subsiture T into eq (2) get Ry = 3262.66 N

R = (Rx2 + Ry2) = 8960.13 N

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