A shop sign weighing 230 N is supported by a uniform 140 N beam as shown in Fig.

Question

A shop sign weighing 230 N is supported by a uniform 140 N beam as shown in Fig. 9-54. Find the tension in the guy wire. N Find the horizontal and vertical forces exerted by the hinge on the beam. horizontal N left or right? vertical N left or right?

Explanation / Answer

A) To find tension in the wire, we'll calculate the moment about the base of the beam: weight of beam = 140 N acting at l=1.7m/2=0.85 m weight of sign = 230 N acting at l=1.7m only the vertical component of force in the wire will be used because the horizontal component passes through the base therefore Tvert=Tsin35 acting 1.35 m from the base so here's the Moment eq -230x1.7 (down) - 140x0.85 ( down ) + Tsin35 x 1.35 = 0 T=(230x1.7 + 145x0.85)/(1.35xsin35) =675.1N (up and to the right ) B) from above the T_vert=Tsin35 = 387.2 N (upwards) and T_horiz=Tcos35=553.0 N (inward) Now we can find vert and hor forces at the base Horizontal====> horizontal Force + 553 N (inward ) = 0 horizontal force = -553 N (wall is pushing outward ) Vert====>Sign + beam + T_vert + vert_base_force = 0 -235 (downward ) -145 (downward ) + 387.2 (up) +vert_base_force=0 vert_base_force = 235 +145 - 387.2= -7.2 N ( down )

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