A beam of mass M = 163.27kg is connected to a vertical wall by a hinge. The othe

Question

A beam of mass M = 163.27kg is connected to a vertical wall by a hinge. The other end of the beam is held by a tie rope. Determine the tension in the tie rope and teh reaction froce at the hinge (you have to determine the horizontal and vertical components of the raction force) if the beam makes and angle equaling 40 degrees with the vertical

NOTE: the correct answer includes proper units! Roundoff you answers to 2 sig figs

The tension in the tie rope is T= _____

Components of the reaction force are Rx= _____ and Ry= _____

Explanation / Answer

The mass of the beam is M = 163.27 kg The angle made by the beam with vertical is ? = 40 Let R be the reaction at the hinge and T be th etension in the rope Taking torques at the hinge in counter clockwise direction, as the beam is in equilibrium Tcos40*L - Mgcos40*L/2 = 0 T = Mg/2 T = 163.27*9.8/ 2 T = 800.023 N For the equilibrium, Sum of the horizontal forces = 0 RH = T Therefore the reaction forec is RH= 800.023 N Sum of the vertical forces = 0 RV = Mg Therefore the reaction forec is RV = 1600.046 N Therefore the reaction force is R = v(RH2 + RV2) R = 1788.9 N

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