Question #125630

A uniform horizontal beam with a length of 8m and a weight of 200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0° with the beam. If a 600N person stands 2m from the wall , find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.

Expert's answer

"\\sum{M_A}=0: -2P-4F+8T\\sin53\u00b0=0\\to"

"T=\\frac{2P+4F}{8\\sin53\u00b0}=\\frac{2\\cdot 600+4\\cdot200}{8\\cdot\\sin53\u00b0}=313N"

"R_x=T\\cos53\u00b0=313\\cdot\\cos53\u00b0=188N"

"R_y=P+F-T\\sin53\u00b0=600+200-313\\cdot\\sin53\u00b0=550N"

"R=\\sqrt{R_x^2+R_y^2}=\\sqrt{188^2+550^2}=581N"

"\\alpha=tan^{-1}(\\frac{R_y}{R_x})=tan^{-1}(\\frac{550}{188})\\approx71\u00b0"

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