Question

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.

Answer 1

$\sum{M_A}=0: -2P-4F+8T\sin53°=0\to$

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

$R_x=T\cos53°=313\cdot\cos53°=188N$

$R_y=P+F-T\sin53°=600+200-313\cdot\sin53°=550N$

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

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