Answer to Question #135248 in Physics for Ariel

Question #135248
The foot of a uniform ladder is on a rough horizontal ground, and the top rests against a smooth vertical wall. The weight of the ladder is 400 N, and a man weighing 800 N stands on the ladder one-quarter of its lenght from the bottom. If the inclination of the ladder to the horizontal is 30 0 , find the reaction at the wall and the total force at the ground.
1
Expert's answer
2020-09-28T08:06:41-0400

The total force at the ground,


"N_g=400+800=1200(N)"


The reaction at the wall,


"\\Sigma M_{gr}=0:-R\\cdot l\\sin30\u00b0+800\\cdot\\frac{1}{4}l\\cos30\u00b0+400\\cdot \\frac{1}{2}l\\cos30\u00b0=0"


"R\\cdot l\\sin30\u00b0=800\\cdot\\frac{1}{4}l\\cos30\u00b0+400\\cdot \\frac{1}{2}l\\cos30\u00b0"


"R=\\frac{800\\cdot\\frac{1}{4}\\cos30\u00b0+400\\cdot \\frac{1}{2}\\cos30\u00b0}{\\sin30\u00b0}=693(N)"






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