Answer to Question #172199 in Physics for Ian Atienza

Question

A 800 N mass is hanging on a 10 m length board. The board weighs 200 N and is supported by a wall and a rope. The rope and the board has an angle between them of 30º and the rope is 2 m from the right end of the board. FInd the tension in the rope and the force by the wall on a board.

Answer 1

Equilibrium of moments relative to point O:

$$-10W_2-5W_1+8T\text{ sin}30°=0,\\ T=2250\text{ N}.$$

Equilibrium of forces:

$$y: T\text{ sin}30°+R_y-W_1-W_2=0,\\ x: R_x-T\text{ cos}30°=0.\\\space\\ R_y=-125\text{ N},\\ R_x=1950\text{ N},\\ R=\sqrt{R_x^2+R_y^2}=1953\text{ N} .$$