Answer to Question #172199 in Physics for Ian Atienza

Question #172199

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.


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Expert's answer
2021-03-17T16:54:41-0400


Equilibrium of moments relative to point O:


10W25W1+8T sin30°=0,T=2250 N.-10W_2-5W_1+8T\text{ sin}30°=0,\\ T=2250\text{ N}.

Equilibrium of forces:


y:T sin30°+RyW1W2=0,x:RxT cos30°=0. Ry=125 N,Rx=1950 N,R=Rx2+Ry2=1953 N.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} .


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