Sir Rhosis, in his characteristic perpetual stupor, stumbles onto his horse and
ID: 1787456 • Letter: S
Question
Sir Rhosis, in his characteristic perpetual stupor, stumbles onto his horse and attempts to ride off to fight windmills. However, he has failed to com pletely lower the drawbridge, leaving it raised 20.0° above the horizontal. He stands befuddled 1.00 m from the edge of the 8.00-m, 1000-kg bridge. The rope sustaining the bridge is attached 5.00 m from the bridge's fric- tionless pivot and is fastened to a vertical wall 12.0m above the pivot. Including protective garb and weapons, Sir Rhosis and his horse altogether weigh 2000 kg. Calculate the (a) tension in the rope and (b) the reaction force at the pivot.Explanation / Answer
from triangle rule
angle made by the rope with the wall , alpha = 24.5 degrees
In equilibrium net torque = 0
T*cosalpha*5*costheta + T*sinalpha*5*sintheta = Mg*l/2*costheta + mg*(l-d)*costheta = 0
T*cos(alpha+theta)*5 = Mg*l/2*costheta + m*g*(l-d)*costheta
T*cos(24.5+20)*5 = (1000*9.8*8/2*cos20) + (2000*9.8*(8-1)*cos20)
T = 46480.7 N <<<---------ANSWER
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part(b)
along horizontal
Fh - T*sinalpha = 0
Fh = T*sinalpha
Fh = 19275.23 N
along vertical
Fv - Mg - mg + T*cosalpha = 0
Fv = (1000*9.8) + (2000*9.8) - (46480.7*cos24.5)
Fv = -12895.6 N
reaction force F = sqrt(Fh^2+Fv^2)
F = 23191.2 N