A 95 kg scaffold is 7 m long. It is hanging with two wires, one from each end. A 420 kg box sits 2.2 m from the left end. What is the tension in the right hand side wire?(g = 9.8 m/s2)
call L the tension in the left wire and R the tension in the right wire the sum of these tensions must equal the weight of the scaffold and box, so we have L+R=(420+95)g=5047N the torques due to the tensions and weights must sum to zero if the scaffold is not to rotate; let's sum torques around the left pivot point, if we do, then: the torque due to L=0 since there is no moment the torque due to the box = 420xgx2.2m=9055.2Nm the torque due to the scaffold = 95 x g x 3.5 = 3258.5Nm (assuming the scaffold has a uniform density, its weight acts at the center of mass) the torque due to R is 7R and is in the opposite sense from the torques from the weights; therefore we have 7R=3258.5+9055.2 =>R=1759.1N and the torque from the left is 5047-1759.1=3287.9
