The tension in the rope   An 800-N billboard worker stands on a 4.0 m scaffold supported by vertical ropes at each end. If the scaffold weighs 500...

 
The tension in the rope
 
An 800-N billboard worker stands on a 4.0 m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?

Asked on by yuki1188

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neela | High School Teacher | (Level 3) Valedictorian

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Let AB be the scaffold . The length of AB = 4m.

Let G be the centre of gravity of the scaffold . Then assuming AB has uniformly dense along the scaffold, AG = AB =2m.

Let postion of the 800N worker be at X and AX =1meter.

To find the tension in the ropes at A and B.

We also presume the system forces is in equilibrium.

The forces in equilibrium are : The weight force of 800N (down ward)  of the worker at X , the weight force of the scaffold 500N (down ward) Ta  and Tb  the tensions at A and B both upward. All forces are at equilibrium. Therefore,

Ta + Tb + 800N + 500N = 0 .....(1)

Taking moments about A,

Ta*0 + Tb*AB (clockwise) - 800* AX anti clock wise - 500* AG anticlockwise = 0 .

Tb*4m = 800*1 + 500*2 = 1800 Nm .

So Tb = 1800/4 N =  450 N upward

Ta =(800+500) - 450 = 850N upward

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