An 800- N billiboard worker stands on a 4.0-m scaffold supported by vertical rop

Question

An 800- N billiboard 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 farther from the worker ? A. 1300 N B. 1800 N C. 450 N D. None of these.

A. 1300 N

B. 1800 N

C. 450 N

D. None of these

sloution:

work weight F1=800 N

distance d1=4m

scaffold weight F2=500 N

distance d2=1 m

this concept belongs to the rotational dynamices

so the total upward force =total downward force

F1d1+F2d2=T*D

800*4+500*1=T*2.05

3700/2.05=T

Tension in the rope T=1800 N

so the correct option is B

note: i want to know why we put 2.05 for D ???? from where we got this number i didnt undwerstand this part !! and also i dont know if this slution right ! plz need help

Explanation / Answer

let,

length of the scaffold, l=4m

weight of the scaffoild, w1=500N

weight of the worker, w2=800N at x=1m (from one end)

tension in the rope at farthest point is T

by using equilibrium condition,

clock wise torques = counter clock wise torques

T*(l)=w2*x+w1*(l/2)

T*(4)=800*1+500*(4/2)

===> T=450 N

tension T=450 N

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