Question

5. A 10-m long plank (of negligible mass) is supported at each end by vertical cables. A person of unknown weight sits on the plank between the cables. The tension in the left cable is 300 N, and in the right cable it is 200 N. How far is the person sitting from the left cable? A. 2.0 m B. 3.0 m C.4.0 m D.6.0 m E. 7.0 m
Can you explain the approach to solving a problem like this? Thank you!

Answer 1

SAY 10m

Let x be the distance of the person from the left end.

First, find the weight of the person

Consider all vertical forces

$\sum F_{y}=0$

$T_{L}+T_{R}-W=0$

$T_{L}+T_{R}=W$

$300N+200N=W$

${\color{Red} W=500N}$

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Take moment about the left end

$\sum M_{L}=0$

$T_{R}*10m-W*x=0$

$T_{R}*10m=W*x$

$\frac{T_{R}*10m}{W}=x$

$\frac{200N*10m}{500N}=x$

${\color{Red} x=4m}$

ANSWER: C. 4.0 m

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